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Maximum/Minimum Problems Solved Using an Algebraic Way
ERIC Educational Resources Information Center
Modica, Erasmo
This article describes some problems of the maximum/minimum type, which are generally solved using calculus at secondary school, but which here are solved algebraically. We prove six algebraic properties and then apply them to this kind of problem. This didactic approach allows pupils to solve these problems even at the beginning of secondary…
Algebraic Thinking: A Problem Solving Approach
ERIC Educational Resources Information Center
Windsor, Will
Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of…
Inhibiting Interference from Prior Knowledge: Arithmetic Intrusions in Algebra Word Problem Solving
ERIC Educational Resources Information Center
Khng, Kiat Hui; Lee, Kerry
In Singapore, 6-12 year-old students are taught to solve algebra word problems with a mix of arithmetic and pre-algebraic strategies; 13-17 year-olds are typically encouraged to replace these strategies with letter-symbolic algebra. We examined whether algebra problem-solving proficiency amongst beginning learners of letter-symbolic algebra is…
Slower Algebra Students Meet Faster Tools: Solving Algebra Word Problems with Graphing Software
ERIC Educational Resources Information Center
Yerushalmy, Michal
The article discusses the ways that less successful mathematics students used graphing software with capabilities similar to a basic graphing calculator to solve algebra problems in context. The study is based on interviewing students who learned algebra for 3 years in an environment where software tools were always present. We found differences…
Promoting Problem Solving across Geometry and Algebra by Using Technology
ERIC Educational Resources Information Center
Erbas, A. Kursat; Ledford, Sara D.; Orrill, Chandra Hawley; Polly, Drew
Technology is a powerful tool in assisting students in problem solving by allowing for multiple representations. The vignette offered in this article provides insight into ways to solve open-ended problems using multiple technologies.
Constructing a Coherent Problem Model to Facilitate Algebra Problem Solving in a Chemistry Context
ERIC Educational Resources Information Center
Ngu, Bing Hiong; Yeung, Alexander Seeshing; Phan, Huy P.
An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant…
Primary School Students' Strategies in Early Algebra Problem Solving Supported by an Online Game
ERIC Educational Resources Information Center
van den Heuvel-Panhuizen, Marja; Kolovou, Angeliki; Robitzsch, Alexander
In this study we investigated the role of a dynamic online game on students' early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10-12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the…
A Schematic-Theoretic View of Problem Solving and Development of Algebraic Thinking
ERIC Educational Resources Information Center
Steele, Diana F.; Johanning, Debra I.
This study explored the problem-solving schemas developed by 7th-grade pre-algebra students as they participated in a teaching experiment that was designed to help students develop effective schemas for solving algebraic problem situations involving contexts of (1) growth and change and (2) size and shape. This article describes the qualities and…
The Effect of Instruction with Graphing Calculators on How General Mathematics Students Naturalistically Solve Algebraic Problems.
ERIC Educational Resources Information Center
Merriweather, Michelle; Tharp, Marcia L.
Focuses on changes in attitude toward mathematics and calculator use and changes in how general mathematics students naturalistically solve algebraic problems. Uses a survey to determine whether a student is rule-based. Concludes that the rule-based students used an equation to solve the algebraic word problem whereas the non-rule-based students…
Persistent and Pernicious Errors in Algebraic Problem Solving
ERIC Educational Resources Information Center
Booth, Julie L.; Barbieri, Christina; Eyer, Francie; Paré-Blagoev, E. Juliana
Students hold many misconceptions as they transition from arithmetic to algebraic thinking, and these misconceptions can hinder their performance and learning in the subject. To identify the errors in Algebra I which are most persistent and pernicious in terms of predicting student difficulty on standardized test items, the present study assessed…
Fostering Analogical Transfer: The Multiple Components Approach to Algebra Word Problem Solving in a Chemistry Context
ERIC Educational Resources Information Center
Ngu, Bing Hiong; Yeung, Alexander Seeshing
Holyoak and Koh (1987) and Holyoak (1984) propose four critical tasks for analogical transfer to occur in problem solving. A study was conducted to test this hypothesis by comparing a multiple components (MC) approach against worked examples (WE) in helping students to solve algebra word problems in chemistry classes. The MC approach incorporated…
Exploring Algebra Based Problem Solving Methods and Strategies of Spanish-Speaking High School Students
ERIC Educational Resources Information Center
Hernandez, Andrea C.
This dissertation analyzes differences found in Spanish-speaking middle school and high school students in algebra-based problem solving. It identifies the accuracy differences between word problems presented in English, Spanish and numerically based problems. The study also explores accuracy differences between each subgroup of Spanish-speaking…
An Evaluation of Interventions to Facilitate Algebra Problem Solving
ERIC Educational Resources Information Center
Mayfield, Kristin H.; Glenn, Irene M.
Three participants were trained on 6 target algebra skills and subsequently received a series of 5 instructional interventions (cumulative practice, tiered feedback, feedback plus solution sequence instruction, review practice, and transfer training) in a multiple baseline across skills design. The effects of the interventions on the performance…
Excel Spreadsheets for Algebra: Improving Mental Modeling for Problem Solving
ERIC Educational Resources Information Center
Engerman, Jason; Rusek, Matthew; Clariana, Roy
This experiment investigates the effectiveness of Excel spreadsheets in a high school algebra class. Students in the experiment group convincingly outperformed the control group on a post lesson assessment. The student responses, teacher observations involving Excel spreadsheet revealed that it operated as a mindtool, which formed the users'…
Assessing Algebraic Solving Ability: A Theoretical Framework
ERIC Educational Resources Information Center
Lian, Lim Hooi; Yew, Wun Thiam
Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…
The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems
ERIC Educational Resources Information Center
Ng, Swee Fong; Lee, Kerry
Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…
Alternative Representations for Algebraic Problem Solving: When Are Graphs Better than Equations?
ERIC Educational Resources Information Center
Mielicki, Marta K.; Wiley, Jennifer
Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…
Application of symbolic and algebraic manipulation software in solving applied mechanics problems
NASA Technical Reports Server (NTRS)
Tsai, Wen-Lang; Kikuchi, Noboru
As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.
Voila: A visual object-oriented iterative linear algebra problem solving environment
Edwards, H.C.; Hayes, L.J.
Application of iterative methods to solve a large linear system of equations currently involves writing a program which calls iterative method subprograms from a large software package. These subprograms have complex interfaces which are difficult to use and even more difficult to program. A problem solving environment specifically tailored to the development and application of iterative methods is needed. This need will be fulfilled by Voila, a problem solving environment which provides a visual programming interface to object-oriented iterative linear algebra kernels. Voila will provide several quantum improvements over current iterative method problem solving environments. First, programming and applying iterative methods is considerably simplified through Voila`s visual programming interface. Second, iterative method algorithm implementations are independent of any particular sparse matrix data structure through Voila`s object-oriented kernels. Third, the compile-link-debug process is eliminated as Voila operates as an interpreter.
Solving Our Algebra Problem: Getting All Students through Algebra I to Improve Graduation Rates
ERIC Educational Resources Information Center
Schachter, Ron
graduation as well as admission to most colleges. But taking algebra also can turn into a pathway for failure, from which some students never recover. In 2010, a national U.S. Department of Education study…
Dynamic Assessment of Algebraic Learning in Predicting Third Graders' Development of Mathematical Problem Solving.
Fuchs, Lynn S; Compton, Donald L; Fuchs, Douglas; Hollenbeck, Kurstin N; Craddock, Caitlin F; Hamlett, Carol L
Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting 3(rd) graders' development of mathematics problem solving. In the fall, 122 3(rd)-grade students were assessed on language, nonverbal reasoning, attentive behavior, calculations, word-problem skill, and DA. On the basis of random assignment, students received 16 weeks of validated instruction on word problems or received 16 weeks of conventional instruction on word problems. Then, students were assessed on word-problem measures proximal and distal to instruction. Structural equation measurement models showed that DA measured a distinct dimension of pretreatment ability and that proximal and distal word-problem measures were needed to account for outcome. Structural equation modeling showed that instruction (conventional vs. validated) was sufficient to account for math word-problem outcome proximal to instruction; by contrast, language, pretreatment math skill, and DA were needed to forecast learning on word-problem outcomes more distal to instruction. Findings are discussed in terms of responsiveness-to-intervention models for preventing and identifying learning disabilities. PMID:19884957
Facilitating Case Reuse during Problem Solving in Algebra-Based Physics
ERIC Educational Resources Information Center
Mateycik, Frances Ann
This research project investigates students' development of problem solving schemata while using strategies that facilitate the process of using solved examples to assist with a new problem (case reuse). Focus group learning interviews were used to explore students' perceptions and understanding of several problem solving strategies. Individual…
Solving a Contextual Problem with the Spreadsheet as an Environment for Algebraic Thinking Development
ERIC Educational Resources Information Center
Nobre, Sandra; Amado, Nelia; Carreira, Susana
In this article we report and discuss a contextual problem solving task that was proposed to a class of 8th grade (13-14-year-old) students. These students had been developing a reasonable experience in the use of the spreadsheet to model relations within contextual problems and chose to use this tool to solve the mentioned problem, engaging in…
A Comparison of Two Mathematics Problem-Solving Strategies: Facilitate Algebra-Readiness
ERIC Educational Resources Information Center
Xin, Yan Ping; Zhang, Dake; Park, Joo Young; Tom, Kinsey; Whipple, Amanda; Si, Luo
The authors compared a conceptual model-based problem-solving (COMPS) approach with a general heuristic instructional approach for teaching multiplication-division word-problem solving to elementary students with learning problems (LP). The results indicate that only the COMPS group significantly improved, from pretests to posttests, their…
LOGO Teaching Sequences on Strategy in Problem-Solving and Story Problems in Algebra. Teacher's Text and Problems.
ERIC Educational Resources Information Center
Lukas, George; And Others
In order to provide high school students with general problem-solving skills, two LOGO computer-assisted instruction units were developed--one on the methods and strategies for solution and a second on the relation between formal and informal representations of problems. In both cases specific problem contexts were used to give definition and…
Using Verbal Protocol Data to Reflect the Quality of Problem Representation in Solving Algebra Word Problems.
ERIC Educational Resources Information Center
Bull, Elizabeth Kay
The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…
Two-stage screening for math problem-solving difficulty using dynamic assessment of algebraic learning.
Fuchs, Lynn S; Compton, Donald L; Fuchs, Douglas; Hollenbeck, Kurstin N; Hamlett, Carol L; Seethaler, Pamela M
The purpose of this study was to explore the utility of a dynamic assessment (DA) of algebraic learning in predicting third graders' development of mathematics word-problem difficulty. In the fall, 122 third-grade students were assessed on a test of math word-problem skill and DA of algebraic learning. In the spring, they were assessed on word-problem performance. Logistic regression was conducted to contrast two models. One relied exclusively on the fall test of math word-problem skill to predict word-problem difficulty on the spring outcome (less than the 25th percentile). The second model relied on a combination of the fall test of math word-problem skill and the fall DA to predict the same outcome. Holding sensitivity at 87.5%, the universal screener alone resulted in a high proportion of false positives, which was practically reduced when DA was included in the prediction model. Findings are discussed in terms of a two-stage process for screening students within a responsiveness-to-intervention prevention model. PMID:21685352
Intensive Scaffolding in an Intelligent Tutoring System for the Learning of Algebraic Word Problem Solving
ERIC Educational Resources Information Center
González-Calero, José Antonio; Arnau, David; Puig, Luis; Arevalillo-Herráez, Miguel
The term intensive scaffolding refers to any set of conceptual scaffolding strategies that always allow the user to find the solution to a problem. Despite the many benefits of scaffolding, some negative effects have also been reported. These are mainly related to the possibility that a student solves the problems without actually engaging in…
Mathematics as Problem Solving.
ERIC Educational Resources Information Center
Soifer, Alexander
This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)
Facilitating case reuse during problem solving in algebra-based physics
NASA Astrophysics Data System (ADS)
Mateycik, Frances Ann
This research project investigates students' development of problem solving schemata while using strategies that facilitate the process of using solved examples to assist with a new problem (case reuse). Focus group learning interviews were used to explore students' perceptions and understanding of several problem solving strategies. Individual clinical interviews were conducted and quantitative examination data were collected to assess students' conceptual understanding, knowledge organization, and problem solving performance on a variety of problem tasks. The study began with a short one-time treatment of two independent, research-based strategies chosen to facilitate case reuse. Exploration of students' perceptions and use of the strategies lead investigators to select one of the two strategies to be implemented over a full semester of focus group interviews. The strategy chosen was structure mapping. Structure maps are defined as visual representations of quantities and their associations. They were created by experts to model the appropriate mental organization of knowledge elements for a given physical concept. Students were asked to use these maps as they were comfortable while problem solving. Data obtained from this phase of our study (Phase I) offered no evidence of improved problem solving schema. The 11 contact hour study was barely sufficient time for students to become comfortable using the maps. A set of simpler strategies were selected for their more explicit facilitation of analogical reasoning, and were used together during two more semester long focus group treatments (Phase II and Phase III of this study). These strategies included the use of a step-by-step process aimed at reducing cognitive load associated with mathematical procedure, direct reflection of principles involved in a given set of problems, and the direct comparison of problem pairs designed to be void of surface similarities (similar objects or object orientations) and sharing
Strategies Used by Second-Year Algebra Students to Solve Problems
ERIC Educational Resources Information Center
Senk, Sharon L.; Thompson, Denisse R.
This Brief Report describes a secondary analysis of the solutions written by 306 second-year algebra students to four constructed-response items representative of content at this level. The type of solution (symbolic, graphical, or numerical) used most frequently varied by item. Curriculum effects were observed. Students studying from the second…
Algebra and Problem-Solving in Down Syndrome: A Study with 15 Teenagers
ERIC Educational Resources Information Center
Martinez, Elisabetta Monari; Pellegrini, Katia
There is a common opinion that mathematics is difficult for persons with Down syndrome, because of a weakness in numeracy and in abstract thinking. Since 1996, some single case studies have suggested that new opportunities in mathematics are possible for these students: some of them learned algebra and also learned to use equations in…
Algebra Word Problem Solving Approaches in a Chemistry Context: Equation Worked Examples versus Text Editing
ERIC Educational Resources Information Center
Ngu, Bing Hiong; Yeung, Alexander Seeshing
Text editing directs students' attention to the problem structure as they classify whether the texts of word problems contain sufficient, missing or irrelevant information for working out a solution. Equation worked examples emphasize the formation of a coherent problem structure to generate a solution. Its focus is on the construction of three…
Fibonacci's Triangle: A Vehicle for Problem Solving.
ERIC Educational Resources Information Center
Ouellette, Hugh
A method for solving certain types of problems is illustrated by problems related to Fibonacci's triangle. The method involves pattern recognition, generalizing, algebraic manipulation, and mathematical induction. (MP)
Some Applications of Algebraic System Solving
ERIC Educational Resources Information Center
Roanes-Lozano, Eugenio
Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact solve"…
Problem Solving through Paper Folding
ERIC Educational Resources Information Center
Wares, Arsalan
The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem-solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…
Solving Absolute Value Equations Algebraically and Geometrically
ERIC Educational Resources Information Center
Shiyuan, Wei
The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.
Characterizing the Development of a Schema for Representing and Solving Algebra Word Problems by Pre-Algebraic Students Engaged in a Structured Diagrammatic Environment
ERIC Educational Resources Information Center
Green, Jan
In recent years, the learning of algebra by all students has become a significant national priority (Moses & Cobb, 2001; National Council of Teachers of Mathematics, 2000). Algebra is considered to be a foundational topic in mathematics (Usiskin, 1988) and some have argued that an understanding of algebra is fundamental to success in today's…
Raisonnements arithmetiques et algebriques dans un contexte de resolution des problemes: difficultes rencontrees par les futurs enseignants (Arithmetic and Algebra Teaching within a Problem-Solving Context: Difficulties Encountered by Future Instructors).
ERIC Educational Resources Information Center
Schmidt, Sylvine; Bednarz, Nadine
Discusses the difficulties observed in the transition from teaching arithmetic to teaching algebra. Future teachers (n=164) were questioned regarding to what extent they were able to shift back and forth between teaching methods within the context of problem solving. Interviews were conducted individually and in a dyad format. (AIM)
Using CAS to Solve Classical Mathematics Problems
ERIC Educational Resources Information Center
Burke, Maurice J.; Burroughs, Elizabeth A.
Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…
ERIC Educational Resources Information Center
Techniques of Problem Solving.
ERIC Educational Resources Information Center
Krantz, Steven G.
The purpose of this book is to teach the basic principles of problem solving in both mathematical and non-mathematical problems. The major components of the book consist of learning to translate verbal discussion into analytical data, learning problem solving methods for attacking collections of analytical questions or data, and building a…
ERIC Educational Resources Information Center
Karrison, Joan; Carroll, Margaret Kelly
Students with language and learning disabilities may have difficulty solving mathematics word problems. Use of a sequential checklist, identifying clues and keywords, and illustrating a problem can all help the student identify and implement the correct computational process. (DB)
Teaching through Problem Solving
ERIC Educational Resources Information Center
Fi, Cos D.; Degner, Katherine M.
Teaching through Problem Solving (TtPS) is an effective way to teach mathematics "for" understanding. It also provides students with a way to learn mathematics "with" understanding. In this article, the authors present a definition of what it means to teach through problem solving. They also describe a professional development vignette that…
ERIC Educational Resources Information Center
Karns, Phyllis Spear
The relationship of educational preparation to the problem- solving performance of 55 hospital employed baccalaureate and associate degree nurses working in Wyoming hospitals was studied. Participant data were collected that might correlate with problem-solving ability: age, years of experience in nursing, years of work experience in a…
Problem Solving and Intelligence.
ERIC Educational Resources Information Center
Resnick, Lauren B.; Glaser, Robert
This paper argues that a major aspect of intelligence is the ability to solve problems and that careful analysis of problem-solving behavior is a means of specifying many of the psychological processes that make up intelligence. The focus is on the mechanisms involved when, in the absence of complete instruction, a person must "invent" a new…
Solving stochastic epidemiological models using computer algebra
NASA Astrophysics Data System (ADS)
Hincapie, Doracelly; Ospina, Juan
Mathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world.
ERIC Educational Resources Information Center
Capobianco, Brenda M.; Tyrie, Nancy
In a unique school-university partnership, methods students collaborated with fifth graders to use the engineering design process to build their problem-solving skills. By placing the problem in the context of a client having particular needs, the problem took on a real-world appeal that students found intriguing and inviting. In this article, the…
Chemical Reaction Problem Solving.
ERIC Educational Resources Information Center
Veal, William
Discusses the role of chemical-equation problem solving in helping students predict reaction products. Methods for helping students learn this process must be taught to students and future teachers by using pedagogical skills within the content of chemistry. Emphasizes that solving chemical reactions should involve creative cognition where…
ERIC Educational Resources Information Center
Carpenter, Thomas P.; And Others
Student weaknesses on problem-solving portions of the NAEP mathematics assessment are discussed using Polya's heuristics as a framework. Recommendations for classroom instruction are discussed. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).
Solving Tommy's Writing Problems.
ERIC Educational Resources Information Center
Burdman, Debra
The article describes an approach by which word processing helps to solve some of the writing problems of learning disabled students. Aspects considered include prewriting, drafting, revising, and completing the story. (CL)
ERIC Educational Resources Information Center
Martinez, Michael E.
Many important human activities involve accomplishing goals without a script. There is no formula for true problem-solving. Heuristic, cognitive "rules of thumb" are the problem-solver's best guide. Learners should understand heuristic tools such as means-end analysis, working backwards, successive approximation, and external representation. Since…
ERIC Educational Resources Information Center
Thorson, Annette, Ed.
This issue of ENC Focus focuses on the topic of inquiry and problem solving. Featured articles include: (1) "Inquiry in the Everyday World of Schools" (Ronald D. Anderson); (2) "In the Cascade Reservoir Restoration Project Students Tackle Real-World Problems" (Clint Kennedy with Advanced Biology Students from Cascade High School); (3) "Project…
Problem Solving Techniques Seminar.
ERIC Educational Resources Information Center
Massachusetts Career Development Inst., Springfield.
This booklet is one of six texts from a workplace literacy curriculum designed to assist learners in facing the increased demands of the workplace. Six problem-solving techniques are developed in the booklet to assist individuals and groups in making better decisions: problem identification, data gathering, data analysis, solution analysis,…
Problem Solving in Electricity.
ERIC Educational Resources Information Center
Caillot, Michel; Chalouhi, Elias
Two studies were conducted to describe how students perform direct current (D-C) circuit problems. It was hypothesized that problem solving in the electricity domain depends largely on good visual processing of the circuit diagram and that this processing depends on the ability to recognize when two or more electrical components are in series or…
NASA Technical Reports Server (NTRS)
CBR Express software solves problems by adapting sorted solutions to new problems specified by a user. It is applicable to a wide range of situations. The technology was originally developed by Inference Corporation for Johnson Space Center's Advanced Software Development Workstation. The project focused on the reuse of software designs, and Inference used CBR as part of the ACCESS prototype software. The commercial CBR Express is used as a "help desk" for customer support, enabling reuse of existing information when necessary. It has been adopted by several companies, among them American Airlines, which uses it to solve reservation system software problems.
Numerical linear algebra for reconstruction inverse problems
NASA Astrophysics Data System (ADS)
Nachaoui, Abdeljalil
Our goal in this paper is to discuss various issues we have encountered in trying to find and implement efficient solvers for a boundary integral equation (BIE) formulation of an iterative method for solving a reconstruction problem. We survey some methods from numerical linear algebra, which are relevant for the solution of this class of inverse problems. We motivate the use of our constructing algorithm, discuss its implementation and mention the use of preconditioned Krylov methods.
ERIC Educational Resources Information Center
Wisconsin Univ. - Stout, Menomonie. Center for Vocational, Technical and Adult Education.
The teacher directed problem solving activities package contains 17 units: Future Community Design, Let's Build an Elevator, Let's Construct a Catapult, Let's Design a Recreational Game, Let's Make a Hand Fishing Reel, Let's Make a Wall Hanging, Let's Make a Yo-Yo, Marooned in the Past, Metrication, Mousetrap Vehicles, The Multi System…
ERIC Educational Resources Information Center
Aznar, Mercedes Martinez; Orcajo, Teresa Ibanez
A teaching unit on genetics and human inheritance using problem-solving methodology was undertaken with fourth-level Spanish Secondary Education students (15 year olds). The goal was to study certain aspects of the students' learning process (concepts, procedures and attitude) when using this methodology in the school environment. The change…
Problem Solving Using Calculators.
ERIC Educational Resources Information Center
Billings, Karen; Moursund, David
The first part in the serialized version of a book on the use of calculators for problem solving is presented. It contains prefaces for teachers and students and a chapter on getting started which includes topics such as symmetries, operations, powers, and chaining. (MP)
Solving Common Mathematical Problems
NASA Technical Reports Server (NTRS)
Luz, Paul L.
Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.
Universal Design Problem Solving
ERIC Educational Resources Information Center
Sterling, Mary C.
Universal design is made up of four elements: accessibility, adaptability, aesthetics, and affordability. This article addresses the concept of universal design problem solving through experiential learning for an interior design studio course in postsecondary education. Students' experiences with clients over age 55 promoted an understanding of…
ERIC Educational Resources Information Center
Moore, Jerilou; Sumrall, William J.
Exploring our patent system is a great way to engage students in creative problem solving. As a result, the authors designed a teaching unit that uses the study of patents to explore one avenue in which scientists and engineers do science. Specifically, through the development of an idea, students learn how science and technology are connected.…
Solving Problems through Circles
ERIC Educational Resources Information Center
Grahamslaw, Laura; Henson, Lisa H.
Several problem-solving interventions that utilise a "circle" approach have been applied within the field of educational psychology, for example, Circle Time, Circle of Friends, Sharing Circles, Circle of Adults and Solution Circles. This research explored two interventions, Solution Circles and Circle of Adults, and used thematic…
Circumference and Problem Solving.
ERIC Educational Resources Information Center
Blackburn, Katie; White, David
The concept of pi is one of great importance to all developed civilization and one that can be explored and mastered by elementary students through an inductive and problem-solving approach. Such an approach is outlined and discussed. The approach involves the following biblical quotation: "And he made a moltin sea ten cubits from one brim to the…
A Computer Algebra Approach to Solving Chemical Equilibria in General Chemistry
ERIC Educational Resources Information Center
Kalainoff, Melinda; Lachance, Russ; Riegner, Dawn; Biaglow, Andrew
In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…
Computer Problem-Solving Coaches
NASA Astrophysics Data System (ADS)
Hsu, Leon; Heller, Kenneth
Computers might be able to play an important role in physics instruction by coaching students to develop good problem-solving skills. Building on previous research on student problem solving and on designing computer programs to teach cognitive skills, we are developing a prototype computer coach to provide students with guided practice in solving problems. In addition to helping students become better problem solvers, such programs can be useful in studying how students learn to solve problems and how and if problem-solving skills can be transferred from a computer to a pencil-and-paper environment.
The Problem-Solving Revolution.
ERIC Educational Resources Information Center
Bardige, Art
Discusses the use of microcomputers and software as problem-solving tools, including comments on "TK! Solver," automatic problem-solving program (reviewed in detail on pp.84-86 in this same issue). Also discusses problem-solving approaches to bridge the disciplines, such as music/physics, junior high science/mathematics (genetics),…
The Identity of Problem Solving
ERIC Educational Resources Information Center
Mamona-Downs, Joanna; Downs, Martin
This paper raises issues motivated by considering the "identity" of problem solving. This means that we are concerned with how other mathematics education topics impinge on problem solving, and with themes that naturally arise within the problem-solving agenda. We claim that some of these issues need more attention by educational research, while…
Fundamentals of the Design and the Operation of an Intelligent Tutoring System for the Learning of the Arithmetical and Algebraic Way of Solving Word Problems
ERIC Educational Resources Information Center
Arnau, David; Arevalillo-Herraez, Miguel; Puig, Luis; Gonzalez-Calero, Jose Antonio
Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate…
Algebra Teachers' Utilization of Problems Requiring Transfer between Algebraic, Numeric, and Graphic Representations
ERIC Educational Resources Information Center
Cunningham, Robert F.
For students to develop an understanding of functions, they must have opportunities to solve problems that require them to transfer between algebraic, numeric, and graphic representations (transfer problems). Research has confirmed student difficulties with certain types of transfer problems and has suggested instructional factors as a possible…
Problem Solving in the Professions.
ERIC Educational Resources Information Center
Jackling, Noel; And Others
It is proposed that algorithms and heuristics are useful in improving professional problem-solving abilities when contextualized within the academic discipline. A basic algorithm applied to problem solving in undergraduate engineering education and a similar algorithm applicable to legal problems are used as examples. Problem complexity and…
A Method for Solving Problems.
ERIC Educational Resources Information Center
Knoop, Robert
Problem solving and decision making are considered to be keys to successful management. A normative method for problem solving is presented, suggesting that the analysis of the problem be structured along a five-step procedure: problem identification, analysis, decision alternatives, decision making, and decision implementation. Follow-up…
Parent Problem Solving: Analysis of Problem Solving in Parenthood Transition.
ERIC Educational Resources Information Center
Alpert, Judith L.; And Others
The general purpose of this study was to explore the possibility of adapting the Means-Ends Problem-Solving procedure (MEPS) to the investigation of the individual's transition to parenthood. Specific purposes were to determine (1) the internal consistency of the Parent Problem-Solving Scale (PPSS), of its subclasses, and of a combined subscale;…
Superitem Test: An Alternative Assessment Tool to Assess Students' Algebraic Solving Ability
ERIC Educational Resources Information Center
Lian, Lim Hooi; Yew, Wun Thiam; Idris, Noraini
Superitem test based on the SOLO model (Structure of the Observing Learning Outcome) has become a powerful alternative assessment tool for monitoring the growth of students' cognitive ability in solving mathematics problems. This article focused on developing a superitem test to assess students' algebraic solving ability through interview method.…
Problem Solving vis Soap Bubbles
ERIC Educational Resources Information Center
Bader, William A.
Describes the use of a scientific phenomenon related to the concept of surface tension as an intriguing vehicle to direct attention to useful problem solving techniques. The need for a definite building process in attempts to solve mathematical problems is stressed. (EB)
Contextual Problem Solving Model Origination
ERIC Educational Resources Information Center
Ernst, Jeremy V.
Problem solving has become a central focus of instructional activity in technology education classrooms at all levels (Boser, 1993). Impact assessment considerations incorporating society, culture, and economics are factors that require high-level deliberation involving critical thinking and the implementation of problem solving strategy. The…
Difficulties in Genetics Problem Solving.
ERIC Educational Resources Information Center
Tolman, Richard R.
Examined problem-solving strategies of 30 high school students as they solved genetics problems. Proposes a new sequence of teaching genetics based on results: meiosis, sex chromosomes, sex determination, sex-linked traits, monohybrid and dihybrid crosses (humans), codominance (humans), and Mendel's pea experiments. (JN)
Learning Impasses in Problem Solving
NASA Technical Reports Server (NTRS)
Hodgson, J. P. E.
Problem Solving systems customarily use backtracking to deal with obstacles that they encounter in the course of trying to solve a problem. This paper outlines an approach in which the possible obstacles are investigated prior to the search for a solution. This provides a solution strategy that avoids backtracking.
Problem Solving, Scaffolding and Learning
ERIC Educational Resources Information Center
Lin, Shih-Yin
Helping students to construct robust understanding of physics concepts and develop good solving skills is a central goal in many physics classrooms. This thesis examine students' problem solving abilities from different perspectives and explores strategies to scaffold students' learning. In studies involving analogical problem solving…
Creative Thinking and Problem Solving.
ERIC Educational Resources Information Center
Lacy, Grace
The booklet considers the nature of creativity in children and examines classroom implications. Among the topics addressed are the following: theories about creativity; research; developments in brain research; the creative process; creative problem solving; the Structure of Intellect Problem Solving (SIPS) model; a rationale for creativity in the…
Numerical stability in problems of linear algebra.
NASA Technical Reports Server (NTRS)
Babuska, I.
Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.
Learning through Problem Solving.
ERIC Educational Resources Information Center
Murray, Hanlie; Olivier, Alwyn; Human, Piet
After conducting several studies on young students' understanding of particular concepts before, during, and after instruction, this paper focuses on the two small scale and several informal teaching experiments based on the idea that the teacher should pose problems to students for which they do not yet have a routine solution method available,…
Transformation Problem Solving Abilities.
ERIC Educational Resources Information Center
Harmel, Sarah Jane
The relationship between transformation problem performance and Guilford Structure of Intellect (SI) abilities is explored. During two group sessions 42 females and 35 males, age 18-39, were administered 12 Guilford SI tests exemplifying all five symbolic content (numeric) operations, and three contents in the divergent production area. Logical…
ERIC Educational Resources Information Center
De Bono, Edward
A group of children were presented with several tasks, including the invention of a sleep machine and a machine to weigh elephants. The tasks were chosen to involve the children in coping with problems of a distinct character. A study of the children's drawings and interpretations shows that children's thinking ability is not very different from…
Solving bearing overheating problems
Jendzurski, T.
Overheating is a major indicator, along with vibration and noise, of an underlying problem affecting a bearing or related components. Because normal operating temperatures vary widely from one application to another, no single temperature is a reliable sign of overheating in every situation. By observing an application when it is running smoothly, a technician can establish a benchmark temperature for a particular bearing arrangement. Wide deviations from this accepted norm generally indicate troublesome overheating. The list of possible causes of over-heating ranges from out-of-round housings and oversize shaft diameters to excessive lubrication and bearing preloading. These causes fall into two major categories: improper or faulty lubrication and mechanical problems, such as incorrect fits and tolerances. These are discussed along with solutions.
Irrelevance in Problem Solving
NASA Technical Reports Server (NTRS)
Levy, Alon Y.
The notion of irrelevance underlies many different works in AI, such as detecting redundant facts, creating abstraction hierarchies and reformulation and modeling physical devices. However, in order to design problem solvers that exploit the notion of irrelevance, either by automatically detecting irrelevance or by being given knowledge about irrelevance, a formal treatment of the notion is required. In this paper we present a general framework for analyzing irrelevance. We discuss several properties of irrelevance and show how they vary in a space of definitions outlined by the framework. We show how irrelevance claims can be used to justify the creation of abstractions thereby suggesting a new view on the work on abstraction.
Supporting Problem Solving in PBL
ERIC Educational Resources Information Center
Jonassen, David
Although the characteristics of PBL (problem focused, student centered, self-directed, etc.) are well known, the components of a problem-based learning environment (PBLE) and the cognitive scaffolds necessary to support learning to solve different kinds of problems with different learners is less clear. This paper identifies the different…
Problem Solving with General Semantics.
ERIC Educational Resources Information Center
Hewson, David
Discusses how to use general semantics formulations to improve problem solving at home or at work--methods come from the areas of artificial intelligence/computer science, engineering, operations research, and psychology. (PA)
Paving a Way to Algebraic Word Problems Using a Nonalgebraic Route
ERIC Educational Resources Information Center
Amit, Miriam; Klass-Tsirulnikov, Bella
A three-stage model for algebraic word problem solving is developed in which students' understanding of the intrinsic logical structure of word problems is strengthened by connecting real-life problems and formal mathematics. (Contains 3 figure.)
A Cognitive Model of Experts' Algebraic Solving Methods
ERIC Educational Resources Information Center
Cortes, Anibal
We studied experts' solving methods and analyzed the nature of mathematical knowledge as well as their efficiency in algebraic calculations. We constructed a model of the experts cognitive functioning (notably teachers) in which the observed automatisms were modeled in terms of schemes and instruments. Mathematical justification of transformation…
Student Difficulties in Mathematizing Word Problems in Algebra
ERIC Educational Resources Information Center
Jupri, Al; Drijvers, Paul
To investigate student difficulties in solving word problems in algebra, we carried out a teaching experiment involving 51 Indonesian students (12/13 year-old) who used a digital mathematics environment. The findings were backed up by an interview study, in which eighteen students (13/14 year-old) were involved. The perspective of mathematization,…
Quantitative Reasoning in Problem Solving
ERIC Educational Resources Information Center
Ramful, Ajay; Ho, Siew Yin
In this article, Ajay Ramful and Siew Yin Ho explain the meaning of quantitative reasoning, describing how it is used in the to solve mathematical problems. They also describe a diagrammatic approach to represent relationships among quantities and provide examples of problems and their solutions.
Students' Problem Solving and Justification
ERIC Educational Resources Information Center
Glass, Barbara; Maher, Carolyn A.
This paper reports on methods of students' justifications of their solution to a problem in the area of combinatorics. From the analysis of the problem solving of 150 students in a variety of settings from high-school to graduate study, four major forms of reasoning evolved: (1) Justification by Cases, (2) Inductive Argument, (3) Elimination…
Robot, computer problem solving system
NASA Technical Reports Server (NTRS)
Becker, J. D.
The development of a computer problem solving system is reported that considers physical problems faced by an artificial robot moving around in a complex environment. Fundamental interaction constraints with a real environment are simulated for the robot by visual scan and creation of an internal environmental model. The programming system used in constructing the problem solving system for the simulated robot and its simulated world environment is outlined together with the task that the system is capable of performing. A very general framework for understanding the relationship between an observed behavior and an adequate description of that behavior is included.
Problem? "No Problem!" Solving Technical Contradictions
ERIC Educational Resources Information Center
Kutz, K. Scott; Stefan, Victor
TRIZ (pronounced TREES), the Russian acronym for the theory of inventive problem solving, enables a person to focus his attention on finding genuine, potential solutions in contrast to searching for ideas that "may" work through a happenstance way. It is a patent database-backed methodology that helps to reduce time spent on the problem,…
Quantum Computing: Solving Complex Problems
DiVincenzo, David [IBM Watson Research Center
One of the motivating ideas of quantum computation was that there could be a new kind of machine that would solve hard problems in quantum mechanics. There has been significant progress towards the experimental realization of these machines (which I will review), but there are still many questions about how such a machine could solve computational problems of interest in quantum physics. New categorizations of the complexity of computational problems have now been invented to describe quantum simulation. The bad news is that some of these problems are believed to be intractable even on a quantum computer, falling into a quantum analog of the NP class. The good news is that there are many other new classifications of tractability that may apply to several situations of physical interest.
Quantum Computing: Solving Complex Problems
DiVincenzo, David
One of the motivating ideas of quantum computation was that there could be a new kind of machine that would solve hard problems in quantum mechanics. There has been significant progress towards the experimental realization of these machines (which I will review), but there are still many questions about how such a machine could solve computational problems of interest in quantum physics. New categorizations of the complexity of computational problems have now been invented to describe quantum simulation. The bad news is that some of these problems are believed to be intractable even on a quantum computer, falling into a quantum analog of the NP class. The good news is that there are many other new classifications of tractability that may apply to several situations of physical interest.
Quantum Computing: Solving Complex Problems
DiVincenzo, David
One of the motivating ideas of quantum computation was that there could be a new kind of machine that would solve hard problems in quantum mechanics. There has been significant progress towards the experimental realization of these machines (which I will review), but there are still many questions about how such a machine could solve computational problems of interest in quantum physics. New categorizations of the complexity of computational problems have now been invented to describe quantum simulation. The bad news is that some of these problems are believed to be intractable even on a quantum computer, falling into a quantum analog of the NP class. The good news is that there are many other new classifications of tractability that may apply to several situations of physical interest.
Robot computer problem solving system
NASA Technical Reports Server (NTRS)
Becker, J. D.; Merriam, E. W.
The conceptual, experimental, and practical aspects of the development of a robot computer problem solving system were investigated. The distinctive characteristics were formulated of the approach taken in relation to various studies of cognition and robotics. Vehicle and eye control systems were structured, and the information to be generated by the visual system is defined.
Solving Problems by Reading Mathematics.
ERIC Educational Resources Information Center
Witkowski, Joseph C.
A course at the University of Georgia is described that helps students acquire problem-solving skills so that ultimately the entire remedial program would be improved, giving students with major deficiencies in basic skills a better chance to succeed in their regular university courses. (MLW)
Robot computer problem solving system
NASA Technical Reports Server (NTRS)
Becker, J. D.; Merriam, E. W.
The conceptual, experimental, and practical phases of developing a robot computer problem solving system are outlined. Robot intelligence, conversion of the programming language SAIL to run under the THNEX monitor, and the use of the network to run several cooperating jobs at different sites are discussed.
ERIC Educational Resources Information Center
Champagne, Audrey B.; And Others
Teachers in elementary schools, supervisors of instruction, and other educational practitioners are the primary audience for this publication. The paper presents philosophical, psychological, and practical reasons for including a problem-solving approach in elementary school instruction. It draws on the writings of John Dewey, Jean Piaget, James…
Customer Service & Team Problem Solving.
ERIC Educational Resources Information Center
Martin, Sabrina Budasi
This curriculum guide provides materials for a six-session, site-specific training course in customer service and team problem solving for the Claretian Medical Center. The course outline is followed the six lesson plans. Components of each lesson plan include a list of objectives, an outline of activities and discussion topics for the lesson,…
Genetics problem solving and worldview
NASA Astrophysics Data System (ADS)
Dale, Esther
The research goal was to determine whether worldview relates to traditional and real-world genetics problem solving. Traditionally, scientific literacy emphasized content knowledge alone because it was sufficient to solve traditional problems. The contemporary definition of scientific literacy is, "The knowledge and understanding of scientific concepts and processes required for personal decision-making, participation in civic and cultural affairs and economic productivity" (NRC, 1996). An expanded definition of scientific literacy is needed to solve socioscientific issues (SSI), complex social issues with conceptual, procedural, or technological associations with science. Teaching content knowledge alone assumes that students will find the scientific explanation of a phenomenon to be superior to a non-science explanation. Formal science and everyday ways of thinking about science are two different cultures (Palmer, 1999). Students address this rift with cognitive apartheid, the boxing away of science knowledge from other types of knowledge (Jedege & Aikenhead, 1999). By addressing worldview, cognitive apartheid may decrease and scientific literacy may increase. Introductory biology students at the University of Minnesota during fall semester 2005 completed a written questionnaire-including a genetics content-knowledge test, four genetic dilemmas, the Worldview Assessment Instrument (WAI) and some items about demographics and religiosity. Six students responded to the interview protocol. Based on statistical analysis and interview data, this study concluded the following: (1) Worldview, in the form of metaphysics, relates to solving traditional genetic dilemmas. (2) Worldview, in the form of agency, relates to solving traditional genetics problems. (3) Thus, worldview must be addressed in curriculum, instruction, and assessment.
Working Memory and Literacy as Predictors of Performance on Algebraic Word Problems
ERIC Educational Resources Information Center
Lee, Kerry; Ng, Swee-Fong; Ng, Ee-Lynn; Lim, Zee-Ying
Previous studies on individual differences in mathematical abilities have shown that working memory contributes to early arithmetic performance. In this study, we extended the investigation to algebraic word problem solving. A total of 151 10-year-olds were administered algebraic word problems and measures of working memory, intelligence quotient…
Reversible Reasoning and the Working Backwards Problem Solving Strategy
ERIC Educational Resources Information Center
Ramful, Ajay
Making sense of mathematical concepts and solving mathematical problems may demand different forms of reasoning. These could be either domain-based, such as algebraic, geometric or statistical reasoning, while others are more general such as inductive/deductive reasoning. This article aims at giving visibility to a particular form of reasoning…
Problem Solving Abilities and Perceptions in Alternative Certification Mathematics Teachers
ERIC Educational Resources Information Center
Evans, Brian R.
It is important for teacher educators to understand new alternative certification middle and high school teachers' mathematical problem solving abilities and perceptions. Teachers in an alternative certification program in New York were enrolled in a proof-based algebra course. At the beginning and end of a semester participants were given a…
Integrating Study Skills and Problem Solving into Remedial Mathematics
ERIC Educational Resources Information Center
Cornick, Jonathan; Guy, G. Michael; Beckford, Ian
Students at a large urban community college enrolled in seven classes of an experimental remedial algebra programme, which integrated study skills instruction and collaborative problem solving. A control group of seven classes was taught in a traditional lecture format without study skills instruction. Student performance in the course was…
Modeling Applied to Problem Solving
NASA Astrophysics Data System (ADS)
Pawl, Andrew; Barrantes, Analia; Pritchard, David E.
We describe a modeling approach to help students learn expert problem solving. Models are used to present and hierarchically organize the syllabus content and apply it to problem solving, but students do not develop and validate their own Models through guided discovery. Instead, students classify problems under the appropriate instructor-generated Model by selecting a system to consider and describing the interactions that are relevant to that system. We believe that this explicit System, Interactions and Model (S.I.M.) problem modeling strategy represents a key simplification and clarification of the widely disseminated modeling approach originated by Hestenes and collaborators. Our narrower focus allows modeling physics to be integrated into (as opposed to replacing) a typical introductory college mechanics course, while preserving the emphasis on understanding systems and interactions that is the essence of modeling. We have employed the approach in a three-week review course for MIT freshmen who received a D in the fall mechanics course with very encouraging results.
Journey toward Teaching Mathematics through Problem Solving
ERIC Educational Resources Information Center
Sakshaug, Lynae E.; Wohlhuter, Kay A.
Teaching mathematics through problem solving is a challenge for teachers who learned mathematics by doing exercises. How do teachers develop their own problem solving abilities as well as their abilities to teach mathematics through problem solving? A group of teachers began the journey of learning to teach through problem solving while taking a…
Problem Solving in the Context of Medicine.
ERIC Educational Resources Information Center
Woods, Donald R.
Reviews the book "Medical Problem Solving: An Analysis of Clinical Reasoning," a seminal book whose conclusions on problem solving in medical fields are still valid today. Discusses major problem-solving findings of this book, the application of the findings to education, and relating knowledge to problem-solving skills. (JRH)
Solving the generalized Langevin equation with the algebraically correlated noise
NASA Astrophysics Data System (ADS)
Srokowski, T.; Płoszajczak, M.
We solve the Langevin equation with the memory kernel. The stochastic force possesses algebraic correlations, proportional to 1/t. The velocity autocorrelation function and related quantities characterizing transport properties are calculated with the assumption that the system is in thermal equilibrium. Stochastic trajectories are simulated numerically, using the kangaroo process as a noise generator. Results of this simulation resemble Lévy walks with divergent moments of the velocity distribution. We consider motion of a Brownian particle, both without any external potential and in the harmonic oscillator field, in particular the escape from a potential well. The results are compared with memory-free calculations for the Brownian particle.
Solving the Dark Matter Problem
Baltz, Ted
Cosmological observations have firmly established that the majority of matter in the universe is of an unknown type, called 'dark matter'. A compelling hypothesis is that the dark matter consists of weakly interacting massive particles (WIMPs) in the mass range around 100 GeV. If the WIMP hypothesis is correct, such particles could be created and studied at accelerators. Furthermore they could be directly detected as the primary component of our galaxy. Solving the dark matter problem requires that the connection be made between the two. We describe some theoretical and experimental avenues that might lead to this connection.
Theoretical and Philosophical Perspectives to Problem Solving.
ERIC Educational Resources Information Center
Sherman, Thomas M.; And Others
Five articles explore various theoretical aspects of problems and problem solving skills. Highlights include strategies to learn problem solving skills; knowledge structures; metacognition; behavioral processes and cognitive psychology; erotetic logic; creativity as an aspect of computer problem solving; and programing as a problem-solving…
Tracking Problem Solving by Multivariate Pattern Analysis and Hidden Markov Model Algorithms
Anderson, John R.
Multivariate pattern analysis can be combined with hidden Markov model algorithms to track the second-by-second thinking as people solve complex problems. Two applications of this methodology are illustrated with a data set taken from children as they interacted with an intelligent tutoring system for algebra. The first "mind reading" application involves using fMRI activity to track what students are doing as they solve a sequence of algebra problems. The methodology achieves considerable accuracy at determining both what problem-solving step the students are taking and whether they are performing that step correctly. The second "model discovery" application involves using statistical model evaluation to determine how many substates are involved in performing a step of algebraic problem solving. This research indicates that different steps involve different numbers of substates and these substates are associated with different fluency in algebra problem solving. PMID:21820455
Robot computer problem solving system
NASA Technical Reports Server (NTRS)
Merriam, E. W.; Becker, J. D.
A robot computer problem solving system which represents a robot exploration vehicle in a simulated Mars environment is described. The model exhibits changes and improvements made on a previously designed robot in a city environment. The Martian environment is modeled in Cartesian coordinates; objects are scattered about a plane; arbitrary restrictions on the robot's vision have been removed; and the robot's path contains arbitrary curves. New environmental features, particularly the visual occlusion of objects by other objects, were added to the model. Two different algorithms were developed for computing occlusion. Movement and vision capabilities of the robot were established in the Mars environment, using LISP/FORTRAN interface for computational efficiency. The graphical display program was redesigned to reflect the change to the Mars-like environment.
Research on Computers and Problem Solving.
ERIC Educational Resources Information Center
Burton, John K.; And Others
Eight articles review and report on research involving computers and problem solving skills. Topics discussed include research design; problem solving skills and programing languages, including BASIC and LOGO; computer anxiety; diagnostic programs for arithmetic problems; and relationships between ability and problem solving scores and between…
King Oedipus and the Problem Solving Process.
ERIC Educational Resources Information Center
Borchardt, Donald A.
An analysis of the problem solving process reveals at least three options: (1) finding the cause, (2) solving the problem, and (3) anticipating potential problems. These methods may be illustrated by examining "Oedipus Tyrannus," a play in which a king attempts to deal with a problem that appears to be beyond his ability to solve, and applying…
Disciplinary Foundations for Solving Interdisciplinary Scientific Problems
ERIC Educational Resources Information Center
Zhang, Dongmei; Shen, Ji
Problem-solving has been one of the major strands in science education research. But much of the problem-solving research has been conducted on discipline-based contexts; little research has been done on how students, especially individuals, solve interdisciplinary problems. To understand how individuals reason about interdisciplinary problems, we…
Community-powered problem solving.
Gouillart, Francis; Billings, Douglas
Traditionally, companies have managed their constituencies with specific processes: marketing to customers, procuring from vendors, developing HR policies for employees, and so on. The problem is, such processes focus on repeatability and compliance, so they can lead to stagnation. Inviting your constituencies to collectively help you solve problems and exploit opportunities--"co-creation"--is a better approach. It allows you to continually tap the skills and insights of huge numbers of stakeholders and develop new ways to produce value for all. The idea is to provide stakeholders with platforms (physical and digital forums) on which they can interact, get them to start exploring new experiences and connections, and let the system grow organically. A co-creation initiative by a unit of Becton, Dickinson and Company demonstrates how this works. A global leader in syringes, BD set out to deepen its ties with hospital customers and help them reduce the incidence of infections from unsafe injection and syringe disposal practices. The effort began with a cross-functional internal team, brought in the hospital procurement and supply managers BD had relationships with, and then reached out to hospitals' infection-prevention and occupational health leaders. Eventually product designers, nurses, sustainability staffers, and even hospital CFOs were using the platform, contributing data that generated new best practices and reduced infections. PMID:23593769
Problem Solving in the General Mathematics Classroom
ERIC Educational Resources Information Center
Troutman, Andria Price; Lichtenberg, Betty Plunkett
Five steps common to different problem solving models are listed. Next, seven specific abilities related to solving problems are discussed and examples given. Sample activities, appropriate to help in developing these specific abilities, are suggested. (LS)
Using Logo to Develop Problem Solving Skills.
ERIC Educational Resources Information Center
Denenberg, Stewart A.
Proposes using computer programing teaching problem solving. Describes the problem-solving technique of Top-Down Design, discusses its application to LOGO, and provides examples of programs using LOGO. (MDH)
Math Ties: Problem Solving, Logic Teasers, and Math Puzzles All "Tied" To the Math Curriculum. Book B1.
ERIC Educational Resources Information Center
Santi, Terri
This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 6-8, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, exponents, fractions, pre-algebra, algebra, geometry, number theory, set theory, ratio, proportion, percent, probability,…
Perspectives on Problem Solving and Instruction
ERIC Educational Resources Information Center
van Merrienboer, Jeroen J. G.
Most educators claim that problem solving is important, but they take very different perspective on it and there is little agreement on how it should be taught. This article aims to sort out the different perspectives and discusses problem solving as a goal, a method, and a skill. As a goal, problem solving should not be limited to well-structured…
Developing Creativity through Collaborative Problem Solving
ERIC Educational Resources Information Center
Albert, Lillie R.; Kim, Rina
This paper discusses an alternative approach for developing problem solving experiences for students. The major argument is that students can develop their creativity by engaging in collaborative problem solving activities in which they apply a variety of mathematical methods creatively to solve problems. The argument is supported by: considering…
Kindergarten Students Solving Mathematical Word Problems
ERIC Educational Resources Information Center
Johnson, Nickey Owen
The purpose of this study was to explore problem solving with kindergarten students. This line of inquiry is highly significant given that Common Core State Standards emphasize deep, conceptual understanding in mathematics as well as problem solving in kindergarten. However, there is little research on problem solving with kindergarten students.…
Collis-Romberg Mathematical Problem Solving Profiles.
ERIC Educational Resources Information Center
Collis, K. F.; Romberg, T. A.
Problem solving has become a focus of mathematics programs in Australia in recent years, necessitating the assessment of students' problem-solving abilities. This manual provides a problem-solving assessment and teaching resource package containing four elements: (1) profiles assessment items; (2) profiles diagnostic forms for recording individual…
Affect and Problem Solving: Two Theoretical Perspectives.
ERIC Educational Resources Information Center
McLeod, Douglas B.
Cognitive factors related to problem solving have been explored, but affective factors also play an important role in the teaching of mathematical problem solving. This paper outlines the theories of George Mandler and Bernard Weiner, providing a useful background for research related to affect and problem solving. Data related to the two theories…
LEGO Robotics: An Authentic Problem Solving Tool?
ERIC Educational Resources Information Center
Castledine, Alanah-Rei; Chalmers, Chris
With the current curriculum focus on correlating classroom problem solving lessons to real-world contexts, are LEGO robotics an effective problem solving tool? This present study was designed to investigate this question and to ascertain what problem solving strategies primary students engaged with when working with LEGO robotics and whether the…
How to encourage university students to solve physics problems requiring mathematical skills: the 'adventurous problem solving' approach
NASA Astrophysics Data System (ADS)
DeMul, Frits F. M.; Batlle, Cristina Martin i.; DeBruijn, Imme; Rinzema, Kees
Teaching physics to first-year university students (in the USA: junior/senior level) is often hampered by their lack of skills in the underlying mathematics, and that in turn may block their understanding of the physics and their ability to solve problems. Examples are vector algebra, differential expressions and multi-dimensional integrations, and the Gauss and Ampère laws learnt in electromagnetism courses. To enhance those skills in a quick and efficient way we have developed 'Integrating Mathematics in University Physics', in which students are provided with a selection of problems (exercises) that explicitly deal with the relation between physics and mathematics. The project is based on computer-assisted instruction (CAI), and available via the Internet (http://tnweb.tn.utwente.nl/onderwijs/; or http://www.utwente.nl/; search or click to: CONECT). Normally, in CAI a predefined student-guiding sequence for problem solving is used (systematic problem solving). For self-learning this approach was found to be far too rigid. Therefore, we developed the 'adventurous problem solving' (APS) method. In this new approach, the student has to find the solution by developing his own problem-solving strategy in an interactive way. The assessment of mathematical answers to physical questions is performed using a background link with an algebraic symbolic language interpreter. This manuscript concentrates on the subject of APS.
Introducing Algebraic Structures through Solving Equations: Vertical Content Knowledge for K-12 Mathematics Teachers
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…
Representational Format, Student Choice, and Problem Solving in Physics
NASA Astrophysics Data System (ADS)
Kohl, P. B.; Finkelstein, N. D.
Student problem-solving ability appears to be tied to the representational format of the problem (math, pictorial, graphical, verbal). In a study of a 367-student algebra-based physics class, we examine student problem solving ability on homework problems given in four different representational formats, with problems as close to isomorphic as possible. In addition, we examine students' capacity for assessing their own representational competence by giving follow-up quizzes in which the students can choose between various problem formats. We report student performance and consider factors that may influence their ability or choices. As a control, part of the class was assigned a random-format follow-up quiz where students received quiz formats at random. We find that there are statistically significant performance differences between isomorphic problems. We also find that allowing students to choose which representational format they use improves student performance under some circumstances and degrades it in others.
Teaching Top-Down Problem Solving.
ERIC Educational Resources Information Center
Patrick, Charles
Top-down problem solving is a methodical approach to obtaining real solutions for open-ended problems common in the realms of engineering and science. The technique provides a means for logically understanding a problem prior to attempting a solution. Steps in the top-down problem-solving method include the following: (1) identifying a need; (2)…
Super 7: Daily Exercises in Problem Solving.
ERIC Educational Resources Information Center
Hamilton, Octavia
This book is a year-long program of daily exercises in problem solving for 2nd and 3rd grade students that presents 144 lessons, each with seven problems. The problems cover number sense, computation, measurements, geometry, problem solving, and patterns. The material is presented in a sequential fashion with concepts repeated and expanded, and…
Flowing toward Correct Contributions during Group Problem Solving: A Statistical Discourse Analysis
ERIC Educational Resources Information Center
Chiu, Ming Ming
Groups that created more correct ideas (correct contributions or CCs) might be more likely to solve a problem, and students' recent actions (micro-time context) might aid CC creation. 80 high school students worked in groups of 4 on an algebra problem. Groups with higher mathematics grades or more CCs were more likely to solve the problem. Dynamic…
Process Inquiry: Analysis of Oral Problem-Solving Skills in Mathematics of Engineering Students
ERIC Educational Resources Information Center
Trance, Naci John C.
This paper presents another effort in determining the difficulty of engineering students in terms of solving word problems. Students were presented with word problems in algebra. Then, they were asked to solve the word problems orally; that is, before they presented their written solutions, they were required to explain how they understood the…
Analog Processor To Solve Optimization Problems
NASA Technical Reports Server (NTRS)
Duong, Tuan A.; Eberhardt, Silvio P.; Thakoor, Anil P.
Proposed analog processor solves "traveling-salesman" problem, considered paradigm of global-optimization problems involving routing or allocation of resources. Includes electronic neural network and auxiliary circuitry based partly on concepts described in "Neural-Network Processor Would Allocate Resources" (NPO-17781) and "Neural Network Solves 'Traveling-Salesman' Problem" (NPO-17807). Processor based on highly parallel computing solves problem in significantly less time.
Rees algebras, Monomial Subrings and Linear Optimization Problems
NASA Astrophysics Data System (ADS)
Dupont, Luis A.
In this thesis we are interested in studying algebraic properties of monomial algebras, that can be linked to combinatorial structures, such as graphs and clutters, and to optimization problems. A goal here is to establish bridges between commutative algebra, combinatorics and optimization. We study the normality and the Gorenstein property-as well as the canonical module and the a-invariant-of Rees algebras and subrings arising from linear optimization problems. In particular, we study algebraic properties of edge ideals and algebras associated to uniform clutters with the max-flow min-cut property or the packing property. We also study algebraic properties of symbolic Rees algebras of edge ideals of graphs, edge ideals of clique clutters of comparability graphs, and Stanley-Reisner rings.
Strengthening Programs through Problem Solving.
ERIC Educational Resources Information Center
Dyer, Jim
Describes a secondary agricultural education program that was a dumping ground for academically disadvantaged students. Discusses how such a program can be improved by identifying problems and symptoms, treating problems, and goal setting. (JOW)
Problem-Solving Test: Pyrosequencing
ERIC Educational Resources Information Center
Szeberenyi, Jozsef
Terms to be familiar with before you start to solve the test: Maxam-Gilbert sequencing, Sanger sequencing, gel electrophoresis, DNA synthesis reaction, polymerase chain reaction, template, primer, DNA polymerase, deoxyribonucleoside triphosphates, orthophosphate, pyrophosphate, nucleoside monophosphates, luminescence, acid anhydride bond,…
Error Detection Processes in Problem Solving.
ERIC Educational Resources Information Center
Allwood, Carl Martin
Describes a study which analyzed problem solvers' error detection processes by instructing subjects to think aloud when solving statistical problems. Effects of evaluative episodes on error detection, detection of different error types, error detection processes per se, and relationship of error detection behavior to problem-solving proficiency…
Distributed problem solving by pilots and dispatchers
NASA Technical Reports Server (NTRS)
Orasanu, Judith; Wich, Mike; Fischer, Ute; Jobe, Kim; Mccoy, Elaine; Beatty, Roger; Smith, Phil
The study addressed the following question: Are flight planning problems solved differently by PILOTS and DISPATCHERS when they work alone versus when they work together? Aspect of their performance that were of interest include the following: Problem perception and definition; Problem solving strategies and information use; Options considered; Solution and rational; and errors.
General Description of Human Problem Solving.
ERIC Educational Resources Information Center
Klein, Gary A.; Weitzenfeld, Julian
A theoretical model relating problem identification to problem solving is presented. The main purpose of the study is to increase understanding of decision making among Air Force educators. The problem-solving process is defined as the generation and evaluation of alternatives that will accomplish what is needed and the reidentification of what is…
Applications of Symmetry to Problem Solving.
ERIC Educational Resources Information Center
Leikin, Roza; Berman, Abraham; Zaslavsky, Orit
Symmetry is an important mathematical concept that plays an extremely important role as a problem solving technique. Presents examples of problems from several branches of mathematics that can be solved using different types of symmetry. Discusses teachers' attitudes and beliefs regarding the use of symmetry in the solutions of these problems.…
Problem solving in health services organizations.
Rakich, J S; Krigline, A B
Health services organization managers at all levels are constantly confronted with problems. Conditions encountered that initiate the need for problem solving are opportunity, threat, crisis, deviation, and improvement. A general problem-solving model presenting an orderly process by which managers can approach this important task is described. An example of the model applied to the current strategic climate is presented. PMID:10158720
Solving Large-scale Eigenvalue Problems in SciDACApplications
Yang, Chao
Large-scale eigenvalue problems arise in a number of DOE applications. This paper provides an overview of the recent development of eigenvalue computation in the context of two SciDAC applications. We emphasize the importance of Krylov subspace methods, and point out its limitations. We discuss the value of alternative approaches that are more amenable to the use of preconditioners, and report the progression using the multi-level algebraic sub-structuring techniques to speed up eigenvalue calculation. In addition to methods for linear eigenvalue problems, we also examine new approaches to solving two types of non-linear eigenvalue problems arising from SciDAC applications.
Mobile serious games for collaborative problem solving.
Sanchez, Jaime; Mendoza, Claudia; Salinas, Alvaro
This paper presents the results obtained from the implementation of a series of learning activities based on mobile serious games (MSG) for the development of problem-solving and collaborative skills in Chilean 8th grade students. Three MSGs were developed and played by teams of four students, who had to solve the problems posed by the game collaboratively. The data shows that the experimental group had a higher perception of their own skills of collaboration and of the plan execution dimension of problem solving than the control group, providing empirical evidence regarding the contribution of MSGs to the development of collaborative problem-solving skills. PMID:19592762
A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.
Benhammouda, Brahim
Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems. PMID:27330880
Disciplinary Foundations for Solving Interdisciplinary Scientific Problems
NASA Astrophysics Data System (ADS)
Zhang, Dongmei; Shen, Ji
Problem-solving has been one of the major strands in science education research. But much of the problem-solving research has been conducted on discipline-based contexts; little research has been done on how students, especially individuals, solve interdisciplinary problems. To understand how individuals reason about interdisciplinary problems, we conducted an interview study with 16 graduate students coming from a variety of disciplinary backgrounds. During the interviews, we asked participants to solve two interdisciplinary science problems on the topic of osmosis. We investigated participants' problem reasoning processes and probed in their attitudes toward general interdisciplinary approach and specific interdisciplinary problems. Through a careful inductive content analysis of their responses, we studied how disciplinary, cognitive, and affective factors influenced their interdisciplinary problems-solving. We found that participants' prior discipline-based science learning experiences had both positive and negative influences on their interdisciplinary problem-solving. These influences were embodied in their conceptualization of the interdisciplinary problems, the strategies they used to integrate different disciplinary knowledge, and the attitudes they had toward interdisciplinary approach in general and specific interdisciplinary problems. This study sheds light on interdisciplinary science education by revealing the complex relationship between disciplinary learning and interdisciplinary problem-solving.
Pen Pals: Practicing Problem Solving
ERIC Educational Resources Information Center
Lampe, Kristen A.; Uselmann, Linda
This article describes a semester-long pen-pal project in which preservice teachers composed mathematical problems and the middle school students worked for solutions. The college students assessed the solution and the middle school students provided feedback regarding the problem itself. (Contains 6 figures.)
Readiness for Solving Story Problems.
ERIC Educational Resources Information Center
Dunlap, William F.
Readiness activities are described which are designed to help learning disabled (LD) students learn to perform computations in story problems. Activities proceed from concrete objects to numbers and involve the students in devising story problems. The language experience approach is incorporated with the enactive, iconic, and symbolic levels of…
Does Early Algebraic Reasoning Differ as a Function of Students' Difficulty with Calculations versus Word Problems?
Powell, Sarah R; Fuchs, Lynn S
According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2(nd)- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty. PMID:25309044
Curricular Reforms That Improve Students' Attitudes and Problem-Solving Performance
ERIC Educational Resources Information Center
Teodorescu, Raluca E.; Bennhold, Cornelius; Feldman, Gerald; Medsker, Larry
We present the most recent steps undertaken to reform the introductory algebra-based course at The George Washington University. The reform sought to help students improve their problem-solving performance. Our pedagogy relies on didactic constructs such as the" GW-ACCESS problem-solving protocol," "instructional sequences" and…
NASA Astrophysics Data System (ADS)
Easton, Don
This note is a description of a student solution to a problem. I found the solution exciting because it exemplifies the kind of solution by analogy that Feynman describes in The Feynman Lectures on Physics.
Problem Solving, Patterns, Probability, Pascal, and Palindromes.
ERIC Educational Resources Information Center
Hylton-Lindsay, Althea Antoinette
Presents a problem-solving activity, the birth order problem, and several solution-seeking strategies. Includes responses of current and prospective teachers and a comparison of various strategies. (YDS)
Neural Network Solves "Traveling-Salesman" Problem
NASA Technical Reports Server (NTRS)
Thakoor, Anilkumar P.; Moopenn, Alexander W.
Experimental electronic neural network solves "traveling-salesman" problem. Plans round trip of minimum distance among N cities, visiting every city once and only once (without backtracking). This problem is paradigm of many problems of global optimization (e.g., routing or allocation of resources) occuring in industry, business, and government. Applied to large number of cities (or resources), circuits of this kind expected to solve problem faster and more cheaply.
Solving the Tulsa ozone problem
Wagner, K.K.; Wilson, J.D.; Gibeau, E.
Local governments and interested parties in Tulsa, Oklahoma are planning actions to keep Tulsa in compliance with the ozone ambient air quality standard. Based on recent data Tulsa exceeds the new eight hour average national ambient air quality standard for ozone and occasionally exceeds the previous one hour standard. Currently, Tulsa is in attainment of the former one-hour ozone standard. The first planning step is to integrate the existing information about Tulsa`s ozone problem. Prior studies of Tulsa ozone are reviewed. Tulsa`s recent air quality and meteorological monitoring are evaluated. Emission inventory estimates are assessed. Factors identified with Tulsa`s ozone problem are the transport of ozone and precursor gases, a possible role for biogenic emissions, and a simplistic ozone forecasting method. The integration of information found that current air quality and meteorological monitoring is meager. Observations of volatile organic compounds and NO{sub y} are absent. Prior intensive studies in 1977 and 1985 are more than ten years old and lack relevance to today`s problem. Emission inventory estimates are scarce and uncertain. The current knowledge base was judged inadequate to properly characterize the present ozone problem. Actions are recommended to enlarge the information base to address Tulsa`s ozone problem.
Solving global optimization problems on GPU cluster
NASA Astrophysics Data System (ADS)
Barkalov, Konstantin; Gergel, Victor; Lebedev, Ilya
The paper contains the results of investigation of a parallel global optimization algorithm combined with a dimension reduction scheme. This allows solving multidimensional problems by means of reducing to data-independent subproblems with smaller dimension solved in parallel. The new element implemented in the research consists in using several graphic accelerators at different computing nodes. The paper also includes results of solving problems of well-known multiextremal test class GKLS on Lobachevsky supercomputer using tens of thousands of GPU cores.
Taking "From Scratch" out of Problem Solving
ERIC Educational Resources Information Center
Brown, Wayne
Solving problems and creating processes and procedures from the ground up has long been part of the IT department's way of operating. IT staffs will continue to encounter new problems to solve and new technologies to be implemented. They also must involve their constituents in the creation of solutions. Nonetheless, for many issues they no longer…
A Problem-Solving Model for Instruction.
ERIC Educational Resources Information Center
Scott, Roger O.
This second in a series of three papers on the Associated Staff Training Program of the Foreign Language Innovative Curriculum Study concentrates on the problem solving strategy employed by the program's specially trained innovative agents--the Instructional Systems Consultants (ISC). The problem-solving method used is first illustrated by citing…
Conceptual Problem Solving in High School Physics
ERIC Educational Resources Information Center
Docktor, Jennifer L.; Strand, Natalie E.; Mestre, José P.; Ross, Brian H.
Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an…
Solving Problems in Genetics II: Conceptual Restructuring
ERIC Educational Resources Information Center
Orcajo, Teresa Ibanez; Aznar, Mercedes Martinez
This paper presents the results of part of an investigation carried out with fourth-level Spanish secondary education students (15 years old), in which we implemented a teaching unit based on problem-solving methodology as an investigation to teach genetics and human inheritance curricular contents. By solving open problems, the students…
Problem Solving Software for Math Classes.
ERIC Educational Resources Information Center
Troutner, Joanne
Described are 10 computer software programs for problem solving related to mathematics. Programs described are: (1) Box Solves Story Problems; (2) Safari Search; (3) Puzzle Tanks; (4) The King's Rule; (5) The Factory; (6) The Royal Rules; (7) The Enchanted Forest; (8) Gears; (9) The Super Factory; and (10) Creativity Unlimited. (RH)
Solving Problems with Charts & Tables. Pipefitter.
ERIC Educational Resources Information Center
Greater Baton Rouge Chamber of Commerce, LA.
Developed as part of the ABCs of Construction National Workplace Literacy Project, this instructional module is designed to help individuals employed as pipefitters learn to solve problems with charts and tables. Outlined in the first section is a five-step procedure for solving problems involving tables and/or charts: identifying the question to…
Student Modeling Based on Problem Solving Times
ERIC Educational Resources Information Center
Pelánek, Radek; Jarušek, Petr
Student modeling in intelligent tutoring systems is mostly concerned with modeling correctness of students' answers. As interactive problem solving activities become increasingly common in educational systems, it is useful to focus also on timing information associated with problem solving. We argue that the focus on timing is natural for certain…
Metacognition: Student Reflections on Problem Solving
ERIC Educational Resources Information Center
Wismath, Shelly; Orr, Doug; Good, Brandon
Twenty-first century teaching and learning focus on the fundamental skills of critical thinking and problem solving, creativity and innovation, and collaboration and communication. Metacognition is a crucial aspect of both problem solving and critical thinking, but it is often difficult to get students to engage in authentic metacognitive…
Mathematical Problem Solving through Sequential Process Analysis
ERIC Educational Resources Information Center
Codina, A.; Cañadas, M. C.; Castro, E.
Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…
Problem Solving and Technology. ACESIA Monograph 2.
ERIC Educational Resources Information Center
Lomon, Earle L.; And Others
The two articles dealing with problem solving and technology in this publication should be useful to those developing the kinds of materials, experiences, and thinking that elementary school industrial arts offers children. The first article accepts problem solving as an educational goal and reports a timely and universally acceptable approach.…
Geographic Information Systems: Implications for Problem Solving.
ERIC Educational Resources Information Center
Audet, Richard H.; Abegg, Gerald L.
Compares expert-/novice-based problem-solving behaviors with a Geographic Information Systems program. Uses naturalistic methods to analyze problem-solving strategies for occurrence of thematic elements. Reports that experts relied on logical formulations to query the database while novices used trial-and-error methods and midlevel cognitive…
Children Solving Problems. The Developing Child Series.
ERIC Educational Resources Information Center
Thornton, Stephanie
The developmental increase in the ability to solve problems is a puzzle. Does it come from basic changes in mental skills, or is it a matter of practice? This book from the Developing Child series synthesizes recent research examining children's problem-solving skills development. Chapter 1 presents the major themes: (1) there is increasing…
Dynamic Problem Solving: A New Assessment Perspective
ERIC Educational Resources Information Center
Greiff, Samuel; Wustenberg, Sascha; Funke, Joachim
This article addresses two unsolved measurement issues in dynamic problem solving (DPS) research: (a) unsystematic construction of DPS tests making a comparison of results obtained in different studies difficult and (b) use of time-intensive single tasks leading to severe reliability problems. To solve these issues, the MicroDYN approach is…
Could HPS Improve Problem-Solving?
ERIC Educational Resources Information Center
Coelho, Ricardo Lopes
It is generally accepted nowadays that History and Philosophy of Science (HPS) is useful in understanding scientific concepts, theories and even some experiments. Problem-solving strategies are a significant topic, since students' careers depend on their skill to solve problems. These are the reasons for addressing the question of whether problem…
Problem Solving Interactions on Electronic Networks.
ERIC Educational Resources Information Center
Waugh, Michael; And Others
Arguing that electronic networking provides a medium which is qualitatively superior to the traditional classroom for conducting certain types of problem solving exercises, this paper details the Water Problem Solving Project, which was conducted on the InterCultural Learning Network in 1985 and 1986 with students from the United States, Mexico,…
Teaching and Learning through Problem Solving
ERIC Educational Resources Information Center
Ollerton, Mike
In this article, the author relates some problem solving work with primary schools to Department for Children, Schools, and Families (DfES) support. In four primary schools in the West Midlands, the focus was teaching mathematics through problem solving, based on materials published on the DfES "standards" website. The author noticed the way…
Measuring Problem Solving Skills in "Portal 2"
ERIC Educational Resources Information Center
Shute, Valerie J.; Wang, Lubin
This paper examines possible improvement to problem solving skills as a function of playing the video game "Portal 2." Stealth assessment is used in the game to evaluate students' problem solving abilities--specifically basic and flexible rule application. The stealth assessment measures will be validated against commonly accepted…
A Multivariate Model of Physics Problem Solving
ERIC Educational Resources Information Center
Taasoobshirazi, Gita; Farley, John
A model of expertise in physics problem solving was tested on undergraduate science, physics, and engineering majors enrolled in an introductory-level physics course. Structural equation modeling was used to test hypothesized relationships among variables linked to expertise in physics problem solving including motivation, metacognitive planning,…
Problem Solving Software: What Does It Teach?
ERIC Educational Resources Information Center
Duffield, Judith A.
The purpose of this study was to examine the potential of computer-assisted instruction (CAI) for teaching problem solving skills. It was conducted in three phases. During the first phase, two pieces of problem solving software, "The King's Rule" and "Safari Search," were identified and analyzed. During the second phase, two groups of six…
Developing Legal Problem-Solving Skills.
ERIC Educational Resources Information Center
Nathanson, Stephen
A law professor explains how he came to view legal problem solving as the driving concept in law school curriculum design and draws on personal experience and a survey of students concerning teaching methods in a commercial law course. He outlines six curriculum design principles for teaching legal problem solving. (MSE)
Beyond Computation: Improving Mathematical Problem Solving.
ERIC Educational Resources Information Center
Anderson, Jennifer M.; Olson, Jennifer S.; Wrobel, Margaret L.
This action research describes a program for improving mathematical problem solving skills. The targeted population consisted of first grade students in a transient, middle class community as well as third and sixth grade students from a growing, middle to upper class in Illinois. The concerns of problem solving were documented through teacher…
Pre-Service Class Teacher' Ability in Solving Mathematical Problems and Skills in Solving Daily Problems
ERIC Educational Resources Information Center
Aljaberi, Nahil M.; Gheith, Eman
This study aims to investigate the ability of pre-service class teacher at University of Petrain solving mathematical problems using Polya's Techniques, their level of problem solving skills in daily-life issues. The study also investigates the correlation between their ability to solve mathematical problems and their level of problem solving…
Solving the wrong hierarchy problem
NASA Astrophysics Data System (ADS)
Blinov, Nikita; Hook, Anson
Many theories require augmenting the Standard Model with additional scalar fields with large order one couplings. We present a new solution to the hierarchy problem for these scalar fields. We explore parity- and Z_2 -symmetric theories where the Standard Model Higgs potential has two vacua. The parity or Z_2 copy of the Higgs lives in the minimum far from the origin while our Higgs occupies the minimum near the origin of the potential. This approach results in a theory with multiple light scalar fields but with only a single hierarchy problem, since the bare mass is tied to the Higgs mass by a discrete symmetry. The new scalar does not have a new hierarchy problem associated with it because its expectation value and mass are generated by dimensional transmutation of the scalar quartic coupling. The location of the second Higgs minimum is not a free parameter, but is rather a function of the matter content of the theory. As a result, these theories are extremely predictive. We develop this idea in the context of a solution to the strong CP problem. We show this mechanism postdicts the top Yukawa to be within 1 σ of the currently measured value and predicts scalar color octets with masses in the range 9-200 TeV.
Solving a Spacecraft Design Problem
NASA Technical Reports Server (NTRS)
Fisher, D. K.
We have probably all been amazed at the ingenuity of spacecraft engineers when we see some of the solutions they invent for such problems as landing a roving vehicle on Mars-as engineers at the Jet Propulsion Laboratory did for NASA's Mars Pathfinder project-without using retro-rockets or even putting a spacecraft in orbit first.
Robot, computer problem solving system
NASA Technical Reports Server (NTRS)
Becker, J. D.; Merriam, E. W.
The TENEX computer system, the ARPA network, and computer language design technology was applied to support the complex system programs. By combining the pragmatic and theoretical aspects of robot development, an approach is created which is grounded in realism, but which also has at its disposal the power that comes from looking at complex problems from an abstract analytical point of view.
Solving the wrong hierarchy problem
Blinov, Nikita; Hook, Anson
Many theories require augmenting the Standard Model with additional scalar fields with large order one couplings. We present a new solution to the hierarchy problem for these scalar fields. We explore parity- and Z2-symmetric theories where the Standard Model Higgs potential has two vacua. The parity or Z2 copy of the Higgs lives in the minimum far from the origin while our Higgs occupies the minimum near the origin of the potential. This approach results in a theory with multiple light scalar fields but with only a single hierarchy problem, since the bare mass is tied to the Higgs massmore » by a discrete symmetry. The new scalar does not have a new hierarchy problem associated with it because its expectation value and mass are generated by dimensional transmutation of the scalar quartic coupling. The location of the second Higgs minimum is not a free parameter, but is rather a function of the matter content of the theory. As a result, these theories are extremely predictive. We develop this idea in the context of a solution to the strong CP problem. Lastly, we show this mechanism postdicts the top Yukawa to be within 1σ of the currently measured value and predicts scalar color octets with masses in the range 9-200 TeV.« less
Sour landfill gas problem solved
Nagl, G.; Cantrall, R.
In Broward County, Fla., near Pompano Beach, Waste Management of North America (WMNA, a subsidiary of WMX Technologies, Oak Brook, IL) operates the Central Sanitary Landfill and Recycling Center, which includes the country`s largest landfill gas-to-energy plant. The landfill consists of three collection sites: one site is closed, one is currently receiving garbage, and one will open in the future. Approximately 9 million standard cubic feet (scf) per day of landfill gas is collected from approximately 300 wells spread over the 250-acre landfill. With a dramatic increase of sulfur-containing waste coming to a South Florida landfill following Hurricane Andrew, odors related to hydrogen sulfide became a serious problem. However, in a matter of weeks, an innovative desulfurization unit helped calm the landfill operator`s fears. These very high H{sub 2}S concentrations caused severe odor problems in the surrounding residential area, corrosion problems in the compressors, and sulfur dioxide (SO{sub 2}) emission problems in the exhaust gas from the turbine generators.
The effects of cumulative practice on mathematics problem solving.
Mayfield, Kristin H; Chase, Philip N
This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving. PMID:12102132
Assertiveness and problem solving in midwives
Yurtsal, Zeliha Burcu; Özdemir, Levent
Background: Midwifery profession is required to bring solutions to problems and a midwife is expected to be an assertive person and to develop midwifery care. This study was planned to examine the relationship between assertiveness and problem-solving skills of midwives. Materials and Methods: This cross-sectional study was conducted with 201 midwives between July 2008 and February 2009 in the city center of Sivas. The Rathus Assertiveness Schedule (RAS) and Problem Solving Inventory (PSI) were used to determine the level of assertiveness and problem-solving skills of midwives. Statistical methods were used as mean, standard deviation, percentage, Student's T, ANOVA and Tukey HSD, Kruskal Wallis, Fisher Exact, Pearson Correlation and Chi-square tests and P < 0.05. Results: The RAS mean scores and the PSI mean scores showed statistically significant differences in terms of a midwife's considering herself as a member of the health team, expressing herself within the health care team, being able to say "no" when necessary, cooperating with her colleagues, taking part in problem-solving skills training. A statistically significant negative correlation was found between the RAS and PSI scores. The RAS scores decreased while the problem-solving scores increased (r: -0451, P < 0.01). Conclusions: There were significant statistical differences between assertiveness levels and problem solving skills of midwives, and midwives who were assertive solved their problems better than did others. Assertiveness and problem-solving skills training will contribute to the success of the midwifery profession. Midwives able to solve problems, and display assertive behaviors will contribute to the development of midwifery profession. PMID:26793247
Cognitive Problems (Disorientation, Perception, Attention, Learning and Problem-Solving)
... SOMEONE WITH EMOTIONAL & BEHAVIORAL NEEDS Cognitive Problems (Disorientation, Perception, Attention, Learning & Problem-Solving) Cognition is the process ... What Are Some Other Cognitive Problems? What Is Perception? Remember What Is Attention or Concentration? More Resources ...
Lesion mapping of social problem solving
Colom, Roberto; Paul, Erick J.; Chau, Aileen; Solomon, Jeffrey; Grafman, Jordan H.
Accumulating neuroscience evidence indicates that human intelligence is supported by a distributed network of frontal and parietal regions that enable complex, goal-directed behaviour. However, the contributions of this network to social aspects of intellectual function remain to be well characterized. Here, we report a human lesion study (n = 144) that investigates the neural bases of social problem solving (measured by the Everyday Problem Solving Inventory) and examine the degree to which individual differences in performance are predicted by a broad spectrum of psychological variables, including psychometric intelligence (measured by the Wechsler Adult Intelligence Scale), emotional intelligence (measured by the Mayer, Salovey, Caruso Emotional Intelligence Test), and personality traits (measured by the Neuroticism-Extraversion-Openness Personality Inventory). Scores for each variable were obtained, followed by voxel-based lesion–symptom mapping. Stepwise regression analyses revealed that working memory, processing speed, and emotional intelligence predict individual differences in everyday problem solving. A targeted analysis of specific everyday problem solving domains (involving friends, home management, consumerism, work, information management, and family) revealed psychological variables that selectively contribute to each. Lesion mapping results indicated that social problem solving, psychometric intelligence, and emotional intelligence are supported by a shared network of frontal, temporal, and parietal regions, including white matter association tracts that bind these areas into a coordinated system. The results support an integrative framework for understanding social intelligence and make specific recommendations for the application of the Everyday Problem Solving Inventory to the study of social problem solving in health and disease. PMID:25070511
Lesion mapping of social problem solving.
Barbey, Aron K; Colom, Roberto; Paul, Erick J; Chau, Aileen; Solomon, Jeffrey; Grafman, Jordan H
Accumulating neuroscience evidence indicates that human intelligence is supported by a distributed network of frontal and parietal regions that enable complex, goal-directed behaviour. However, the contributions of this network to social aspects of intellectual function remain to be well characterized. Here, we report a human lesion study (n = 144) that investigates the neural bases of social problem solving (measured by the Everyday Problem Solving Inventory) and examine the degree to which individual differences in performance are predicted by a broad spectrum of psychological variables, including psychometric intelligence (measured by the Wechsler Adult Intelligence Scale), emotional intelligence (measured by the Mayer, Salovey, Caruso Emotional Intelligence Test), and personality traits (measured by the Neuroticism-Extraversion-Openness Personality Inventory). Scores for each variable were obtained, followed by voxel-based lesion-symptom mapping. Stepwise regression analyses revealed that working memory, processing speed, and emotional intelligence predict individual differences in everyday problem solving. A targeted analysis of specific everyday problem solving domains (involving friends, home management, consumerism, work, information management, and family) revealed psychological variables that selectively contribute to each. Lesion mapping results indicated that social problem solving, psychometric intelligence, and emotional intelligence are supported by a shared network of frontal, temporal, and parietal regions, including white matter association tracts that bind these areas into a coordinated system. The results support an integrative framework for understanding social intelligence and make specific recommendations for the application of the Everyday Problem Solving Inventory to the study of social problem solving in health and disease. PMID:25070511
The Cyclic Nature of Problem Solving: An Emergent Multidimensional Problem-Solving Framework
ERIC Educational Resources Information Center
Carlson, Marilyn P.; Bloom, Irene
This paper describes the problem-solving behaviors of 12 mathematicians as they completed four mathematical tasks. The emergent problem-solving framework draws on the large body of research, as grounded by and modified in response to our close observations of these mathematicians. The resulting "Multidimensional Problem-Solving Framework" has four…
Reflection on problem solving in introductory and advanced physics
NASA Astrophysics Data System (ADS)
Mason, Andrew J.
Reflection is essential in order to learn from problem solving. This thesis explores issues related to how reflective students are and how we can improve their capacity for reflection on problem solving. We investigate how students naturally reflect in their physics courses about problem solving and evaluate strategies that may teach them reflection as an integral component of problem-solving. Problem categorization based upon similarity of solution is a strategy to help them reflect about the deep features of the problems related to the physics principles involved. We find that there is a large overlap between the introductory and graduate students in their ability to categorize. Moreover, introductory students in the calculus-based courses performed better categorization than those in the algebra-based courses even though the categorization task is conceptual. Other investigations involved exploring if reflection could be taught as a skill on individual and group levels. Explicit self-diagnosis in recitation investigated how effectively students could diagnose their own errors on difficult problems, how much scaffolding was necessary for this purpose, and how effective transfer was to other problems employing similar principles. Difficulty in applying physical principles and difference between the self-diagnosed and transfer problems affected performance. We concluded that a sustained intervention is required to learn effective problem-solving strategies. Another study involving reflection on problem solving with peers suggests that those who reflected with peers drew more diagrams and had a larger gain from the midterm to final exam. Another study in quantum mechanics involved giving common problems in midterm and final exams and suggested that advanced students do not automatically reflect on their mistakes. Interviews revealed that even advanced students often focus mostly on exams rather than learning and building a robust knowledge structure. A survey was
Spatial visualization in physics problem solving.
Kozhevnikov, Maria; Motes, Michael A; Hegarty, Mary
Three studies were conducted to examine the relation of spatial visualization to solving kinematics problems that involved either predicting the two-dimensional motion of an object, translating from one frame of reference to another, or interpreting kinematics graphs. In Study 1, 60 physics-naíve students were administered kinematics problems and spatial visualization ability tests. In Study 2, 17 (8 high- and 9 low-spatial ability) additional students completed think-aloud protocols while they solved the kinematics problems. In Study 3, the eye movements of fifteen (9 high- and 6 low-spatial ability) students were recorded while the students solved kinematics problems. In contrast to high-spatial students, most low-spatial students did not combine two motion vectors, were unable to switch frames of reference, and tended to interpret graphs literally. The results of the study suggest an important relationship between spatial visualization ability and solving kinematics problems with multiple spatial parameters. PMID:21635308
Could HPS Improve Problem-Solving?
NASA Astrophysics Data System (ADS)
Coelho, Ricardo Lopes
It is generally accepted nowadays that History and Philosophy of Science (HPS) is useful in understanding scientific concepts, theories and even some experiments. Problem-solving strategies are a significant topic, since students' careers depend on their skill to solve problems. These are the reasons for addressing the question of whether problem solving could be improved by means of HPS. Three typical problems in introductory courses of mechanics—the inclined plane, the simple pendulum and the Atwood machine—are taken as the object of the present study. The solving strategies of these problems in the eighteenth and nineteenth century constitute the historical component of the study. Its philosophical component stems from the foundations of mechanics research literature. The use of HPS leads us to see those problems in a different way. These different ways can be tested, for which experiments are proposed. The traditional solving strategies for the incline and pendulum problems are adequate for some situations but not in general. The recourse to apparent weights in the Atwood machine problem leads us to a new insight and a solving strategy for composed Atwood machines. Educational implications also concern the development of logical thinking by means of the variety of lines of thought provided by HPS.
Solving inversion problems with neural networks
NASA Technical Reports Server (NTRS)
Kamgar-Parsi, Behzad; Gualtieri, J. A.
A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.
Problem Solving through an Optimization Problem in Geometry
ERIC Educational Resources Information Center
Poon, Kin Keung; Wong, Hang-Chi
This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…
Task Variables in Mathematical Problem Solving.
ERIC Educational Resources Information Center
Goldin, Gerald A., Ed.; McClintock, C. Edwin, Ed.
A framework for research in problem solving is provided by categorizing and defining variables describing problem tasks. A model is presented in an article by Kulm for the classification of task variables into broad categories. The model attempts to draw realtionships between these categories of task variables and the stages of problem solving…
Collaborative Problem Solving in Shared Space
ERIC Educational Resources Information Center
Lin, Lin; Mills, Leila A.; Ifenthaler, Dirk
The purpose of this study was to examine collaborative problem solving in a shared virtual space. The main question asked was: How will the performance and processes differ between collaborative problem solvers and independent problem solvers over time? A total of 104 university students (63 female and 41 male) participated in an experimental…
Problem Solving: Can Anybody Do It?
ERIC Educational Resources Information Center
Bennett, Stuart W.
This paper examines the definition of a problem and at the process of problem solving. An analysis of a number of first and third year chemistry examination papers from English universities revealed that over ninety per cent of the "problems" fell into the "algorithm" category. Using Bloom's taxonomy and the same examination papers, we found that…
Solving Problems with the Percentage Bar
ERIC Educational Resources Information Center
van Galen, Frans; van Eerde, Dolly
At the end of primary school all children more of less know what a percentage is, but yet they often struggle with percentage problems. This article describes a study in which students of 13 and 14 years old were given a written test with percentage problems and a week later were interviewed about the way they solved some of these problems. In a…
Conceptual problem solving in high school physics
NASA Astrophysics Data System (ADS)
Docktor, Jennifer L.; Strand, Natalie E.; Mestre, José P.; Ross, Brian H.
Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in writing before solving a problem. The CPS approach was implemented by high school physics teachers at three schools for major theorems and conservation laws in mechanics and CPS-taught classes were compared to control classes taught using traditional problem solving methods. Information about the teachers' implementation of the approach was gathered from classroom observations and interviews, and the effectiveness of the approach was evaluated from a series of written assessments. Results indicated that teachers found CPS easy to integrate into their curricula, students engaged in classroom discussions and produced problem solutions of a higher quality than before, and students scored higher on conceptual and problem solving measures.
Organizational Structure and Complex Problem Solving
ERIC Educational Resources Information Center
Becker, Selwyn W.; Baloff, Nicholas
The problem-solving efficiency of different organization structures is discussed in relation to task requirements and the appropriate organizational behavior, to group adaptation to a task over time, and to various group characteristics. (LN)
Physics: Quantum problems solved through games
NASA Astrophysics Data System (ADS)
Maniscalco, Sabrina
Humans are better than computers at performing certain tasks because of their intuition and superior visual processing. Video games are now being used to channel these abilities to solve problems in quantum physics. See Letter p.210
Using Problem Solving to Teach the Disabled.
ERIC Educational Resources Information Center
Cardon, Phillip L.; Scott, Michael L.
Technology education can and should play a role in the development of ideas through problem solving to assist teachers of students with disabilities. Technology teachers can adapt the Engineering for Success model in working with these students. (JOW)
Tracking children's mental states while solving algebra equations.
Anderson, John R; Betts, Shawn; Ferris, Jennifer L; Fincham, Jon M
Behavioral and function magnetic resonance imagery (fMRI) data were combined to infer the mental states of students as they interacted with an intelligent tutoring system. Sixteen children interacted with a computer tutor for solving linear equations over a six-day period (days 0-5), with days 1 and 5 occurring in an fMRI scanner. Hidden Markov model algorithms combined a model of student behavior with multi-voxel imaging pattern data to predict the mental states of students. We separately assessed the algorithms' ability to predict which step in a problem-solving sequence was performed and whether the step was performed correctly. For day 1, the data patterns of other students were used to predict the mental states of a target student. These predictions were improved on day 5 by adding information about the target student's behavioral and imaging data from day 1. Successful tracking of mental states depended on using the combination of a behavioral model and multi-voxel pattern analysis, illustrating the effectiveness of an integrated approach to tracking the cognition of individuals in real time as they perform complex tasks. PMID:21932262
Does Early Algebraic Reasoning Differ as a Function of Students' Difficulty with Calculations versus Word Problems?
ERIC Educational Resources Information Center
Powell, Sarah R.; Fuchs, Lynn S.
According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 second-grade students, we administered: (1) measures of calculations and…
Innovative problem solving by wild spotted hyenas
Benson-Amram, Sarah; Holekamp, Kay E.
Innovative animals are those able to solve novel problems or invent novel solutions to existing problems. Despite the important ecological and evolutionary consequences of innovation, we still know very little about the traits that vary among individuals within a species to make them more or less innovative. Here we examine innovative problem solving by spotted hyenas (Crocuta crocuta) in their natural habitat, and demonstrate for the first time in a non-human animal that those individuals exhibiting a greater diversity of initial exploratory behaviours are more successful problem solvers. Additionally, as in earlier work, we found that neophobia was a critical inhibitor of problem-solving success. Interestingly, although juveniles and adults were equally successful in solving the problem, juveniles were significantly more diverse in their initial exploratory behaviours, more persistent and less neophobic than were adults. We found no significant effects of social rank or sex on success, the diversity of initial exploratory behaviours, behavioural persistence or neophobia. Our results suggest that the diversity of initial exploratory behaviours, akin to some measures of human creativity, is an important, but largely overlooked, determinant of problem-solving success in non-human animals. PMID:22874748
Innovative problem solving by wild spotted hyenas.
Benson-Amram, Sarah; Holekamp, Kay E
Innovative animals are those able to solve novel problems or invent novel solutions to existing problems. Despite the important ecological and evolutionary consequences of innovation, we still know very little about the traits that vary among individuals within a species to make them more or less innovative. Here we examine innovative problem solving by spotted hyenas (Crocuta crocuta) in their natural habitat, and demonstrate for the first time in a non-human animal that those individuals exhibiting a greater diversity of initial exploratory behaviours are more successful problem solvers. Additionally, as in earlier work, we found that neophobia was a critical inhibitor of problem-solving success. Interestingly, although juveniles and adults were equally successful in solving the problem, juveniles were significantly more diverse in their initial exploratory behaviours, more persistent and less neophobic than were adults. We found no significant effects of social rank or sex on success, the diversity of initial exploratory behaviours, behavioural persistence or neophobia. Our results suggest that the diversity of initial exploratory behaviours, akin to some measures of human creativity, is an important, but largely overlooked, determinant of problem-solving success in non-human animals. PMID:22874748
Clifford algebra approach to the coincidence problem for planar lattices.
Rodríguez, M A; Aragón, J L; Verde-Star, L
The problem of coincidences of planar lattices is analyzed using Clifford algebra. It is shown that an arbitrary coincidence isometry can be decomposed as a product of coincidence reflections and this allows planar coincidence lattices to be characterized algebraically. The cases of square, rectangular and rhombic lattices are worked out in detail. One of the aims of this work is to show the potential usefulness of Clifford algebra in crystallography. The power of Clifford algebra for expressing geometric ideas is exploited here and the procedure presented can be generalized to higher dimensions. PMID:15724067
Review on solving the forward problem in EEG source analysis
Hallez, Hans; Vanrumste, Bart; Grech, Roberta; Muscat, Joseph; De Clercq, Wim; Vergult, Anneleen; D'Asseler, Yves; Camilleri, Kenneth P; Fabri, Simon G; Van Huffel, Sabine; Lemahieu, Ignace
solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method. Conclusion Solving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem. PMID:18053144
The Hochschild cohomology problem for von Neumann algebras
Sinclair, Allan M.; Smith, Roger R.
In 1967, when Kadison and Ringrose began the development of continuous cohomology theory for operator algebras, they conjectured that the cohomology groups Hn(M, M), n ≥ 1, for a von Neumann algebra M, should all be zero. This conjecture, which has important structural implications for von Neumann algebras, has been solved affirmatively in the type I, II∞, and III cases, leaving open only the type II1 case. In this paper, we describe a positive solution when M is type II1 and has a Cartan subalgebra and a separable predual. PMID:9520373
The hochschild cohomology problem for von neumann algebras.
Sinclair, A M; Smith, R R
In 1967, when Kadison and Ringrose began the development of continuous cohomology theory for operator algebras, they conjectured that the cohomology groups Hn(M, M), n >/= 1, for a von Neumann algebra M, should all be zero. This conjecture, which has important structural implications for von Neumann algebras, has been solved affirmatively in the type I, IIinfinity, and III cases, leaving open only the type II1 case. In this paper, we describe a positive solution when M is type II1 and has a Cartan subalgebra and a separable predual. PMID:9520373
The Functional Equivalence of Problem Solving Skills
ERIC Educational Resources Information Center
Simon, Herbert A.
This analysis of solutions to the Tower of Hanoi Problem underscores the importance of subject-by-subject analysis of "What is learned" in understanding human behavior in problem-solving situations, and provides a technique for describing subjects' task performance programs in detail. (Author/BJG)
Using Bibliotherapy To Teach Problem Solving.
ERIC Educational Resources Information Center
Forgan, James W.
This article discusses how students with high-incidence disabilities can benefit from using bibliotherapy by learning to become proactive problem solvers. A sample lesson plan is presented based on a teaching framework for bibliotherapy and problem solving that contains the elements of prereading, guided reading, post-reading discussion, and a…
GIS Live and Web Problem Solving
ERIC Educational Resources Information Center
Hagevik, R.; Hales, D.; Harrell, J.
GIS Live is a live, interactive, web problem-solving (WPS) program that partners Geographic Information Systems (GIS) professionals with educators to implement geospatial technologies as curriculum-learning tools. It is a collaborative effort of many government agencies, educational institutions, and professional organizations. Problem-based…
Using Programmable Calculators to Solve Electrostatics Problems.
ERIC Educational Resources Information Center
Yerian, Stephen C.; Denker, Dennis A.
Provides a simple routine which allows first-year physics students to use programmable calculators to solve otherwise complex electrostatic problems. These problems involve finding electrostatic potential and electric field on the axis of a uniformly charged ring. Modest programing skills are required of students. (DH)
Problem-Solving Competitions: Just the Solution!
ERIC Educational Resources Information Center
Riley, Tracy L.; Karnes, Frances A.
This article describes competitions across a range of curricular areas that develop students' problem solving skills by setting authentic, real-world tasks. As individuals or members of a team, students in these competitions are challenged with finding solutions to problems faced not only in today's scientific and technological world, but also in…
Spatial Visualization in Physics Problem Solving
ERIC Educational Resources Information Center
Kozhevnikov, Maria; Motes, Michael A.; Hegarty, Mary
Three studies were conducted to examine the relation of spatial visualization to solving kinematics problems that involved either predicting the two-dimensional motion of an object, translating from one frame of reference to another, or interpreting kinematics graphs. In Study 1, 60 physics-naive students were administered kinematics problems and…
Teaching Teamwork and Problem Solving Concurrently
ERIC Educational Resources Information Center
Goltz, Sonia M.; Hietapelto, Amy B.; Reinsch, Roger W.; Tyrell, Sharon K.
Teamwork and problem-solving skills have frequently been identified by business leaders as being key competencies; thus, teaching methods such as problem-based learning and team-based learning have been developed. However, the focus of these methods has been on teaching one skill or the other. A key argument for teaching the skills concurrently is…
Pose and Solve Varignon Converse Problems
ERIC Educational Resources Information Center
Contreras, José N.
The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…
Reinventing the Wheel: Design and Problem Solving
ERIC Educational Resources Information Center
Blasetti, Sean M.
This article describes a design problem that not only takes students through the technological design process, but it also provides them with real-world problem-solving experience as it relates to the manufacturing and engineering fields. It begins with a scenario placing the student as a custom wheel designer for an automotive manufacturing…
Reflect ... for Better Problem Solving and Reasoning.
ERIC Educational Resources Information Center
Krulik, Stephen; Rudnick, Jesse A.
Elaborates the final step of Polya's heuristic model, reflecting, to improve students' problem-solving performance. After checking answers for accuracy, the following steps are suggested: (1) test reasonableness and practicality; (2) write a summary paragraph; (3) find other solutions; (4) change the conditions; and (5) extend the problem. (MKR)
Solving Geometry Problems via Mechanical Principles
ERIC Educational Resources Information Center
Man, Yiu Kwong
The application of physical principles in solving mathematics problems have often been neglected in the teaching of physics or mathematics, especially at the secondary school level. This paper discusses how to apply the mechanical principles to geometry problems via concrete examples, which aims at providing insight and inspirations to physics or…
Model Formulation for Physics Problem Solving. Draft.
ERIC Educational Resources Information Center
Novak, Gordon S., Jr.
The major task in solving a physics problem is to construct an appropriate model of the problem in terms of physical principles. The functions performed by such a model, the information which needs to be represented, and the knowledge used in selecting and instantiating an appropriate model are discussed. An example of a model for a mechanics…
Problem solving and decisionmaking: An integration
NASA Technical Reports Server (NTRS)
Dieterly, D. L.
An attempt was made to redress a critical fault of decisionmaking and problem solving research-a lack of a standard method to classify problem or decision states or conditions. A basic model was identified and expanded to indicate a possible taxonomy of conditions which may be used in reviewing previous research or for systematically pursuing new research designs. A generalization of the basic conditions was then made to indicate that the conditions are essentially the same for both concepts, problem solving and decisionmaking.
Solving the Langevin equation with stochastic algebraically correlated noise
NASA Astrophysics Data System (ADS)
Płoszajczak, M.; Srokowski, T.
The long time tail in the velocity and force autocorrelation function has been found recently in molecular dynamics simulations of peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. In this paper we propose a Markovian process, the multidimensional kangaroo process, which permits the description of various algebraically correlated stochastic processes.
The Effect of Learning Environments Based on Problem Solving on Students' Achievements of Problem Solving
ERIC Educational Resources Information Center
Karatas, Ilhan; Baki, Adnan
Problem solving is recognized as an important life skill involving a range of processes including analyzing, interpreting, reasoning, predicting, evaluating and reflecting. For that reason educating students as efficient problem solvers is an important role of mathematics education. Problem solving skill is the centre of mathematics curriculum.…
Encouraging Sixth-Grade Students' Problem-Solving Performance by Teaching through Problem Solving
ERIC Educational Resources Information Center
Bostic, Jonathan D.; Pape, Stephen J.; Jacobbe, Tim
This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students' problem-solving…
Students' Errors in Solving the Permutation and Combination Problems Based on Problem Solving Steps of Polya
ERIC Educational Resources Information Center
Sukoriyanto; Nusantara, Toto; Subanji; Chandra, Tjang Daniel
This article was written based on the results of a study evaluating students' errors in problem solving of permutation and combination in terms of problem solving steps according to Polya. Twenty-five students were asked to do four problems related to permutation and combination. The research results showed that the students still did a mistake in…
Enhancing chemistry problem-solving achievement using problem categorization
NASA Astrophysics Data System (ADS)
Bunce, Diane M.; Gabel, Dorothy L.; Samuel, John V.
The enhancement of chemistry students' skill in problem solving through problem categorization is the focus of this study. Twenty-four students in a freshman chemistry course for health professionals are taught how to solve problems using the explicit method of problem solving (EMPS) (Bunce & Heikkinen, 1986). The EMPS is an organized approach to problem analysis which includes encoding the information given in a problem (Given, Asked For), relating this to what is already in long-term memory (Recall), and planning a solution (Overall Plan) before a mathematical solution is attempted. In addition to the EMPS training, treatment students receive three 40-minute sessions following achievement tests in which they are taught how to categorize problems. Control students use this time to review the EMPS solutions of test questions. Although problem categorization is involved in one section of the EMPS (Recall), treatment students who received specific training in problem categorization demonstrate significantly higher achievement on combination problems (those problems requiring the use of more than one chemical topic for their solution) at (p = 0.01) than their counterparts. Significantly higher achievement for treatment students is also measured on an unannounced test (p = 0.02). Analysis of interview transcripts of both treatment and control students illustrates a Rolodex approach to problem solving employed by all students in this study. The Rolodex approach involves organizing equations used to solve problems on mental index cards and flipping through them, matching units given when a new problem is to be solved. A second phenomenon observed during student interviews is the absence of a link in the conceptual understanding of the chemical concepts involved in a problem and the problem-solving skills employed to correctly solve problems. This study shows that explicit training in categorization skills and the EMPS can lead to higher achievement in complex problem-solving
Why students still can't solve physics problems after solving over 2000 problems
NASA Astrophysics Data System (ADS)
Byun, Taejin; Lee, Gyoungho
This study investigates the belief that solving a large number of physics problems helps students better learn physics. We investigated the number of problems solved, student confidence in solving these problems, academic achievement, and the level of conceptual understanding of 49 science high school students enrolled in upper-level physics classes from Spring 2010 to Summer 2011. The participants solved an average of 2200 physics problems before entering high school. Despite having solved so many problems, no statistically significant correlation was found between the number of problems solved and academic achievement on either a mid-term or physics competition examination. In addition, no significant correlation was found between the number of physics problems solved and performance on the Force Concept Inventory (FCI). Lastly, four students were selected from the 49 participants with varying levels of experience and FCI scores for a case study. We determined that their problem solving and learning strategies was more influential in their success than the number of problems they had solved.
AI tools in computer based problem solving
NASA Technical Reports Server (NTRS)
Beane, Arthur J.
The use of computers to solve value oriented, deterministic, algorithmic problems, has evolved a structured life cycle model of the software process. The symbolic processing techniques used, primarily in research, for solving nondeterministic problems, and those for which an algorithmic solution is unknown, have evolved a different model, much less structured. Traditionally, the two approaches have been used completely independently. With the advent of low cost, high performance 32 bit workstations executing identical software with large minicomputers and mainframes, it became possible to begin to merge both models into a single extended model of computer problem solving. The implementation of such an extended model on a VAX family of micro/mini/mainframe systems is described. Examples in both development and deployment of applications involving a blending of AI and traditional techniques are given.
Cognitive Load in Algebra: Element Interactivity in Solving Equations
ERIC Educational Resources Information Center
Ngu, Bing Hiong; Chung, Siu Fung; Yeung, Alexander Seeshing
Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side…
Problem solving in a distributed environment
NASA Technical Reports Server (NTRS)
Rashid, R. F.
Distributed problem solving is anayzed as a blend of two disciplines: (1) problem solving and ai; and (2) distributed systems (monitoring). It may be necessary to distribute because the application itself is one of managing distributed resources (e.g., distributed sensor net) and communication delays preclude centralized processing, or it may be desirable to distribute because a single computational engine may not satisfy the needs of a given task. In addition, considerations of reliability may dictate distribution. Examples of multi-process language environment are given.
Problem solving with genetic algorithms and Splicer
NASA Technical Reports Server (NTRS)
Bayer, Steven E.; Wang, Lui
Genetic algorithms are highly parallel, adaptive search procedures (i.e., problem-solving methods) loosely based on the processes of population genetics and Darwinian survival of the fittest. Genetic algorithms have proven useful in domains where other optimization techniques perform poorly. The main purpose of the paper is to discuss a NASA-sponsored software development project to develop a general-purpose tool for using genetic algorithms. The tool, called Splicer, can be used to solve a wide variety of optimization problems and is currently available from NASA and COSMIC. This discussion is preceded by an introduction to basic genetic algorithm concepts and a discussion of genetic algorithm applications.
Insightful problem solving in an Asian elephant.
Foerder, Preston; Galloway, Marie; Barthel, Tony; Moore, Donald E; Reiss, Diana
The "aha" moment or the sudden arrival of the solution to a problem is a common human experience. Spontaneous problem solving without evident trial and error behavior in humans and other animals has been referred to as insight. Surprisingly, elephants, thought to be highly intelligent, have failed to exhibit insightful problem solving in previous cognitive studies. We tested whether three Asian elephants (Elephas maximus) would use sticks or other objects to obtain food items placed out-of-reach and overhead. Without prior trial and error behavior, a 7-year-old male Asian elephant showed spontaneous problem solving by moving a large plastic cube, on which he then stood, to acquire the food. In further testing he showed behavioral flexibility, using this technique to reach other items and retrieving the cube from various locations to use as a tool to acquire food. In the cube's absence, he generalized this tool utilization technique to other objects and, when given smaller objects, stacked them in an attempt to reach the food. The elephant's overall behavior was consistent with the definition of insightful problem solving. Previous failures to demonstrate this ability in elephants may have resulted not from a lack of cognitive ability but from the presentation of tasks requiring trunk-held sticks as potential tools, thereby interfering with the trunk's use as a sensory organ to locate the targeted food. PMID:21876741
Solving the Unknown with Algebra: Poster/Teaching Guide for Pre-Algebra Students. Expect the Unexpected with Math[R
ERIC Educational Resources Information Center
Actuarial Foundation, 2013
"Solving the Unknown with Algebra" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) standards and designed to help students practice pre-algebra skills including using formulas, solving for unknowns, and manipulating equations. Developed by The Actuarial Foundation with Scholastic, this program provides…
Solving multiconstraint assignment problems using learning automata.
Horn, Geir; Oommen, B John
This paper considers the NP-hard problem of object assignment with respect to multiple constraints: assigning a set of elements (or objects) into mutually exclusive classes (or groups), where the elements which are "similar" to each other are hopefully located in the same class. The literature reports solutions in which the similarity constraint consists of a single index that is inappropriate for the type of multiconstraint problems considered here and where the constraints could simultaneously be contradictory. This feature, where we permit possibly contradictory constraints, distinguishes this paper from the state of the art. Indeed, we are aware of no learning automata (or other heuristic) solutions which solve this problem in its most general setting. Such a scenario is illustrated with the static mapping problem, which consists of distributing the processes of a parallel application onto a set of computing nodes. This is a classical and yet very important problem within the areas of parallel computing, grid computing, and cloud computing. We have developed four learning-automata (LA)-based algorithms to solve this problem: First, a fixed-structure stochastic automata algorithm is presented, where the processes try to form pairs to go onto the same node. This algorithm solves the problem, although it requires some centralized coordination. As it is desirable to avoid centralized control, we subsequently present three different variable-structure stochastic automata (VSSA) algorithms, which have superior partitioning properties in certain settings, although they forfeit some of the scalability features of the fixed-structure algorithm. All three VSSA algorithms model the processes as automata having first the hosting nodes as possible actions; second, the processes as possible actions; and, third, attempting to estimate the process communication digraph prior to probabilistically mapping the processes. This paper, which, we believe, comprehensively reports the
Analytical derivation: An epistemic game for solving mathematically based physics problems
NASA Astrophysics Data System (ADS)
Bajracharya, Rabindra R.; Thompson, John R.
Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.
Solving the hard problem of Bertrand's paradox
Aerts, Diederik; Sassoli de Bianchi, Massimiliano
Bertrand's paradox is a famous problem of probability theory, pointing to a possible inconsistency in Laplace's principle of insufficient reason. In this article, we show that Bertrand's paradox contains two different problems: an "easy" problem and a "hard" problem. The easy problem can be solved by formulating Bertrand's question in sufficiently precise terms, so allowing for a non-ambiguous modelization of the entity subjected to the randomization. We then show that once the easy problem is settled, also the hard problem becomes solvable, provided Laplace's principle of insufficient reason is applied not to the outcomes of the experiment, but to the different possible "ways of selecting" an interaction between the entity under investigation and that producing the randomization. This consists in evaluating a huge average over all possible "ways of selecting" an interaction, which we call a universal average. Following a strategy similar to that used in the definition of the Wiener measure, we calculate such universal average and therefore solve the hard problem of Bertrand's paradox. The link between Bertrand's problem of probability theory and the measurement problem of quantum mechanics is also briefly discussed.
The development and nature of problem-solving among first-semester calculus students
NASA Astrophysics Data System (ADS)
Dawkins, Paul Christian; Mendoza Epperson, James A.
This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem-solving
Computer Enhanced Problem Solving Skill Acquisition.
ERIC Educational Resources Information Center
Slotnick, Robert S.
Discusses the implementation of interactive educational software that was designed to enhance critical thinking, scientific reasoning, and problem solving in a university psychology course. Piagetian and computer learning perspectives are explained; the courseware package, PsychWare, is described; and the use of heuristics and algorithms in…
ADHD and Problem-Solving in Play
ERIC Educational Resources Information Center
Borg, Suzanne
This paper reports a small-scale study to determine whether there is a difference in problem-solving abilities, from a play perspective, between individuals who are diagnosed as ADHD and are on medication and those not on medication. Ten children, five of whom where on medication and five not, diagnosed as ADHD predominantly inattentive type, were…
Correlates of Problem-Solving Flexibility.
ERIC Educational Resources Information Center
Greenberger, Ellen; And Others
Problem solving flexibility (PSF), an ability commonly assessed in creativity batteries, was studied in a sample of middle class children (grades 1 through 3, average IQ 114), tested on questions resembling Guilford's consequences procedure. An hypothesis linking PSF with alertness to and interest in the environment was generally supported, more…
Problem-Solving Skills for Office Supervisors.
ERIC Educational Resources Information Center
Hathaway, Sandy
This package contains a selection of exercises designed to facilitate learning of problem-solving/communication skills within the area of office supervision. It does not provide the learning material or lesson plans. Section 1 is an overview that explains the scope of the material, learning methods, use of the teaching package, teaching resources,…
Complex Problem Solving--More than Reasoning?
ERIC Educational Resources Information Center
Wustenberg, Sascha; Greiff, Samuel; Funke, Joachim
This study investigates the internal structure and construct validity of Complex Problem Solving (CPS), which is measured by a "Multiple-Item-Approach." It is tested, if (a) three facets of CPS--"rule identification" (adequateness of strategies), "rule knowledge" (generated knowledge) and "rule application" (ability to control a system)--can be…
Option X, Level B Problem Solving.
ERIC Educational Resources Information Center
Hawaii State Dept. of Education, Honolulu. Office of Instructional Services.
This guide outlines an Option X course on problem solving techniques. The 16 learner objectives identified in the Mathematics Program Guide stress applications orientation to concepts about numbers and operations and common plane and solid figures. Techniques covered include working with diagrams, organizing information, using patterns,…
Design and Problem Solving in Technology Education.
ERIC Educational Resources Information Center
Custer, Rodney L.
Collectively, technological literacy embraces everything from intelligent consumerism to concerns about environmental degradation, ethics, and elitism. Technological problem solving can have social, ecological, or technological goals and may be categorized by four types: invention, design, trouble shooting, and procedures. Every citizen should be…
Taylor series to solve friction problems
NASA Astrophysics Data System (ADS)
Béchet, Fabien; Lejeune, Arnaud; Potier-Ferry, Michel
Thin metallic sheet transportation appears in numerous manufacturing processes such as continuous annealing, levelling or galvanization. It involves various nonlinear phenomena and, in particular, contact with friction. We develop a numerical method to solve this kind of mechanical problem, using shell finite elements and the Asymptotic Numerical Method (ANM). This article focuses on the treatment of the friction equations with ANM.
Assessing Mathematical Problem Solving Using Comparative Judgement
ERIC Educational Resources Information Center
Jones, Ian; Swan, Malcolm; Pollitt, Alastair
There is an increasing demand from employers and universities for school leavers to be able to apply their mathematical knowledge to problem solving in varied and unfamiliar contexts. These aspects are however neglected in most examinations of mathematics and, consequentially, in classroom teaching. One barrier to the inclusion of mathematical…
Making Problem-Solving Simulations More Realistic.
ERIC Educational Resources Information Center
Cotton, Samuel E.
Many problem-solving activities include mathematical principles but students do not use them during the design and experimentation phases before creating a prototype or product. Restricting the amount and/or type of materials available to students will require them to calculate and requisition the materials needed. (JOW)
Models of Strategy for Solving Physics Problems.
ERIC Educational Resources Information Center
Larkin, Jill H.
A set of computer implemented models are presented which can assist in developing problem solving strategies. The three levels of expertise which are covered are beginners (those who have completed at least one university physics course), intermediates (university level physics majors in their third year of study), and professionals (university…
Is Problem Solving Dependent on Language?
ERIC Educational Resources Information Center
Baldo, J.V.; Dronkers, N.F.; Wilkins, D.; Ludy, C.; Raskin, P.; Kim, J.
There has been a long-standing debate in the fields of philosophy and cognitive science surrounding the relationship of language to cognition, but the exact nature of this relationship is still unclear (Sokolov, 1968/1972). In the current study, we explored the role of language in one aspect of cognition, namely problem solving, by administering…
Teaching, Learning and Assessing Statistical Problem Solving
ERIC Educational Resources Information Center
Marriott, John; Davies, Neville; Gibson, Liz
In this paper we report the results from a major UK government-funded project, started in 2005, to review statistics and handling data within the school mathematics curriculum for students up to age 16. As a result of a survey of teachers we developed new teaching materials that explicitly use a problem-solving approach for the teaching and…
Structural and Linguistic Variables in Problem Solving.
ERIC Educational Resources Information Center
Jerman, Max; Mirman, Sanford
This paper reports on an experiment designed to investigate the effect of structural and linguistic variables on level of difficulty in solving arithmetic word problems. Identification of such variables is intended to assist curriculum writers in preparing exercises at a specified level of difficulty for students at various age levels. The study…
Collaborative Problem Solving Methods towards Critical Thinking
ERIC Educational Resources Information Center
Yin, Khoo Yin; Abdullah, Abdul Ghani Kanesan; Alazidiyeen, Naser Jamil
This research attempts to examine the collaborative problem solving methods towards critical thinking based on economy (AE) and non economy (TE) in the SPM level among students in the lower sixth form. The quasi experiment method that uses the modal of 3X2 factorial is applied. 294 lower sixth form students from ten schools are distributed…
Effective Practices (Part 4): Problem Solving.
ERIC Educational Resources Information Center
Moursund, Dave
Discusses the use of computers to help with problem solving. Topics include information science, including effective procedure and procedural thinking; templates; artificially intelligent agents and expert systems; and applications in education, including the goal of computer literacy for all students, and integrated software packages such as…
Nanomedicine: Problem Solving to Treat Cancer
ERIC Educational Resources Information Center
Hemling, Melissa A.; Sammel, Lauren M.; Zenner, Greta; Payne, Amy C.; Crone, Wendy C.
Many traditional classroom science and technology activities often ask students to complete prepackaged labs that ensure that everyone arrives at the same "scientifically accurate" solution or theory, which ignores the important problem-solving and creative aspects of scientific research and technological design. Students rarely have the…
Partial Metacognitive Blindness in Collaborative Problem Solving
ERIC Educational Resources Information Center
Ng, Kit Ee Dawn
This paper investigates the impact of group dynamics on metacognitive behaviours of students (aged 13-14) during group collaborative problem solving attempts involving a design-based real-world applications project. It was discovered that group dynamics mediated the impact of metacognitive judgments related red flag situations and metacognitive…
Solving Wicked Problems through Action Learning
ERIC Educational Resources Information Center
Crul, Liselore
This account of practice outlines the Oxyme Action Learning Program which was conducted as part of the Management Challenge in my final year of the MSc in Coaching and Behavioral Change at Henley Business School. The central research questions were: (1) how action learning can help to solve wicked problems and (2) what the effect of an action…
Problem-solving for better health.
Smith, B; Barnett, S; Collado, D; Connor, M; DePasquale, J; Gross, L; McDermott, V; Sykes, A
An outline is given of an approach to the health-for-all goals which involves optimizing resource use, prioritizing people's well-being, achieving excellence and a measurable impact at all levels of care, and solving health problems in a broad developmental context. PMID:8141991
How Instructional Designers Solve Workplace Problems
ERIC Educational Resources Information Center
Fortney, Kathleen S.; Yamagata-Lynch, Lisa C.
This naturalistic inquiry investigated how instructional designers engage in complex and ambiguous problem solving across organizational boundaries in two corporations. Participants represented a range of instructional design experience, from novices to experts. Research methods included a participant background survey, observations of…
Problem Solving. Workplace Education Program Curriculum.
ERIC Educational Resources Information Center
Burkhart, Jennifer
The BUILD Program (Businesses United to Increase Literacy Development) was conducted from June 1991 through December 1992 as a cooperative workplace literacy program joining Arapahoe Community College and four companies in Littleton, Colorado. This document consists of three modules for the problem-solving and computer learning systems classes of…
Student Problem Solving in High School Genetics.
ERIC Educational Resources Information Center
Stewart, James
Describes set of specific steps (procedural knowledge) used when solving monohybrid/dihybrid cross problems and extent to which students could justify execution of each step in terms of their conceptual knowledge of genetics and meiosis. Implications for genetics instruction are discussed. (JN)
Facilitating problem solving in high school chemistry
NASA Astrophysics Data System (ADS)
Gabel, Dorothy L.; Sherwood, Robert D.
The major purpose for conducting this study was to determine whether certain instructional strategies were superior to others in teaching high school chemistry students problem solving. The effectiveness of four instructional strategies for teaching problem solving to students of various proportional reasoning ability, verbal and visual preference, and mathematics anxiety were compared in this aptitude by treatment interaction study. The strategies used were the factor-label method, analogies, diagrams, and proportionality. Six hundred and nine high school students in eight schools were randomly assigned to one of four teaching strategies within each classroom. Students used programmed booklets to study the mole concept, the gas laws, stoichiometry, and molarity. Problem-solving ability was measured by a series of immediate posttests, delayed posttests and the ACS-NSTA Examination in High School Chemistry. Results showed that mathematics anxiety is negatively correlated with science achievement and that problem solving is dependent on students' proportional reasoning ability. The factor-label method was found to be the most desirable method and proportionality the least desirable method for teaching the mole concept. However, the proportionality method was best for teaching the gas laws. Several second-order interactions were found to be significant when mathematics anxiety was one of the aptitudes involved.
Raise the Bar on Problem Solving
ERIC Educational Resources Information Center
Englard, Lisa
In a 1981 diagnostic test, the Ministry of Education in Singapore found its country facing a challenge: Only 46 percent of students in grades 2-4 could solve word problems that were presented without such key words as "altogether" or "left." Yet today, according to results from the Trends in International Mathematics and Science Study (TIMSS…
Informal Evaluation Strategies for Real Problem Solving
ERIC Educational Resources Information Center
Ellis, Arthur K.; Alleman-Brooks, Janet
Examples of possible methods for unobtrusively evaluating student progress through real problem solving outcomes without formal testing are illustrated. These methods include the use of interviews, artifacts, observations, I learned statements, checklists, flow of discussion charts, and self-awareness exercises. (MN)
Mental Imagery in Creative Problem Solving.
ERIC Educational Resources Information Center
Polland, Mark J.
In order to investigate the relationship between mental imagery and creative problem solving, a study of 44 separate accounts reporting mental imagery experiences associated with creative discoveries were examined. The data included 29 different scientists, among them Albert Einstein and Stephen Hawking, and 9 artists, musicians, and writers,…
Problem Solving and Behavior Therapy Revisited
ERIC Educational Resources Information Center
Nezu, Arthur M.
Over three decades ago, D'Zurilla and Goldfried (1971) published a seminal article delineating a model of problem-solving training geared to enhance social competence and decrease psychological distress. Since that time, a substantial amount of research has been conducted to test various hypotheses that this model has engendered. Much of this…
Should Children Learn to Solve Problems?
ERIC Educational Resources Information Center
Watras, Joseph
In this comparative essay, the author discusses the opposing educational theories of John Dewey and Gregory Bateson. While Dewey believed that the scientific method was the dominant method of solving problems and thereby acquiring knowledge that mattered, Bateson warned that this one-sided approach would lead to actions that could destroy the…
Problem-Solving Test: Tryptophan Operon Mutants
ERIC Educational Resources Information Center
Szeberenyi, Jozsef
This paper presents a problem-solving test that deals with the regulation of the "trp" operon of "Escherichia coli." Two mutants of this operon are described: in mutant A, the operator region of the operon carries a point mutation so that it is unable to carry out its function; mutant B expresses a "trp" repressor protein unable to bind…
Instruction Emphasizing Effort Improves Physics Problem Solving
ERIC Educational Resources Information Center
Li, Daoquan
Effectively using strategies to solve complex problems is an important educational goal and is implicated in successful academic performance. However, people often do not spontaneously use the effective strategies unless they are motivated to do so. The present study was designed to test whether educating students about the importance of effort in…
ERIC Educational Resources Information Center
ARPACK: Solving large scale eigenvalue problems
NASA Astrophysics Data System (ADS)
Lehoucq, Rich; Maschhoff, Kristi; Sorensen, Danny; Yang, Chao
ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems. The package is designed to compute a few eigenvalues and corresponding eigenvectors of a general n by n matrix A. It is most appropriate for large sparse or structured matrices A where structured means that a matrix-vector product w
Problem-Solving Models for Computer Literacy: Getting Smarter at Solving Problems. Student Lessons.
ERIC Educational Resources Information Center
Moursund, David
This book is intended for use as a student guide. It is about human problem solving and provides information on how the mind works, placing a major emphasis on the role of computers as an aid in problem solving. The book is written with the underlying philosophy of discovery-based learning based on two premises: first, through the appropriate…
Understanding Individual Problem-Solving Style: A Key to Learning and Applying Creative Problem Solving
ERIC Educational Resources Information Center
Treffinger, Donald J.; Selby, Edwin C.; Isaksen, Scott G.
More than five decades of research and development have focused on making the Creative Problem Solving process and tools accessible across a wide range of ages and contexts. Recent evidence indicates that when individuals, in both school and corporate settings, understand their own style of problem solving, they are able to learn and apply process…
Assessing Affect after Mathematical Problem Solving Tasks: Validating the Chamberlin Affective Instrument for Mathematical Problem Solving
ERIC Educational Resources Information Center
Chamberlin, Scott A.; Powers, Robert A.
The focus of the article is the validation of an instrument to assess gifted students' affect after mathematical problem solving tasks. Participants were 225 students identified by their district as gifted in grades four to six. The Chamberlin Affective Instrument for Mathematical Problem Solving was used to assess feelings, emotions, and…
Preschoolers' Cooperative Problem Solving: Integrating Play and Problem Solving
ERIC Educational Resources Information Center
Ramani, Geetha B.; Brownell, Celia A.
Cooperative problem solving with peers plays a central role in promoting children's cognitive and social development. This article reviews research on cooperative problem solving among preschool-age children in experimental settings and social play contexts. Studies suggest that cooperative interactions with peers in experimental settings are…
Problem-Framing: A perspective on environmental problem-solving
NASA Astrophysics Data System (ADS)
Bardwell, Lisa V.
The specter of environmental calamity calls for the best efforts of an involved public. Ironically, the way people understand the issues all too often serves to discourage and frustrate rather than motivate them to action. This article draws from problem-solving perspectives offered by cognitive psychology and conflict management to examine a framework for thinking about environmental problems that promises to help rather than hinder efforts to address them. Problem-framing emphasizes focusing on the problem definition. Since how one defines a problem determines one's understanding of and approach to that problem, being able to redefine or reframe a problem and to explore the "problem space" can help broaden the range of alternatives and solutions examined. Problem-framing incorporates a cognitive perspective on how people respond to information. It explains why an emphasis on problem definition is not part of people's typical approach to problems. It recognizes the importance of structure and of having ways to organize that information on one's problem-solving effort. Finally, problem-framing draws on both cognitive psychology and conflict management for strategies to manage information and to create a problem-solving environment that not only encourages participation but can yield better approaches to our environmental problems.
Problem solving stages in the five square problem.
Fedor, Anna; Szathmáry, Eörs; Öllinger, Michael
According to the restructuring hypothesis, insight problem solving typically progresses through consecutive stages of search, impasse, insight, and search again for someone, who solves the task. The order of these stages was determined through self-reports of problem solvers and has never been verified behaviorally. We asked whether individual analysis of problem solving attempts of participants revealed the same order of problem solving stages as defined by the theory and whether their subjective feelings corresponded to the problem solving stages they were in. Our participants tried to solve the Five-Square problem in an online task, while we recorded the time and trajectory of their stick movements. After the task they were asked about their feelings related to insight and some of them also had the possibility of reporting impasse while working on the task. We found that the majority of participants did not follow the classic four-stage model of insight, but had more complex sequences of problem solving stages, with search and impasse recurring several times. This means that the classic four-stage model is not sufficient to describe variability on the individual level. We revised the classic model and we provide a new model that can generate all sequences found. Solvers reported insight more often than non-solvers and non-solvers reported impasse more often than solvers, as expected; but participants did not report impasse more often during behaviorally defined impasse stages than during other stages. This shows that impasse reports might be unreliable indicators of impasse. Our study highlights the importance of individual analysis of problem solving behavior to verify insight theory. PMID:26300794
Problem solving stages in the five square problem
Fedor, Anna; Szathmáry, Eörs; Öllinger, Michael
According to the restructuring hypothesis, insight problem solving typically progresses through consecutive stages of search, impasse, insight, and search again for someone, who solves the task. The order of these stages was determined through self-reports of problem solvers and has never been verified behaviorally. We asked whether individual analysis of problem solving attempts of participants revealed the same order of problem solving stages as defined by the theory and whether their subjective feelings corresponded to the problem solving stages they were in. Our participants tried to solve the Five-Square problem in an online task, while we recorded the time and trajectory of their stick movements. After the task they were asked about their feelings related to insight and some of them also had the possibility of reporting impasse while working on the task. We found that the majority of participants did not follow the classic four-stage model of insight, but had more complex sequences of problem solving stages, with search and impasse recurring several times. This means that the classic four-stage model is not sufficient to describe variability on the individual level. We revised the classic model and we provide a new model that can generate all sequences found. Solvers reported insight more often than non-solvers and non-solvers reported impasse more often than solvers, as expected; but participants did not report impasse more often during behaviorally defined impasse stages than during other stages. This shows that impasse reports might be unreliable indicators of impasse. Our study highlights the importance of individual analysis of problem solving behavior to verify insight theory. PMID:26300794
Optimal Planning and Problem-Solving
NASA Technical Reports Server (NTRS)
Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg
CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.
Solving Problems in Genetics II: Conceptual restructuring
NASA Astrophysics Data System (ADS)
Ibáñez Orcajo, Teresa; Martínez Aznar, Mercedes
This paper presents the results of part of an investigation carried out with fourth-level Spanish secondary education students (15 years old), in which we implemented a teaching unit based on problem-solving methodology as an investigation to teach genetics and human inheritance curricular contents. By solving open problems, the students experienced a conceptual restructuring that stayed with them over time and involved the following specific theories: the location of hereditary information, the transmission of hereditary information, and the appearance of new characteristic. The learning connections between these specific theories were also studied. Furthermore, these results were compared with a control group that worked with closed problems, the usual approach to genetics teaching in Spanish classrooms. Consequently, we were able to verify that our methodology results in better learning.
The Effects of Schema-Broadening Instruction on Second Graders' Word-Problem Performance and Their Ability to Represent Word Problems with Algebraic Equations: A Randomized Control Study
ERIC Educational Resources Information Center
Fuchs, Lynn S.; Zumeta, Rebecca O.; Schumacher, Robin Finelli; Powell, Sarah R.; Seethaler, Pamela M.; Hamlett, Carol L.; Fuchs, Douglas
The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders' word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which…
Solving combinatorial problems: the 15-puzzle.
Pizlo, Zygmunt; Li, Zheng
We present a series of experiments in which human subjects were tested with a well-known combinatorial problem called the 15-puzzle and in different-sized variants of this puzzle. Subjects can solve these puzzles reliably by systematically building a solution path, without performing much search and without using distances among the states of the problem. The computational complexity of the underlying mental mechanisms is very low. We formulated a computational model of the underlying cognitive processes on the basis of our results. This model applied a pyramid algorithm to individual stages of each problem. The model's performance proved to be quite similar to the subjects' performance. PMID:16496727
Colorado Assessment of Problem Solving (CAPS) -- Identifying student's problem solving skills
NASA Astrophysics Data System (ADS)
Adams, Wendy; Wieman, Carl
Problem solving is central to any physics curriculum and physics educators have put extensive effort into understanding successful problem solving; however, there is currently no efficient way to evaluate problem solving skill. Attempts have been made in the past; however, knowledge of the principles required to solve the subject problem are so absolutely critical that they completely overshadow any other skills students may use when solving a problem. The work presented here is unique because CAPS removes the requirement that the student already have a grasp of physics concepts. CAPS has been developed and validated at Colorado and measures a person's competence in 44 separate skills that are used when solving a wide range of in-depth problems including classical mechanics and quantum mechanics problems. Understanding the specific processes that impact how a person solves a problem identifies which components are specific to physics and those that transfer across discipline, and provides insight for improved methods for teaching. 1. Supported in part by funding from National Science Foundation
Geogebra for Solving Problems of Physics
NASA Astrophysics Data System (ADS)
Kllogjeri, Pellumb; Kllogjeri, Adrian
Today is highly speed progressing the computer-based education, which allowes educators and students to use educational programming language and e-tutors to teach and learn, to interact with one another and share together the results of their work. In this paper we will be concentrated on the use of GeoGebra programme for solving problems of physics. We have brought an example from physics of how can be used GeoGebra for finding the center of mass(centroid) of a picture(or system of polygons). After the problem is solved graphically, there is an application of finding the center of a real object(a plate)by firstly, scanning the object and secondly, by inserting its scanned picture into the drawing pad of GeoGebra window and lastly, by finding its centroid. GeoGebra serve as effective tool in problem-solving. There are many other applications of GeoGebra in the problems of physics, and many more in different fields of mathematics.
A connectionist model for diagnostic problem solving
NASA Technical Reports Server (NTRS)
Peng, Yun; Reggia, James A.
A competition-based connectionist model for solving diagnostic problems is described. The problems considered are computationally difficult in that (1) multiple disorders may occur simultaneously and (2) a global optimum in the space exponential to the total number of possible disorders is sought as a solution. The diagnostic problem is treated as a nonlinear optimization problem, and global optimization criteria are decomposed into local criteria governing node activation updating in the connectionist model. Nodes representing disorders compete with each other to account for each individual manifestation, yet complement each other to account for all manifestations through parallel node interactions. When equilibrium is reached, the network settles into a locally optimal state. Three randomly generated examples of diagnostic problems, each of which has 1024 cases, were tested, and the decomposition plus competition plus resettling approach yielded very high accuracy.
Interactive Problem Solving Tutorials Through Visual Programming
NASA Astrophysics Data System (ADS)
Undreiu, Lucian; Schuster, David; Undreiu, Adriana
We have used LabVIEW visual programming to build an interactive tutorial to promote conceptual understanding in physics problem solving. This programming environment is able to offer a web-accessible problem solving experience that enables students to work at their own pace and receive feedback. Intuitive graphical symbols, modular structures and the ability to create templates are just a few of the advantages this software has to offer. The architecture of an application can be designed in a way that allows instructors with little knowledge of LabVIEW to easily personalize it. Both the physics solution and the interactive pedagogy can be visually programmed in LabVIEW. Our physics pedagogy approach is that of cognitive apprenticeship, in that the tutorial guides students to develop conceptual understanding and physical insight into phenomena, rather than purely formula-based solutions. We demonstrate how this model is reflected in the design and programming of the interactive tutorials.
Expert Mining for Solving Social Harmony Problems
NASA Astrophysics Data System (ADS)
Gu, Jifa; Song, Wuqi; Zhu, Zhengxiang; Liu, Yijun
Social harmony problems are being existed in social system, which is an open giant complex system. For solving such kind of problems the Meta-synthesis system approach proposed by Qian XS et al will be applied. In this approach the data, information, knowledge, model, experience and wisdom should be integrated and synthesized. Data mining, text mining and web mining are good techniques for using data, information and knowledge. Model mining, psychology mining and expert mining are new techniques for mining the idea, opinions, experiences and wisdom. In this paper we will introduce the expert mining, which is based on mining the experiences, knowledge and wisdom directly from experts, managers and leaders.
Optimization neural network for solving flow problems.
Perfetti, R
This paper describes a neural network for solving flow problems, which are of interest in many areas of application as in fuel, hydro, and electric power scheduling. The neural network consist of two layers: a hidden layer and an output layer. The hidden units correspond to the nodes of the flow graph. The output units represent the branch variables. The network has a linear order of complexity, it is easily programmable, and it is suited for analog very large scale integration (VLSI) realization. The functionality of the proposed network is illustrated by a simulation example concerning the maximal flow problem. PMID:18263420
Comprehension and computation in Bayesian problem solving
Johnson, Eric D.; Tubau, Elisabet
Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian inferences relative to normalized formats (e.g., probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on "transparent" Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e., transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct vs. incorrect reasoners depart, and how individual differences might influence this time point. PMID:26283976
Exploiting Quantum Resonance to Solve Combinatorial Problems
NASA Technical Reports Server (NTRS)
Zak, Michail; Fijany, Amir
Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.
The Effect of a Problem-Solving Teaching Method on Student Problem-Solving Processes.
ERIC Educational Resources Information Center
Frank, David V.; Herron, J. Dudley
A problem-solving method of teaching was used in the recitation sections of a freshmen chemistry course for science and engineering majors at Purdue University. The method was based on prior research which revealed that good problem solvers formed better representations and used heuristics more often than poor problem solvers. Consequently, the…
An efficient algorithm for the contig ordering problem under algebraic rearrangement distance.
Lu, Chin Lung
Assembling a genome from short reads currently obtained by next-generation sequencing techniques often results in a collection of contigs, whose relative position and orientation along the genome being sequenced are unknown. Given two sets of contigs, the contig ordering problem is to order and orient the contigs in each set such that the genome rearrangement distance between the resulting sets of ordered and oriented contigs is minimized. In this article, we utilize the permutation groups in algebra to propose a near-linear time algorithm for solving the contig ordering problem under algebraic rearrangement distance, where the algebraic rearrangement distance between two sets of ordered and oriented contigs is the minimum weight of applicable rearrangement operations required to transform one set into the other. PMID:26247343
Inverse Modelling Problems in Linear Algebra Undergraduate Courses
ERIC Educational Resources Information Center
Martinez-Luaces, Victor E.
This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…
An efficient algorithm for solving the gravity problem of finding a density in a horizontal layer
NASA Astrophysics Data System (ADS)
Akimova, Elena N.; Martyshko, Peter S.; Misilov, Vladimir E.; Kosivets, Rostislav A.
An efficient algorithm for solving the inverse gravity problem of finding a variable density in a horizontal layer using gravitational data is constructed. After the discretization and approximation, the problem reduces to solving a system of linear algebraic equations. The idea of this algorithm is based on exploiting the block-Toeplitz structure of coefficients matrix. Utilizing this algorithm drastically reduces the memory usage, as well as the computation time. The algorithm was parallelized and implemented using the Uran supercomputer. A model problem with synthetic gravitational data was solved.
Status Effects in Group Problem Solving: Group and Individual Level Analyses.
ERIC Educational Resources Information Center
Chiu, Ming Ming
Eighty ninth graders who solved an algebra problem in groups of four showed status effects at the individual level. The students had filled out preactivity questionnaires about mathematical status and social status and a postactivity leadership questionnaire. Hierarchical regressions and path analyses show that, at the group level, solution score…
Tracking Problem Solving by Multivariate Pattern Analysis and Hidden Markov Model Algorithms
ERIC Educational Resources Information Center
Anderson, John R.
Multivariate pattern analysis can be combined with Hidden Markov Model algorithms to track the second-by-second thinking as people solve complex problems. Two applications of this methodology are illustrated with a data set taken from children as they interacted with an intelligent tutoring system for algebra. The first "mind reading" application…
The Effect of General Versus Specific Heuristics in Mathematical Problem-Solving Tasks.
ERIC Educational Resources Information Center
Smith, James Philip
This study investigated differences in problem-solving performance following instruction varying in the type of heuristic advice given. The subjects, 176 college students with two years of high school mathematics experience, were provided programed instruction over a three-week period in three topic areas: finite geometry, Boolean algebra, and…
A Flipped Pedagogy for Expert Problem Solving
NASA Astrophysics Data System (ADS)
Pritchard, David
The internet provides free learning opportunities for declarative (Wikipedia, YouTube) and procedural (Kahn Academy, MOOCs) knowledge, challenging colleges to provide learning at a higher cognitive level. Our ``Modeling Applied to Problem Solving'' pedagogy for Newtonian Mechanics imparts strategic knowledge - how to systematically determine which concepts to apply and why. Declarative and procedural knowledge is learned online before class via an e-text, checkpoint questions, and homework on edX.org (see http://relate.mit.edu/physicscourse); it is organized into five Core Models. Instructors then coach students on simple ``touchstone problems'', novel exercises, and multi-concept problems - meanwhile exercising three of the four C's: communication, collaboration, critical thinking and problem solving. Students showed 1.2 standard deviations improvement on the MIT final exam after three weeks instruction, a significant positive shift in 7 of the 9 categories in the CLASS, and their grades improved by 0.5 standard deviation in their following physics course (Electricity and Magnetism).
Solving the Swath Segment Selection Problem
NASA Technical Reports Server (NTRS)
Knight, Russell; Smith, Benjamin
Several artificial-intelligence search techniques have been tested as means of solving the swath segment selection problem (SSSP) -- a real-world problem that is not only of interest in its own right, but is also useful as a test bed for search techniques in general. In simplest terms, the SSSP is the problem of scheduling the observation times of an airborne or spaceborne synthetic-aperture radar (SAR) system to effect the maximum coverage of a specified area (denoted the target), given a schedule of downlinks (opportunities for radio transmission of SAR scan data to a ground station), given the limit on the quantity of SAR scan data that can be stored in an onboard memory between downlink opportunities, and given the limit on the achievable downlink data rate. The SSSP is NP complete (short for "nondeterministic polynomial time complete" -- characteristic of a class of intractable problems that can be solved only by use of computers capable of making guesses and then checking the guesses in polynomial time).
Numerical Problem Solving Using Mathcad in Undergraduate Reaction Engineering
ERIC Educational Resources Information Center
Parulekar, Satish J.
Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…
Teaching Problem Solving Skills to Elementary Age Students with Autism
ERIC Educational Resources Information Center
Cote, Debra L.; Jones, Vita L.; Barnett, Crystal; Pavelek, Karin; Nguyen, Hoang; Sparks, Shannon L.
Students with disabilities need problem-solving skills to promote their success in solving the problems of daily life. The research into problem-solving instruction has been limited for students with autism. Using a problem-solving intervention and the Self Determined Learning Model of Instruction, three elementary age students with autism were…
Young Children's Analogical Problem Solving: Gaining Insights from Video Displays
ERIC Educational Resources Information Center
Chen, Zhe; Siegler, Robert S.
This study examined how toddlers gain insights from source video displays and use the insights to solve analogous problems. Two- to 2.5-year-olds viewed a source video illustrating a problem-solving strategy and then attempted to solve analogous problems. Older but not younger toddlers extracted the problem-solving strategy depicted in the video…
Solving optimization problems on computational grids.
Wright, S. J.; Mathematics and Computer Science
Multiprocessor computing platforms, which have become more and more widely available since the mid-1980s, are now heavily used by organizations that need to solve very demanding computational problems. Parallel computing is now central to the culture of many research communities. Novel parallel approaches were developed for global optimization, network optimization, and direct-search methods for nonlinear optimization. Activity was particularly widespread in parallel branch-and-bound approaches for various problems in combinatorial and network optimization. As the cost of personal computers and low-end workstations has continued to fall, while the speed and capacity of processors and networks have increased dramatically, 'cluster' platforms have become popular in many settings. A somewhat different type of parallel computing platform know as a computational grid (alternatively, metacomputer) has arisen in comparatively recent times. Broadly speaking, this term refers not to a multiprocessor with identical processing nodes but rather to a heterogeneous collection of devices that are widely distributed, possibly around the globe. The advantage of such platforms is obvious: they have the potential to deliver enormous computing power. Just as obviously, however, the complexity of grids makes them very difficult to use. The Condor team, headed by Miron Livny at the University of Wisconsin, were among the pioneers in providing infrastructure for grid computations. More recently, the Globus project has developed technologies to support computations on geographically distributed platforms consisting of high-end computers, storage and visualization devices, and other scientific instruments. In 1997, we started the metaneos project as a collaborative effort between optimization specialists and the Condor and Globus groups. Our aim was to address complex, difficult optimization problems in several areas, designing and implementing the algorithms and the software
Can compactifications solve the cosmological constant problem?
NASA Astrophysics Data System (ADS)
Hertzberg, Mark P.; Masoumi, Ali
Recently, there have been claims in the literature that the cosmological constant problem can be dynamically solved by specific compactifications of gravity from higher-dimensional toy models. These models have the novel feature that in the four-dimensional theory, the cosmological constant Λ is much smaller than the Planck density and in fact accumulates at Λ = 0. Here we show that while these are very interesting models, they do not properly address the real cosmological constant problem. As we explain, the real problem is not simply to obtain Λ that is small in Planck units in a toy model, but to explain why Λ is much smaller than other mass scales (and combinations of scales) in the theory. Instead, in these toy models, all other particle mass scales have been either removed or sent to zero, thus ignoring the real problem. To this end, we provide a general argument that the included moduli masses are generically of order Hubble, so sending them to zero trivially sends the cosmological constant to zero. We also show that the fundamental Planck mass is being sent to zero, and so the central problem is trivially avoided by removing high energy physics altogether. On the other hand, by including various large mass scales from particle physics with a high fundamental Planck mass, one is faced with a real problem, whose only known solution involves accidental cancellations in a landscape.
The Problem of Assessing Problem Solving: Can Comparative Judgement Help?
ERIC Educational Resources Information Center
Jones, Ian; Inglis, Matthew
School mathematics examination papers are typically dominated by short, structured items that fail to assess sustained reasoning or problem solving. A contributory factor to this situation is the need for student work to be marked reliably by a large number of markers of varied experience and competence. We report a study that tested an…
A Process Analysis of Engineering Problem Solving and Assessment of Problem Solving Skills
ERIC Educational Resources Information Center
Grigg, Sarah J.
In the engineering profession, one of the most critical skills to possess is accurate and efficient problem solving. Thus, engineering educators should strive to help students develop skills needed to become competent problem solvers. In order to measure the development of skills, it is necessary to assess student performance, identify any…
"I'm Not Very Good at Solving Problems": An Exploration of Students' Problem Solving Behaviours
ERIC Educational Resources Information Center
Muir, Tracey; Beswick, Kim; Williamson, John
This paper reports one aspect of a larger study which looked at the strategies used by a selection of grade 6 students to solve six non-routine mathematical problems. The data revealed that the students exhibited many of the behaviours identified in the literature as being associated with novice and expert problem solvers. However, the categories…
Problem-Solving Appraisal and Human Adjustment: A Review of 20 Years of Research Using the Problem Solving Inventory
ERIC Educational Resources Information Center
Heppner, P. Paul; Witty, Thomas E.; Dixon, Wayne A.
This article reviews and synthesizes more than 120 studies from 20 years (1982-2002) of research that has examined problem-solving appraisal as measured by the Problem Solving Inventory (PSI). The goals of the article are fourfold: (a) introduce the construct of problem-solving appraisal and the PSI within the applied problem-solving literature,…
Scientific problem solving by expert systems
NASA Astrophysics Data System (ADS)
Good, Ron
Human expert problem solving in science is defined and used to account for scientific discovery. These ideas, attributed largely to Herbert Simon, are used in a description of BACON.5, a machine expert problem solver that discovers scientific laws using data-driven heuristics and expectations such as symmetry. Trial-and-error search of data-driven scientific discovery is drastically reduced when the BACON.5 system is altered to include expectations, such as symmetry, which have been influential in real (i.e., human) discoveries of scientific laws. A discussion of the implications of BACON.5-type research for traditional science education research recognizes the importance of a qualitative understanding of the relationships among pieces of a physical or biological system.
Solving large sparse eigenvalue problems on supercomputers
NASA Technical Reports Server (NTRS)
Philippe, Bernard; Saad, Youcef
An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations are also discussed.
Incubation and Intuition in Creative Problem Solving
Gilhooly, Kenneth J.
Creative problem solving, in which novel solutions are required, has often been seen as involving a special role for unconscious processes (Unconscious Work) which can lead to sudden intuitive solutions (insights) when a problem is set aside during incubation periods. This notion of Unconscious Work during incubation periods is supported by a review of experimental studies and particularly by studies using the Immediate Incubation paradigm. Other explanations for incubation effects, in terms of Intermittent Work or Beneficial Forgetting are considered. Some recent studies of divergent thinking, using the Alternative Uses task, carried out in my laboratory regarding Immediate vs. Delayed Incubation and the effects of resource competition from interpolated activities are discussed. These studies supported a role for Unconscious Work as against Intermittent Conscious work or Beneficial Forgetting in incubation. PMID:27499745
Incubation and Intuition in Creative Problem Solving.
Gilhooly, Kenneth J
Creative problem solving, in which novel solutions are required, has often been seen as involving a special role for unconscious processes (Unconscious Work) which can lead to sudden intuitive solutions (insights) when a problem is set aside during incubation periods. This notion of Unconscious Work during incubation periods is supported by a review of experimental studies and particularly by studies using the Immediate Incubation paradigm. Other explanations for incubation effects, in terms of Intermittent Work or Beneficial Forgetting are considered. Some recent studies of divergent thinking, using the Alternative Uses task, carried out in my laboratory regarding Immediate vs. Delayed Incubation and the effects of resource competition from interpolated activities are discussed. These studies supported a role for Unconscious Work as against Intermittent Conscious work or Beneficial Forgetting in incubation. PMID:27499745
Solving Math Problems Approximately: A Developmental Perspective
Ganor-Stern, Dana
Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults' ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner. PMID:27171224
Cooperative problem solving in rooks (Corvus frugilegus).
Seed, Amanda M; Clayton, Nicola S; Emery, Nathan J
Recent work has shown that captive rooks, like chimpanzees and other primates, develop cooperative alliances with their conspecifics. Furthermore, the pressures hypothesized to have favoured social intelligence in primates also apply to corvids. We tested cooperative problem-solving in rooks to compare their performance and cognition with primates. Without training, eight rooks quickly solved a problem in which two individuals had to pull both ends of a string simultaneously in order to pull in a food platform. Similar to chimpanzees and capuchin monkeys, performance was better when within-dyad tolerance levels were higher. In contrast to chimpanzees, rooks did not delay acting on the apparatus while their partner gained access to the test room. Furthermore, given a choice between an apparatus that could be operated individually over one that required the action of two individuals, four out of six individuals showed no preference. These results may indicate that cooperation in chimpanzees is underpinned by more complex cognitive processes than that in rooks. Such a difference may arise from the fact that while both chimpanzees and rooks form cooperative alliances, chimpanzees, but not rooks, live in a variable social network made up of competitive and cooperative relationships. PMID:18364318
Assessing Cognitive Learning of Analytical Problem Solving
NASA Astrophysics Data System (ADS)
Billionniere, Elodie V.
Introductory programming courses, also known as CS1, have a specific set of expected outcomes related to the learning of the most basic and essential computational concepts in computer science (CS). However, two of the most often heard complaints in such courses are that (1) they are divorced from the reality of application and (2) they make the learning of the basic concepts tedious. The concepts introduced in CS1 courses are highly abstract and not easily comprehensible. In general, the difficulty is intrinsic to the field of computing, often described as "too mathematical or too abstract." This dissertation presents a small-scale mixed method study conducted during the fall 2009 semester of CS1 courses at Arizona State University. This study explored and assessed students' comprehension of three core computational concepts---abstraction, arrays of objects, and inheritance---in both algorithm design and problem solving. Through this investigation students' profiles were categorized based on their scores and based on their mistakes categorized into instances of five computational thinking concepts: abstraction, algorithm, scalability, linguistics, and reasoning. It was shown that even though the notion of computational thinking is not explicit in the curriculum, participants possessed and/or developed this skill through the learning and application of the CS1 core concepts. Furthermore, problem-solving experiences had a direct impact on participants' knowledge skills, explanation skills, and confidence. Implications for teaching CS1 and for future research are also considered.
Functional reasoning in diagnostic problem solving
NASA Technical Reports Server (NTRS)
Sticklen, Jon; Bond, W. E.; Stclair, D. C.
This work is one facet of an integrated approach to diagnostic problem solving for aircraft and space systems currently under development. The authors are applying a method of modeling and reasoning about deep knowledge based on a functional viewpoint. The approach recognizes a level of device understanding which is intermediate between a compiled level of typical Expert Systems, and a deep level at which large-scale device behavior is derived from known properties of device structure and component behavior. At this intermediate functional level, a device is modeled in three steps. First, a component decomposition of the device is defined. Second, the functionality of each device/subdevice is abstractly identified. Third, the state sequences which implement each function are specified. Given a functional representation and a set of initial conditions, the functional reasoner acts as a consequence finder. The output of the consequence finder can be utilized in diagnostic problem solving. The paper also discussed ways in which this functional approach may find application in the aerospace field.
Problem Solving Interventions: Impact on Young Children with Developmental Disabilities
ERIC Educational Resources Information Center
Diamond, Lindsay Lile
Problem-solving skills are imperative to a child's growth and success across multiple environments, including general and special education. Problem solving is comprised of: (a) attention to the critical aspects of a problem, (b) generation of solution(s) to solve the problem, (c) application of a solution(s) to the identified problem, and…
Experimenting with Classroom Formats To Encourage Problem Solving.
ERIC Educational Resources Information Center
Fernandez, Eileen; Kazimir, Jessica; Vandemeulebroeke, Lynn; Burgos, Carlos
Describes how modifying familiar classroom formats in a college geometry class helped encourage student problem solving. Demonstrates these modified formats in the context of problems students explored, which resemble the problem-solving settings of mathematicians. (KHR)
Inference of S-system models of genetic networks by solving one-dimensional function optimization problems.
Kimura, S; Araki, D; Matsumura, K; Okada-Hatakeyama, M
Voit and Almeida have proposed the decoupling approach as a method for inferring the S-system models of genetic networks. The decoupling approach defines the inference of a genetic network as a problem requiring the solutions of sets of algebraic equations. The computation can be accomplished in a very short time, as the approach estimates S-system parameters without solving any of the differential equations. Yet the defined algebraic equations are non-linear, which sometimes prevents us from finding reasonable S-system parameters. In this study, we propose a new technique to overcome this drawback of the decoupling approach. This technique transforms the problem of solving each set of algebraic equations into a one-dimensional function optimization problem. The computation can still be accomplished in a relatively short time, as the problem is transformed by solving a linear programming problem. We confirm the effectiveness of the proposed approach through numerical experiments. PMID:22155075
Glycoprotein Structural Genomics: Solving the Glycosylation Problem
Chang, Veronica T.; Crispin, Max; Aricescu, A. Radu; Harvey, David J.; Nettleship, Joanne E.; Fennelly, Janet A.; Yu, Chao; Boles, Kent S.; Evans, Edward J.; Stuart, David I.; Dwek, Raymond A.; Jones, E. Yvonne; Owens, Raymond J.; Davis, Simon J.
Summary Glycoproteins present special problems for structural genomic analysis because they often require glycosylation in order to fold correctly, whereas their chemical and conformational heterogeneity generally inhibits crystallization. We show that the "glycosylation problem" can be solved by expressing glycoproteins transiently in mammalian cells in the presence of the N-glycosylation processing inhibitors, kifunensine or swainsonine. This allows the correct folding of the glycoproteins, but leaves them sensitive to enzymes, such as endoglycosidase H, that reduce the N-glycans to single residues, enhancing crystallization. Since the scalability of transient mammalian expression is now comparable to that of bacterial systems, this approach should relieve one of the major bottlenecks in structural genomic analysis. PMID:17355862
Optimized fourth-order Runge-Kutta method for solving oscillatory problems
NASA Astrophysics Data System (ADS)
Hussain, Kasim; Ismail, Fudziah; Senu, Norazak; Rabiei, Faranak
In this article, we develop a Runge-Kutta method with invalidation of phase lag, phase lag's derivatives and amplification error to solve second-order initial value problem (IVP) with oscillating solutions. The new method depends on the explicit Runge-Kutta method of algebraic order four. Numerical tests from its implementation to well-known oscillatory problems illustrate the robustness and competence of the new method as compared to the well-known Runge-Kutta methods in the scientific literature.
Problem Solving and Chemical Equilibrium: Successful versus Unsuccessful Performance.
ERIC Educational Resources Information Center
Camacho, Moises; Good, Ron
Describes the problem-solving behaviors of experts and novices engaged in solving seven chemical equilibrium problems. Lists 27 behavioral tendencies of successful and unsuccessful problem solvers. Discusses several implications for a problem solving theory, think-aloud techniques, adequacy of the chemistry domain, and chemistry instruction.…
The Impact of Student Thinking Journals and Generic Problem Solving Software on Problem Solving Performance.
ERIC Educational Resources Information Center
Sullivan, Gary E.
This study examined the effects of specially designed thinking journal activities that have been attributed with encouraging reflective thinking, on instruction using generic, or content-free, problem solving software. Sixty-three fourth grade students participated in four instructional sessions using the software package called "Moptown Hotel."…
Unsupervised neural networks for solving Troesch's problem
NASA Astrophysics Data System (ADS)
Muhammad, Asif Zahoor Raja
In this study, stochastic computational intelligence techniques are presented for the solution of Troesch's boundary value problem. The proposed stochastic solvers use the competency of a feed-forward artificial neural network for mathematical modeling of the problem in an unsupervised manner, whereas the learning of unknown parameters is made with local and global optimization methods as well as their combinations. Genetic algorithm (GA) and pattern search (PS) techniques are used as the global search methods and the interior point method (IPM) is used for an efficient local search. The combination of techniques like GA hybridized with IPM (GA-IPM) and PS hybridized with IPM (PS-IPM) are also applied to solve different forms of the equation. A comparison of the proposed results obtained from GA, PS, IPM, PS-IPM and GA-IPM has been made with the standard solutions including well known analytic techniques of the Adomian decomposition method, the variational iterational method and the homotopy perturbation method. The reliability and effectiveness of the proposed schemes, in term of accuracy and convergence, are evaluated from the results of statistical analysis based on sufficiently large independent runs.
Journey into Problem Solving: A Gift from Polya
ERIC Educational Resources Information Center
Lederman, Eric
In "How to Solve It", accomplished mathematician and skilled communicator George Polya describes a four-step universal solving technique designed to help students develop mathematical problem-solving skills. By providing a glimpse at the grace with which experts solve problems, Polya provides definable methods that are not exclusive to…
The Competent Use of the Analytic Method in the Solution of Algebraic Word Problems: A Didactical Model Based on a Numerical Approach with Junior High Students
ERIC Educational Resources Information Center
Rubio, Guillermo; del Valle, Rafael
The study proves that a didactical model based in a method to solve word problems of increasing complexity which uses a numerical approach was essential to develop the analytical ability and the competent use of the algebraic language with students from three different performance levels in elementary algebra. It is shown that before using the…
Academic Achievement, Situational Stress, and Problem-Solving Flexibility
ERIC Educational Resources Information Center
Rollins, Boyd C.; Calder, Colleen
Tested two hypotheses: (1) academic underachievers will have less problem solving flexibility during failure than during success; and (2) academic overachievers will have more problem solving flexibility during failure than during success. Subjects were tenth grade boys. (Author/SDH)
Is conceptual understanding compromised by a problem-solving emphasis in an introductory physics course?
NASA Astrophysics Data System (ADS)
Ridenour, J.; Feldman, G.; Teodorescu, R.; Medsker, L.; Benmouna, N.
Developing competency in problem solving and enhancing conceptual understanding are primary objectives in introductory physics, and many techniques and tools are available to help instructors achieve them. Pedagogically, we use an easy-to-implement intervention, the ACCESS protocol, to develop and assess problem-solving skills in our SCALE-UP classroom environment for algebra-based physics. Based on our research and teaching experience, an important question has emerged: while primarily targeting improvements in problem-solving and cognitive development, is it necessary that conceptual understanding be compromised? To address this question, we gathered and analyzed information about student abilities, backgrounds, and instructional preferences. We report on our progress and give insights into matching the instructional tools to student profiles in order to achieve optimal learning in group-based active learning. The ultimate goal of our work is to integrate individual student learning needs into a pedagogy that moves students closer to expert-like status in problem solving.
Effect of scaffolding on helping introductory physics students solve quantitative problems involving strong alternative conceptions
NASA Astrophysics Data System (ADS)
Lin, Shih-Yin; Singh, Chandralekha
It is well known that introductory physics students often have alternative conceptions that are inconsistent with established physical principles and concepts. Invoking alternative conceptions in the quantitative problem-solving process can derail the entire process. In order to help students solve quantitative problems involving strong alternative conceptions correctly, appropriate scaffolding support can be helpful. The goal of this study is to examine how different scaffolding supports involving analogical problem-solving influence introductory physics students' performance on a target quantitative problem in a situation where many students' solution process is derailed due to alternative conceptions. Three different scaffolding supports were designed and implemented in calculus-based and algebra-based introductory physics courses involving 410 students to evaluate the level of scaffolding needed to help students learn from an analogical problem that is similar in the underlying principles involved but for which the problem-solving process is not derailed by alternative conceptions. We found that for the quantitative problem involving strong alternative conceptions, simply guiding students to work through the solution of the analogical problem first was not enough to help most students discern the similarity between the two problems. However, if additional scaffolding supports that directly helped students examine and repair their knowledge elements involving alternative conceptions were provided, e.g., by guiding students to contemplate related issues and asking them to solve the targeted problem on their own first before learning from the analogical problem provided, students were more likely to discern the underlying similarities between the problems and avoid getting derailed by alternative conceptions when solving the targeted problem. We also found that some scaffolding supports were more effective in the calculus-based course than in the algebra
FOURTH SEMINAR TO THE MEMORY OF D.N. KLYSHKO: Algebraic solution of the synthesis problem for coded sequences
NASA Astrophysics Data System (ADS)
Leukhin, Anatolii N.
The algebraic solution of a 'complex' problem of synthesis of phase-coded (PC) sequences with the zero level of side lobes of the cyclic autocorrelation function (ACF) is proposed. It is shown that the solution of the synthesis problem is connected with the existence of difference sets for a given code dimension. The problem of estimating the number of possible code combinations for a given code dimension is solved. It is pointed out that the problem of synthesis of PC sequences is related to the fundamental problems of discrete mathematics and, first of all, to a number of combinatorial problems, which can be solved, as the number factorisation problem, by algebraic methods by using the theory of Galois fields and groups.
Problem Solving in the School Curriculum from a Design Perspective
ERIC Educational Resources Information Center
Toh, Tin Lam; Leong, Yew Hoong; Dindyal, Jaguthsing; Quek, Khiok Seng
In this symposium, the participants discuss some preliminary data collected from their problem solving project which uses a design experiment approach. Their approach to problem solving in the school curriculum is in tandem with what Schoenfeld (2007) claimed: "Crafting instruction that would make a wide range of problem-solving strategies…
Teacher Practices with Toddlers during Social Problem Solving Opportunities
ERIC Educational Resources Information Center
Gloeckler, Lissy; Cassell, Jennifer
This article explores how teachers can foster an environment that facilitates social problem solving when toddlers experience conflict, emotional dysregulation, and aggression. This article examines differences in child development and self-regulation outcomes when teachers engage in problem solving "for" toddlers and problem solving "with"…
Solving Complex Problems: A Convergent Approach to Cognitive Load Measurement
ERIC Educational Resources Information Center
Zheng, Robert; Cook, Anne
The study challenged the current practices in cognitive load measurement involving complex problem solving by manipulating the presence of pictures in multiple rule-based problem-solving situations and examining the cognitive load resulting from both off-line and online measures associated with complex problem solving. Forty-eight participants…
The Authentic Performance-Based Assessment of Problem Solving.
ERIC Educational Resources Information Center
Curtis, David; Denton, Rob
A new authentic performance-based approach to assessing problem solving was developed for use in vocational education and other programs in Australia. The process of developing the problem-solving assessment instrument and process included the following phases: (1) exploration of the theoretical conceptions of problem solving; (2) identification…
Conflict Management: A Premarital Training Program in Mutual Problem Solving.
ERIC Educational Resources Information Center
Ridley, Carl A.; And Others
Evaluated the effectiveness of a structured educational program to train premarital couples in communication and mutual problem-solving skills. Couples (N=26) participated in a problem-solving training program, while similar couples (N=28) participated in a relationship discussion group. The problem-solving group showed a greater increase in…
Surveying Graduate Students' Attitudes and Approaches to Problem Solving
ERIC Educational Resources Information Center
Mason, Andrew; Singh, Chandralekha
Students' attitudes and approaches to problem solving in physics can profoundly influence their motivation to learn and development of expertise. We developed and validated an Attitudes and Approaches to Problem Solving survey by expanding the Attitudes toward Problem Solving survey of Marx and Cummings and administered it to physics graduate…
Teaching Problem Solving in Secondary School Mathematics Classrooms
ERIC Educational Resources Information Center
Lam, Toh Tin; Guan, Tay Eng; Seng, Quek Khiok; Hoong, Leong Yew; Choon, Toh Pee; Him, Ho Foo; Jaguthsing, Dindyal
This paper reports an innovative approach to teaching problem solving in secondary school mathematics classrooms based on a specifically designed problem-solving module.This approach adopts the science practical paradigm and rides on the works of Polya and Schoenfeld in order to give greater emphasis to the problem solving processes. We report the…
The Influence of Cognitive Diversity on Group Problem Solving Strategy
ERIC Educational Resources Information Center
Lamm, Alexa J.; Shoulders, Catherine; Roberts, T. Grady; Irani, Tracy A.; Snyder, Lori J. Unruh; Brendemuhl, Joel
Collaborative group problem solving allows students to wrestle with different interpretations and solutions brought forth by group members, enhancing both critical thinking and problem solving skills. Since problem solving in groups is a common practice in agricultural education, instructors are often put in the position of organizing student…
Team-Based Complex Problem Solving: A Collective Cognition Perspective
ERIC Educational Resources Information Center
Hung, Woei
Today, much problem solving is performed by teams, rather than individuals. The complexity of these problems has exceeded the cognitive capacity of any individual and requires a team of members to solve them. The success of solving these complex problems not only relies on individual team members who possess different but complementary expertise,…
A TAPS Interactive Multimedia Package to Solve Engineering Dynamics Problem
ERIC Educational Resources Information Center
Sidhu, S. Manjit; Selvanathan, N.
Purpose: To expose engineering students to using modern technologies, such as multimedia packages, to learn, visualize and solve engineering problems, such as in mechanics dynamics. Design/methodology/approach: A multimedia problem-solving prototype package is developed to help students solve an engineering problem in a step-by-step approach. A…
Interpersonal and Emotional Problem Solving among Narcotic Drug Abusers.
ERIC Educational Resources Information Center
Appel, Philip W.; Kaestner, Elisabeth
Measured problem-solving abilities of narcotics abusers using the modified means-ends problem-solving procedure. Good subjects had more total relevent means (RMs) for solving problems, used more introspective and emotional RMs, and were better at RM recognition, but did not have more sufficient narratives than poor subjects. (Author/BEF)
Perceived Problem Solving, Stress, and Health among College Students
ERIC Educational Resources Information Center
Largo-Wight, Erin; Peterson, P. Michael; Chen, W. William
Objective: To study the relationships among perceived problem solving, stress, and physical health. Methods: The Perceived Stress Questionnaire (PSQ), Personal Problem solving Inventory (PSI), and a stress-related physical health symptoms checklist were used to measure perceived stress, problem solving, and health among undergraduate college…
Problem Solving Strategies for Pharmaceutical/Chemical Technology College Students.
ERIC Educational Resources Information Center
Grant, George F.; Alexander, William E.
Teaching problem solving strategies and steps to first year college students enrolled in the pharmaceutical/chemical technology program as a part of their first year chemistry course focused on teaching the students the basic steps in problem solving and encouraging them to plan carefully and focus on the problem solving process rather than to…
Uncertainty during the Early Stages of Problem Solving
ERIC Educational Resources Information Center
de Hoyos, Maria; Gray, Eddie; Simpson, Adrian
This paper discusses the role of uncertainty during the early stages of problem solving. It is argued that students start the problem solving activity with some degree of uncertainty that may vary from high to low. This degree of uncertainty may affect students' decisions at early stages of the problem solving process. It may be suggested that an…
Teaching Young Children Interpersonal Problem-Solving Skills
ERIC Educational Resources Information Center
Joseph, Gail E.; Strain, Phillip S.
Learning how to problem solve is one of the key developmental milestones in early childhood. Children's problem-solving skills represent a key feature in the development of social competence. Problem solving allows children to stay calm during difficult situations, repair social relations quickly, and get their needs met in ways that are safe and…
Development of a Content Coding System for Marital Problem Solving.
ERIC Educational Resources Information Center
Winemiller, David R.; Mitchell, M. Ellen
While much research has focused on the processes of marital problem solving, the content of marital problem solving has received considerably less attention. This study examined the initial efforts to develop a method for assessing marital problem solving content. Married individuals (N=36) completed a demographic information sheet, the Dyadic…
The Influence of Cognitive Abilities on Mathematical Problem Solving Performance
ERIC Educational Resources Information Center
Bahar, Abdulkadir
Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of students. The…
Internet Computer Coaches for Introductory Physics Problem Solving
ERIC Educational Resources Information Center
Xu Ryan, Qing
The ability to solve problems in a variety of contexts is becoming increasingly important in our rapidly changing technological society. Problem-solving is a complex process that is important for everyday life and crucial for learning physics. Although there is a great deal of effort to improve student problem solving skills throughout the…
Solving Word Problems Using Schemas: A Review of the Literature
ERIC Educational Resources Information Center
Powell, Sarah R.
Solving word problems is a difficult task for students at-risk for or with learning disabilities (LD). One instructional approach that has emerged as a valid method for helping students at-risk for or with LD to become more proficient at word-problem solving is using schemas. A schema is a framework for solving a problem. With a schema, students…
Capturing Problem-Solving Processes Using Critical Rationalism
ERIC Educational Resources Information Center
Chitpin, Stephanie; Simon, Marielle
The examination of problem-solving processes continues to be a current research topic in education. Knowing how to solve problems is not only a key aspect of learning mathematics but is also at the heart of cognitive theories, linguistics, artificial intelligence, and computers sciences. Problem solving is a multistep, higher-order cognitive task…
Using Analogy to Solve a Three-Step Physics Problem
NASA Astrophysics Data System (ADS)
Lin, Shih-Yin; Singh, Chandralekha
In a companion paper, we discuss students' ability to take advantage of what they learn from a solved problem and transfer their learning to solve a quiz problem that has different surface features but the same underlying physics principles. Here, we discuss students' ability to perform analogical reasoning between another pair of problems. Both the problems can be solved using the same physics principles. However, the solved problem provided was a two-step problem (which can be solved by decomposing it into two sub-problems) while the quiz problem was a three-step problem. We find that it is challenging for students to extend what they learned from a two-step problem to solve a three-step problem.
Energy Landscapes and Solved Protein Folding Problems
NASA Astrophysics Data System (ADS)
Wolynes, Peter
Peter G. Wolynes Center for Theoretical Biological Physics Department of Chemistry and Biochemistry and Physics University of California, San Diego La Jolla, CA 92093-0371 Fifteen years ago, how proteins folded into organized structures on the basis of their sequence was a great mystery. By characterizing the energy landscapes of proteins with tools from the statistical mechanics of disordered systems like spin glasses, a "new view' of the folding process became possible. Energy landscape theory provided an incentive to pursue heroic new experiments and to carry out difficult computer simulations addressing protein folding mechanisms. Many aspects of folding kinetics revealed by these studies can be quantitatively understood using the simple idea that the topography of the energy landscape is that of a "rugged funnel". Energy landscape theory provided a quantitative means of characterizing which amino acid sequences can rapidly fold. Algorithms based on energy landscape theory have been used to successfully design novel sequences that fold to a given structure in the laboratory. Energy landscape ideas have begun to transform the prediction of protein structure from sequence data from being an art to being a science. The success of energy landscape- based algorithms in predicting protein structure from sequence will be highlighted. While there is still much to learn about folding mechanisms and much work to do achieving universally reliable structure prediction, many parts of what used to be called "the protein folding problem" can now be considered solved.
Algebraic Approach to the Minimum-Cost Multi-Impulse Orbit-Transfer Problem
NASA Astrophysics Data System (ADS)
Avendaño, M.; Martín-Molina, V.; Martín-Morales, J.; Ortigas-Galindo, J.
We present a purely algebraic formulation (i.e. polynomial equations only) of the minimum-cost multi-impulse orbit transfer problem without time constraints, while keeping all the variables with a precise physical meaning. We apply general algebraic techniques to solve these equations (resultants, Gr\\"obner bases, etc.) in several situations of practical interest of different degrees of generality. For instance, we provide a proof of the optimality of the Hohmann transfer for the minimum fuel 2-impulse circular to circular orbit transfer problem, and we provide a general formula for the optimal 2-impulse in-plane transfer between two rotated elliptical orbits under a mild symmetry assumption on the two points where the impulses are applied (which we conjecture that can be removed).
OpenMP for 3D potential boundary value problems solved by PIES
NASA Astrophysics Data System (ADS)
KuŻelewski, Andrzej; Zieniuk, Eugeniusz
The main purpose of this paper is examination of an application of modern parallel computing technique OpenMP to speed up the calculation in the numerical solution of parametric integral equations systems (PIES). The authors noticed, that solving more complex boundary problems by PIES sometimes requires large computing time. This paper presents the use of OpenMP and fast C++ linear algebra library Armadillo for boundary value problems modelled by 3D Laplace's equation and solved using PIES. The testing example shows that the use of mentioned technologies significantly increases speed of calculations in PIES.
The Effects of Thinking Aloud Pair Problem Solving on High School Students' Chemistry Problem-Solving Performance and Verbal Interactions
ERIC Educational Resources Information Center
Jeon, Kyungmoon; Huffman, Douglas; Noh, Taehee
A problem solving strategy, Thinking Aloud Pair Problem Solving (TAPPS), developed by Arthur Whimbey to help students monitor and understand their own thought process is presented. The TAPPS strategy encouraged the students interact verbally with each other to solve chemistry problems and improve the achievements in chemistry.
Journey into Problem Solving: A Gift from Polya
NASA Astrophysics Data System (ADS)
Lederman, Eric
In How to Solve It, accomplished mathematician and skilled communicator George Polya describes a four-step universal solving technique designed to help students develop mathematical problem-solving skills. By providing a glimpse at the grace with which experts solve problems, Polya provides definable methods that are not exclusive to mathematicians but of interest to cognitive psychologists and problem solvers in all fields. I had the good fortune to be introduced to Polya's ideas in my first undergraduate class in physics.
Analyzing the many skills involved in solving complex physics problems
NASA Astrophysics Data System (ADS)
Adams, Wendy K.; Wieman, Carl E.
We have empirically identified over 40 distinct sub-skills that affect a person's ability to solve complex problems in many different contexts. The identification of so many sub-skills explains why it has been so difficult to teach or assess problem solving as a single skill. The existence of these sub-skills is supported by several studies comparing a wide range of individuals' strengths and weaknesses in these sub-skills, their "problem solving fingerprint," while solving different types of problems including a classical mechanics problem, quantum mechanics problems, and a complex trip-planning problem with no physics. We see clear differences in the problem solving fingerprint of physics and engineering majors compared to the elementary education majors that we tested. The implications of these findings for guiding the teaching and assessing of problem solving in physics instruction are discussed.
Effects of Training in Problem Solving on the Problem-Solving Abilities of Gifted Fourth Graders: A Comparison of the Future Problem Solving and Instrumental Enrichment Programs.
ERIC Educational Resources Information Center
Dufner, Hillrey A.; Alexander, Patricia A.
The differential effects of two different types of problem-solving training on the problem-solving abilities of gifted fourth graders were studied. Two successive classes of gifted fourth graders from Weslaco Independent School District (Texas) were pretested with the Coloured Progressive Matrices (CPM) and Thinking Creatively With Pictures…
Algebraic solution for phase unwrapping problems in multiwavelength interferometry.
Falaggis, Konstantinos; Towers, David P; Towers, Catherine E
Recent advances in multiwavelength interferometry techniques [Appl. Opt.52, 5758 (2013)] give new insights to phase unwrapping problems and allow the fringe order information contained in the measured phase to be extracted with low computational effort. This work introduces an algebraic solution to the phase unwrapping problem that allows the direct calculation of the unknown integer fringe order. The procedure resembles beat-wavelength approaches, but provides greater flexibility in choosing the measurement wavelengths, a larger measurement range, and a higher robustness against noise, due to the ability to correct for errors during the calculation. PMID:24921139
Algebraic multigrid methods applied to problems in computational structural mechanics
NASA Technical Reports Server (NTRS)
Mccormick, Steve; Ruge, John
The development of algebraic multigrid (AMG) methods and their application to certain problems in structural mechanics are described with emphasis on two- and three-dimensional linear elasticity equations and the 'jacket problems' (three-dimensional beam structures). Various possible extensions of AMG are also described. The basic idea of AMG is to develop the discretization sequence based on the target matrix and not the differential equation. Therefore, the matrix is analyzed for certain dependencies that permit the proper construction of coarser matrices and attendant transfer operators. In this manner, AMG appears to be adaptable to structural analysis applications.
Teaching Problem-Solving Skills to Nuclear Engineering Students
ERIC Educational Resources Information Center
Waller, E.; Kaye, M. H.
Problem solving is an essential skill for nuclear engineering graduates entering the workforce. Training in qualitative and quantitative aspects of problem solving allows students to conceptualise and execute solutions to complex problems. Solutions to problems in high consequence fields of study such as nuclear engineering require rapid and…
Strategies, Not Solutions: Involving Students in Problem Solving.
ERIC Educational Resources Information Center
Von Kuster, Lee N.
Defines problem solving, discusses the use of problems developed by students that are relevant to their own lives, presents examples of practical mathematics problems that deal with local situations, discusses fringe benefits of this type of problem solving, and addresses teachers' concern that this method consumes too much time. (MBR)
Algebraic analysis of the phase-calibration problem in the self-calibration procedures
NASA Astrophysics Data System (ADS)
Lannes, A.; Prieur, J.-L.
This paper presents an analysis of the phase-calibration problem encountered in astronomy when mapping incoherent sources with aperture-synthesis devices. More precisely, this analysis concerns the phase-calibration operation involved in the self-calibration procedures of phase-closure imaging. The paper revisits and completes a previous analysis presented by Lannes in the Journal of the Optical Society of America A in 2005. It also benefits from some recent developments made for solving similar problems encountered in global navigation satellite systems. In radio-astronomy, the related optimization problems have been stated and solved hitherto at the phasor level. We present here an analysis conducted at the phase level, from which we derive a method for diagnosing and solving the difficulties of the phasor approach. In the most general case, the techniques to be implemented appeal to the algebraic graph theory and the algebraic number theory. The minima of the objective functionals to be minimized are identified by raising phase-closure integer ambiguities. We also show that in some configurations, to benefit from all the available information, closure phases of order greater than three are to be introduced. In summary, this study leads to a better understanding of the difficulties related to the very principle of phase-closure imaging. To circumvent these difficulties, we propose a strategy both simple and robust.
Problem-solving test: Tryptophan operon mutants.
Szeberényi, József
Terms to be familiar with before you start to solve the test: tryptophan, operon, operator, repressor, inducer, corepressor, promoter, RNA polymerase, chromosome-polysome complex, regulatory gene, cis-acting element, trans-acting element, plasmid, transformation. PMID:21567855
Using a general problem-solving strategy to promote transfer.
Youssef-Shalala, Amina; Ayres, Paul; Schubert, Carina; Sweller, John
Cognitive load theory was used to hypothesize that a general problem-solving strategy based on a make-as-many-moves-as-possible heuristic could facilitate problem solutions for transfer problems. In four experiments, school students were required to learn about a topic through practice with a general problem-solving strategy, through a conventional problem solving strategy or by studying worked examples. In Experiments 1 and 2 using junior high school students learning geometry, low knowledge students in the general problem-solving group scored significantly higher on near or far transfer tests than the conventional problem-solving group. In Experiment 3, an advantage for a general problem-solving group over a group presented worked examples was obtained on far transfer tests using the same curriculum materials, again presented to junior high school students. No differences between conditions were found in Experiments 1, 2, or 3 using test problems similar to the acquisition problems. Experiment 4 used senior high school students studying economics and found the general problem-solving group scored significantly higher than the conventional problem-solving group on both similar and transfer tests. It was concluded that the general problem-solving strategy was helpful for novices, but not for students that had access to domain-specific knowledge. PMID:25000309
Contextualizing Arithmetic into Developmental Elementary Algebra Using Guided Problem Solving
ERIC Educational Resources Information Center
Guy, G. Michael; Cornick, Jonathan; Puri, Karan
Many colleges are finding that the use of acceleration in developmental education is a promising direction for improved student progress toward a degree or certificate. Acceleration has been defined in the literature as the reorganization of curricula and instruction in ways that facilitate the completion of educational requirements in an…
The Poincaré problem, algebraic integrability and dicritical divisors
NASA Astrophysics Data System (ADS)
Galindo, C.; Monserrat, F.
We solve the Poincaré problem for plane foliations with only one dicritical divisor. Moreover, in this case, we give a simple algorithm that decides whether a foliation has a rational first integral and computes it in the affirmative case. We also provide an algorithm to compute a rational first integral of prefixed genus g≠1 of any type of plane foliation F. When the number of dicritical divisors dic(F) is larger than 2, this algorithm depends on suitable families of invariant curves. When dic(F)=2, it proves that the degree of the rational first integral can be bounded only in terms of g, the degree of F and the local analytic type of the dicritical singularities of F. The degree d of a general integral invariant curve is less than or equal to 4. Therefore, the Poincaré problem is solved in this case. There exists a valueλ∈Z>0such thatPF:=|λΔF|is a pencil and the rational mapP2⋯→P1that it defines is a rational first integral ofF. Moreover λ is the minimum of the set{α∈Z>0|dim|αΔF|⩾1}. The above clause (b) supports a very simple algorithm, our forthcoming Algorithm 2, which decides about the existence of a rational first integral of F (and computes it in the positive case) whenever dic(F)=1. Other alternative algorithms are treated in Section 4. Our remaining main results are: Assume thatFhas a rational first integral of genus g. Then, there exists a bound on the degree of the first integral depending only on the degree ofF, the genus g and the local analytic type of the dicritical singularities ofF. There exists an algorithm to decide whetherFhas a rational first integral of genus g (and to compute it, in the affirmative case) whose inputs are: g, a homogeneous 1-form definingFand the minimal resolution of the dicritical singularities ofF. Assume thatFhas a rational first integral of genus g. Then there exists a bound on the degree of the first integral which depends on the degree ofF, the genus g, the local analytic type of the
Cognitive restructuring as an early stage in problem solving
NASA Astrophysics Data System (ADS)
Bodner, George M.; McMillen, Theresa L. B.
This article examines the hypothesis that there are preliminary stages in problem solving which most chemists neglect when trying to teach their students how to solve problems in introductory chemistry courses. It is during these early stages that relevant information is disembedded from the question and the problem is restructured. Unless students can successfully complete these cognitive restructuring stages, they cannot proceed on to the more analytic stages in problem solving that have received more attention from chemists.Preliminary evidence for this hypothesis consists of linear correlations between student ability to handle disembedding and cognitive restructuring tasks in the spatial domain and their ability to solve chemistry problems.
A descriptive study of cooperative problem solving introductory physics labs
NASA Astrophysics Data System (ADS)
Knutson, Paul Aanond
The purpose of this study was to determine the ways in which cooperative problem solving in physics instructional laboratories influenced the students' ability to provide qualitative responses to problems. The literature shows that problem solving involves both qualitative and quantitative skills. Qualitative skills are important because those skills are the foundation for the quantitative aspects of problem solving. (Chi, et al., 1981). The literature also indicates that cooperative problem solving should enhance the students' performance. As a practical matter surveys of departments that require introductory physics classes expect their students to have general qualitative problem solving skills. The students in this study were asked to solve problem(s) before coming to a lab session and then cooperatively assess whether or not their answers were correct by conducting a laboratory activity for which they had to plan the procedure and obtain the necessary results. TA's were expected to provide instruction under a cognitive apprenticeship model. The results showed that the cooperative problem solving laboratories had almost no impact on the students' problem solving skills as measured from the start of a two hour lab session to the end of the lab session...The reason for this may have been that students did not have enough experience in the solving of different kinds of problems in the two domains of Newton's second Law and gravitation to overcome their misconceptions and become competent. Another possibility was that the TA's did not follow the cognitive apprenticeship model as consistently as might have been needed.
The relationship between students' problem solving frames and epistemological beliefs
NASA Astrophysics Data System (ADS)
Wampler, Wendi N.
Introductory undergraduate physics courses aim to help students develop the skills and strategies necessary to solve complex, real world problems, but many students not only leave these courses with serious gaps in their conceptual understanding, but also maintain a novice-like approach to solving problems. Matter and Interactions [M&I] is a curriculum that focuses on a restructuring of physics content knowledge and emphasizes a systematic approach to problem solving, called modeling, which involves the application physical principles to carefully defined systems of objects and interactions (Chabay and Sherwood, 2007a). Because the M&I approach to problem solving is different from many students' previous physics experience, efforts need to be made to attend to their epistemological beliefs and expectations about not only learning physics content knowledge, but problem solving as well. If a student frames solving physics problems as a `plug and chug' type activity, then they are going continue practicing this strategy. Thus, it is important to address students' epistemological beliefs and monitor how they frame the activity of problem solving within the M&I course. This study aims to investigate how students frame problem solving within the context of a large scale implementation of the M&I curriculum, and how, if at all, those frames shift through the semester. By investigating how students frame the act of problem solving in the M&I context, I was able to examine the connection between student beliefs and expectations about problem solving in physics and the skills and strategies used while solving problems in class. To accomplish these goals, I recruited student volunteers from Purdue's introductory, calculus-based physics course and assessed their problem solving approach and espoused epistemological beliefs over the course of a semester. I obtained data through video recordings of the students engaged in small group problem solving during recitation activities
Formulating and Solving Problems in Computational Chemistry.
ERIC Educational Resources Information Center
Norris, A. C.
Considered are the main elements of computational chemistry problems and how these elements can be used to formulate the problems mathematically. Techniques that are useful in devising an appropriate solution are also considered. (Author/TG)
Problem Solving in Calculus with Symbolic Geometry and CAS
ERIC Educational Resources Information Center
Todd, Philip; Wiechmann, James
Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…
Problem-Solving Test: Southwestern Blotting
ERIC Educational Resources Information Center
Szeberényi, József
Terms to be familiar with before you start to solve the test: Southern blotting, Western blotting, restriction endonucleases, agarose gel electrophoresis, nitrocellulose filter, molecular hybridization, polyacrylamide gel electrophoresis, proto-oncogene, c-abl, Src-homology domains, tyrosine protein kinase, nuclear localization signal, cDNA,…
Facilitating Students' Problem Solving across Multiple Representations in Introductory Mechanics
NASA Astrophysics Data System (ADS)
Nguyen, Dong-Hai; Gire, Elizabeth; Rebello, N. Sanjay
Solving problems presented in multiple representations is an important skill for future physicists and engineers. However, such a task is not easy for most students taking introductory physics courses. We conducted teaching/learning interviews with 20 students in a first-semester calculus-based physics course on several topics in introductory mechanics. These interviews helped identify the common difficulties students encountered when solving physics problems posed in multiple representations as well as the hints that help students overcome those difficulties. We found that most representational difficulties arise due to the lack of students' ability to associate physics knowledge with corresponding mathematical knowledge. Based on those findings, we developed, tested and refined a set of problem-solving exercises to help students learn to solve problems in graphical and equational representations. We present our findings on students' common difficulties with graphical and equational representations, the problem-solving exercises and their impact on students' problem solving abilities.
Dimensional Analysis and Qualitative Methods in Problem Solving
ERIC Educational Resources Information Center
Pescetti, D.
The primary application of dimensional analysis (DA) is in problem solving. Typically, the problem description indicates that a physical quantity Y(the unknown) is a function f of other physical quantities A[subscript 1], ..., A[subscript n] (the data). We propose a qualitative problem-solving procedure which consists of a parallel decomposition…
Social Problem-Solving among Adolescents Treated for Depression
Becker-Weidman, Emily G.; Jacobs, Rachel H.; Reinecke, Mark A.; Silva, Susan G.; March, John S.
Studies suggest that deficits in social problem-solving may be associated with increased risk of depression and suicidality in children and adolescents. It is unclear, however, which specific dimensions of social problem-solving are related to depression and suicidality among youth. Moreover, rational problem-solving strategies and problem-solving motivation may moderate or predict change in depression and suicidality among children and adolescents receiving treatment. The effect of social problem-solving on acute treatment outcomes were explored in a randomized controlled trial of 439 clinically depressed adolescents enrolled in the Treatment for Adolescents with Depression Study (TADS). Measures included the Children's Depression Rating Scale-Revised (CDRS-R), the Suicidal Ideation Questionnaire – Grades 7-9 (SIQ-Jr), and the Social Problem Solving Inventory-Revised (SPSI-R). A random coefficients regression model was conducted to examine main and interaction effects of treatment and SPSI-R subscale scores on outcomes during the 12-week acute treatment stage. Negative problem orientation, positive problem orientation, and avoidant problem-solving style were non-specific predictors of depression severity. In terms of suicidality, avoidant problem-solving style and impulsiveness/carelessness style were predictors, whereas negative problem orientation and positive problem orientation were moderators of treatment outcome. Implications of these findings, limitations, and directions for future research are discussed. PMID:19775677
Problem-Solving Support for English Language Learners
ERIC Educational Resources Information Center
Wiest, Lynda R.
Although word problems pose greater language demands, they also encourage more meaningful problem solving and mathematics understanding. With proper instructional support, a student-centered, investigative approach to contextualized problem solving benefits all students. This article presents a lesson built on an author-adapted version of the…
A Tool for Helping Veterinary Students Learn Diagnostic Problem Solving.
ERIC Educational Resources Information Center
Danielson, Jared A.; Bender, Holly S.; Mills, Eric M.; Vermeer, Pamela J.; Lockee, Barbara B.
Describes the result of implementing the Problem List Generator, a computer-based tool designed to help clinical pathology veterinary students learn diagnostic problem solving. Findings suggest that student problem solving ability improved, because students identified all relevant data before providing a solution. (MES)
Solving Information-Based Problems: Evaluating Sources and Information
ERIC Educational Resources Information Center
Brand-Gruwel, Saskia; Stadtler, Marc
The focus of this special section is on the processes involved when solving information-based problems. Solving these problems requires from people that they are able to define the information problem, search and select usable and reliable sources and information and synthesise information into a coherent body of knowledge. An important aspect…
Mathematical Profiles and Problem Solving Abilities of Mathematically Promising Students
ERIC Educational Resources Information Center
Budak, Ibrahim
Mathematically promising students are defined as those who have the potential to become the leaders and problem solvers of the future. The purpose of this research is to reveal what problem solving abilities mathematically promising students show in solving non-routine problems and type of profiles they present in the classroom and during problem…
Problem-Solving during Shared Reading at Kindergarten
ERIC Educational Resources Information Center
Gosen, Myrte N.; Berenst, Jan; de Glopper, Kees
This paper reports on a conversation analytic study of problem-solving interactions during shared reading at three kindergartens in the Netherlands. It illustrates how teachers and pupils discuss book characters' problems that arise in the events in the picture books. A close analysis of the data demonstrates that problem-solving interactions do…
Schema Induction in Problem Solving: A Multidimensional Analysis
ERIC Educational Resources Information Center
Chen, Zhe; Mo, Lei
The present research examined the processes of schema formation in problem solving. In 4 experiments, participants experienced a series of tasks analogous to A. S. Luchins' (1942) water jar problems before attempting to solve isomorphic target problems. Juxtaposing illustrative source instances varying in procedural features along multiple…
A Descriptive Study of Cooperative Problem Solving Introductory Physics Labs
ERIC Educational Resources Information Center
Knutson, Paul Aanond
The purpose of this study was to determine the ways in which cooperative problem solving in physics instructional laboratories influenced the students' ability to provide qualitative responses to problems. The literature shows that problem solving involves both qualitative and quantitative skills. Qualitative skills are important because those…
Solving the Sailors and the Coconuts Problem via Diagrammatic Approach
ERIC Educational Resources Information Center
Man, Yiu-Kwong
In this article, we discuss how to use a diagrammatic approach to solve the classic sailors and the coconuts problem. It provides us an insight on how to tackle this type of problem in a novel and intuitive way. This problem-solving approach will be found useful to mathematics teachers or lecturers involved in teaching elementary number theory,…
Complex Mathematical Problem Solving by Individuals and Dyads.
ERIC Educational Resources Information Center
Vye, Nancy J.; Goldman, Susan R.; Voss, James F.; Hmelo, Cindy; Williams, Susan; Cognition and Technology Group at Vanderbilt University
Describes two studies of mathematical problem solving using an episode from "The Adventures of Jasper Woodbury," a set of curriculum materials that afford complex problem-solving opportunities. Discussion focuses on characteristics of problems that make solutions difficult, kinds of reasoning that dyadic interactions support, and considerations of…
Schoenfeld's Problem Solving Theory in a Student Controlled Learning Environment
ERIC Educational Resources Information Center
Harskamp, E.; Suhre, C.
This paper evaluates the effectiveness of a student controlled computer program for high school mathematics based on instruction principles derived from Schoenfeld's theory of problem solving. The computer program allows students to choose problems and to make use of hints during different episodes of solving problems. Crucial episodes are:…
Top Element Problem and Macneille Completions of Generalized Effect Algebras
NASA Astrophysics Data System (ADS)
RieČanová, Z.; Kalina, M.
Effect algebras (EAs), introduced by D. J. Foulis and M. K. Bennett, as common generalizations of Boolean algebras, orthomodular lattices and MV-algebras, are nondistributive algebraic structures including unsharp elements. Their unbounded versions, called generalized effect algebras, are posets which may have or may have not an EA-MacNeille completion, or cannot be embedded into any complete effect algebra. We give a necessary and sufficient condition for a generalized effect algebra to have an EA-MacNeille completion. Some examples are provided.
Goals and everyday problem solving: examining the link between age-related goals and problem-solving strategy use.
Hoppmann, Christiane A; Coats, Abby Heckman; Blanchard-Fields, Fredda
Qualitative interviews on family and financial problems from 332 adolescents, young, middle-aged, and older adults, demonstrated that developmentally relevant goals predicted problem-solving strategy use over and above problem domain. Four focal goals concerned autonomy, generativity, maintaining good relationships with others, and changing another person. We examined both self- and other-focused problem-solving strategies. Autonomy goals were associated with self-focused instrumental problem solving and generative goals were related to other-focused instrumental problem solving in family and financial problems. Goals of changing another person were related to other-focused instrumental problem solving in the family domain only. The match between goals and strategies, an indicator of problem-solving adaptiveness, showed that young individuals displayed the greatest match between autonomy goals and self-focused problem solving, whereas older adults showed a greater match between generative goals and other-focused problem solving. Findings speak to the importance of considering goals in investigations of age-related differences in everyday problem solving. PMID:17899456
Surveying graduate students' attitudes and approaches to problem solving
NASA Astrophysics Data System (ADS)
Mason, Andrew; Singh, Chandralekha
Students' attitudes and approaches to problem solving in physics can profoundly influence their motivation to learn and development of expertise. We developed and validated an Attitudes and Approaches to Problem Solving survey by expanding the Attitudes toward Problem Solving survey of Marx and Cummings and administered it to physics graduate students. Comparison of their responses to the survey questions about problem solving in their own graduate-level courses vs problem solving in the introductory physics courses provides insight into their expertise in introductory and graduate-level physics. The physics graduate students' responses to the survey questions were also compared with those of introductory physics and astronomy students and physics faculty. We find that, even for problem solving in introductory physics, graduate students' responses to some survey questions are less expertlike than those of the physics faculty. Comparison of survey responses of graduate students and introductory students for problem solving in introductory physics suggests that graduate students' responses are in general more expertlike than those of introductory students. However, survey responses suggest that graduate-level problem solving by graduate students on several measures has remarkably similar trends to introductory-level problem solving by introductory students.
Innovation and problem solving: a review of common mechanisms.
Griffin, Andrea S; Guez, David
Behavioural innovations have become central to our thinking about how animals adjust to changing environments. It is now well established that animals vary in their ability to innovate, but understanding why remains a challenge. This is because innovations are rare, so studying innovation requires alternative experimental assays that create opportunities for animals to express their ability to invent new behaviours, or use pre-existing ones in new contexts. Problem solving of extractive foraging tasks has been put forward as a suitable experimental assay. We review the rapidly expanding literature on problem solving of extractive foraging tasks in order to better understand to what extent the processes underpinning problem solving, and the factors influencing problem solving, are in line with those predicted, and found, to underpin and influence innovation in the wild. Our aim is to determine whether problem solving can be used as an experimental proxy of innovation. We find that in most respects, problem solving is determined by the same underpinning mechanisms, and is influenced by the same factors, as those predicted to underpin, and to influence, innovation. We conclude that problem solving is a valid experimental assay for studying innovation, propose a conceptual model of problem solving in which motor diversity plays a more central role than has been considered to date, and provide recommendations for future research using problem solving to investigate innovation. This article is part of a Special Issue entitled: Cognition in the wild. PMID:25245306
The Family as a Small Problem Solving Group
ERIC Educational Resources Information Center
Tallman, Irving
Analyzes relationship between "open channels of communication" and "centralization of authority", and "cultural" variables in terms of their contributions to optimal problem solving structures and activities. (Author)
Applying Lakatos' Theory to the Theory of Mathematical Problem Solving.
ERIC Educational Resources Information Center
Nunokawa, Kazuhiko
The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)
Understanding the Problem. Problem Solving and Communication Activity Series. The Math Forum: Problems of the Week
ERIC Educational Resources Information Center
Math Forum @ Drexel, 2009
Different techniques for understanding a problem can lead to ideas for never-used-before solutions. Good problem-solvers use a problem-solving strategy and may come back to it frequently while they are working on the problem to refine their strategy, see if they can find better solutions, or find other questions. Writing is an integral part of…
The spatial isomorphism problem for close separable nuclear C*-algebras
Christensen, Erik; Sinclair, Allan M.; Smith, Roger R.; White, Stuart A.; Winter, Wilhelm
The Kadison–Kastler problem asks whether close C*-algebras on a Hilbert space must be spatially isomorphic. We establish this when one of the algebras is separable and nuclear. We also apply our methods to the study of near inclusions of C*-algebras. PMID:20080723
Problem Solved: How To Coach Cognition.
ERIC Educational Resources Information Center
Krynock, Karoline; Robb, Louise
When faced with real-world problems, students devise accurate, logical, and creative solutions using skills connecting to different subject areas. Students are intrigued by assignments involving preservation of species and design of environmentally friendly products and transit systems. Problem-based learning depends on coaching, modeling, and…
How Indirect Supportive Digital Help during and after Solving Physics Problems Can Improve Problem-Solving Abilities
ERIC Educational Resources Information Center
Pol, Henk J.; Harskamp, Egbert G.; Suhre, Cor J. M.; Goedhart, Martin J.
This study investigates the effectiveness of computer-delivered hints in relation to problem-solving abilities in two alternative indirect instruction schemes. In one instruction scheme, hints are available to students immediately after they are given a new problem to solve as well as after they have completed the problem. In the other scheme,…
A Decision Support System for Solving Multiple Criteria Optimization Problems
ERIC Educational Resources Information Center
Filatovas, Ernestas; Kurasova, Olga
In this paper, multiple criteria optimization has been investigated. A new decision support system (DSS) has been developed for interactive solving of multiple criteria optimization problems (MOPs). The weighted-sum (WS) approach is implemented to solve the MOPs. The MOPs are solved by selecting different weight coefficient values for the criteria…
Learning New Problem-Solving Strategies Leads to Changes in Problem Representation
ERIC Educational Resources Information Center
Alibali, Martha W.; Phillips, Karin M. O.; Fischer, Allison D.
Children sometimes solve problems incorrectly because they fail to represent key features of the problems. One potential source of improvements in children's problem representations is learning new problem-solving strategies. Ninety-one 3rd- and 4th-grade students solved mathematical equivalence problems (e.g., 3+4+6=3+__) and completed a…
Solving workplace problems associated with VDTs.
Slovak, A J; Trevers, C
The introduction of VDTs into the vast majority of modern working environments represents a substantial change in the disciplines of work for many people. This paper describes how the health and safety issues associated with this change were managed in one organisation by the acquisition of ergonomics skills and their combination with occupational health surveillance techniques. The results show that ergonomics problems far outweighed symptomatic complaints, but symptomatic complaints were strongly associated with high VDT occupancy. The processes used resulted in high response rates from VDT users and an excellent 'clear-up' rate of problems. The solution of these problems was quantified in terms of difficulty and cost. PMID:15676651
Aquarium Problems: How To Solve Them
ERIC Educational Resources Information Center
DeFilippo, Shirley
Presents some solutions to problems commonly encountered in maintaining a classroom aquarium: pH control, overfeeding, overcrowding of tank populations, incorrect temperature settings, faulty introduction of fish into the tank, and the buildup of too many nitrogenous wastes. (PB)
Solving maximum cut problems in the Adleman-Lipton model.
Xiao, Dongmei; Li, Wenxia; Zhang, Zhizhou; He, Lin
In this paper, we consider a procedure for solving maximum cut problems in the Adleman-Lipton model. The procedure works in O(n2) steps for maximum cut problems of an undirected graph with n vertices. PMID:16236426
Influence of visual cueing and outcome feedback on physics problem solving and visual attention
NASA Astrophysics Data System (ADS)
Rouinfar, Amy
Research has demonstrated that attentional cues overlaid on diagrams and animations can help students attend to the relevant areas and facilitate problem solving. In this study we investigate the influence of visual cues and outcome feedback on students' problem solving, performance, reasoning, and visual attention as they solve conceptual physics problems containing a diagram. The participants (N=90) were enrolled in an algebra-based physics course and were individually interviewed. During each interview students solved four problem sets while their eye movements were recorded. The problem diagrams contained regions that were relevant to solving the problem correctly and separate regions related to common incorrect responses. Each problem set contained an initial problem, six isomorphic training problems, and a transfer problem. Those in the cued condition saw visual cues overlaid on the training problems. Those in the feedback conditions were told if their responses (answer and explanation) were correct or incorrect. Students' verbal responses were used to determine their accuracy. The study produced two major findings. First, short duration visual cues coupled with correctness feedback can improve problem solving performance on a variety of insight physics problems, including transfer problems not sharing the surface features of the training problems, but instead sharing the underlying solution path. Thus, visual cues can facilitate re-representing a problem and overcoming impasse, enabling a correct solution. Importantly, these cueing effects on problem solving did not involve the solvers' attention necessarily embodying the solution to the problem. Instead, the cueing effects were caused by solvers attending to and integrating relevant information in the problems into a solution path. Second, these short duration visual cues when administered repeatedly over multiple training problems resulted in participants becoming more efficient at extracting the relevant
Trends in problem-solving research - Twelve recently described tasks.
NASA Technical Reports Server (NTRS)
Coates, G. D.; Alluisi, E. A.; Morgan, B. B., Jr.
Review of descriptions of the 12 problem-solving tasks developed since the last review (Ray, 1955) of this topic, indicating that the newer tasks are more sophisticated in design and provide for better experimental control than those used prior to 1953. Validity, reliability, sensitivity, trainability, problem structure, and problem difficulty are discussed as criteria for the selection of tasks to be used in studies of skilled problem-solving performance.
Using Problem-Solving Teaching: Theoretical and Philosophical Considerations.
ERIC Educational Resources Information Center
Osborne, Edward W.
A rationale for the teaching of thinking and problem-solving skills is outlined, and the definition of and design for teaching such skills are discussed. Developing the ability of students to think has surfaced in recent years as one of the major purposes of American education. Problem solving has been described as a major type of thinking…
Phenomenographic Study of Students' Problem Solving Approaches in Physics
ERIC Educational Resources Information Center
Walsh, Laura N.; Howard, Robert G.; Bowe, Brian
This paper describes ongoing research investigating student approaches to quantitative and qualitative problem solving in physics. This empirical study was conducted using a phenomenographic approach to analyze data from individual semistructured problem solving interviews with 22 introductory college physics students. The main result of the study…
Toward a Comprehensive Model of Problem-Solving.
ERIC Educational Resources Information Center
Pitt, Ruth B.
Presented is a model of problem solving that incorporates elements of hypothetico-deductive reasoning in the Piagetian sense, and heuristic-algorithmic processing in the information-processing sense. It assumes that people invoke both formal reasoning strategies and learned algorithms whenever they solve problems. The proposed model integrates the…
Childhood Physical Punishment and Problem Solving in Marriage
ERIC Educational Resources Information Center
Cast, Alicia D.; Schweingruber, David; Berns, Nancy
Drawing from social learning theories and symbolic interactionist understandings of social life, the authors suggest that physical punishment teaches aggressive and controlling strategies for solving the problems of living together and hinders the development of important problem-solving skills, specifically the ability to role take with others.…
Concept Learning versus Problem Solving: Is There a Difference?
ERIC Educational Resources Information Center
Nurrenbern, Susan C.; Pickering, Miles
Reports on a study into the relationship between a student's ability to solve problems in chemistry and his/her understanding of molecular concepts. Argues that teaching students to solve problems about chemistry is not equivalent to teaching about the nature of matter. (TW)
Relationship between Problem-Solving Style and Mathematical Literacy
ERIC Educational Resources Information Center
Tai, Wen-Chun; Lin, Su-Wei
Currently, mathematics education is focused on ensuring that students can apply the knowledge and skills they learn to everyday life; students are expected to develop their problem-solving abilities to face challenges by adopting various perspectives. When faced with a problem, students may employ different methods or patterns to solve it. If this…
Conceptual Learning in a Principled Design Problem Solving Environment
ERIC Educational Resources Information Center
Prusak, Naomi; Hershkowitz, Rina; Schwarz, Baruch B.
To what extent can instructional design be based on principles for instilling a culture of problem solving and conceptual learning? This is the main focus of the study described in this paper, in which third grade students participated in a one-year course designed to foster problem solving and mathematical reasoning. The design relied on five…
Effects of Problem-Solving Strategies on Different Ability Levels.
ERIC Educational Resources Information Center
Nichols, Teresa M.
To determine if differing ability levels will affect the acquisition of problem-solving skills and self-esteem as a result of participation in two approaches to teaching problem-solving skills, a study was conducted with sixth graders in a posttest-only control group experimental design. Subjects were 102 sixth graders randomly assigned to 5…
Cognitive Restructuring as a First Step in Problem Solving.
ERIC Educational Resources Information Center
Bodner, George M.; McMillen, Theresa L. B.
Chemists have bemoaned for years their students' inability to solve problems in introductory chemistry courses. However, at least part of this inability must be attributed to the fact that chemists have historically tried to teach their students to solve problems by doing nothing more than working examples. In recent years, chemists have begun to…
The Effects of Age on Perceptual Problem-Solving Strategies.
ERIC Educational Resources Information Center
Lee, Jo Ann; Pollack, Robert H.
Witkin's Embedded Figures Test (EFT) was used to measure the changes with age in field dependence and problem-solving ability. Qualitative data concerning problem-solving strategies and quantitative data were collected. EFT was administered to 12 females in each of the following decades: 20s, 30s, 40s, 50s, 60s, 70s. All subjects were moderately…
The Winning Edge: Tips for Creative Problem-Solving Teams.
ERIC Educational Resources Information Center
Safris, Richard
Intended for coaches of school competitive problem-solving teams, this publication details 70 suggestions for building, motivating, and training problem-solving teams in grades 4 to 8. The tips cover a range of topics related to preparing for competition, the competition itself, and post-competition. The pre-competition suggestions include: (1)…
Chaining in Problem Solving: A Critique and Reinvestigation.
ERIC Educational Resources Information Center
Blumberg, Phyllis
This study investigated the question of whether young children can form response chains in problem solving. After reviewing the literature relating to chaining as a component of problem solving, the author argues that a test of chaining should be free of requirements to recall previously learned material, remember general information, or apply…
Use of External Visual Representations in Probability Problem Solving
ERIC Educational Resources Information Center
Corter, James E.; Zahner, Doris C.
We investigate the use of external visual representations in probability problem solving. Twenty-six students enrolled in an introductory statistics course for social sciences graduate students (post-baccalaureate) solved eight probability problems in a structured interview format. Results show that students spontaneously use self-generated…
Assessing Creative Problem-Solving with Automated Text Grading
ERIC Educational Resources Information Center
Wang, Hao-Chuan; Chang, Chun-Yen; Li, Tsai-Yen
The work aims to improve the assessment of creative problem-solving in science education by employing language technologies and computational-statistical machine learning methods to grade students' natural language responses automatically. To evaluate constructs like creative problem-solving with validity, open-ended questions that elicit…
A New Approach: Computer-Assisted Problem-Solving Systems
ERIC Educational Resources Information Center
Gok, Tolga
Computer-assisted problem solving systems are rapidly growing in educational use and with the advent of the Internet. These systems allow students to do their homework and solve problems online with the help of programs like Blackboard, WebAssign and LON-CAPA program etc. There are benefits and drawbacks of these systems. In this study, the…
A Markov Model Analysis of Problem-Solving Progress.
ERIC Educational Resources Information Center
Vendlinski, Terry
This study used a computerized simulation and problem-solving tool along with artificial neural networks (ANN) as pattern recognizers to identify the common types of strategies high school and college undergraduate chemistry students would use to solve qualitative chemistry problems. Participants were 134 high school chemistry students who used…
Measuring Problem Solving Skills in Plants vs. Zombies 2
ERIC Educational Resources Information Center
Shute, Valerie J.; Moore, Gregory R.; Wang, Lubin
We are using stealth assessment, embedded in "Plants vs. Zombies 2," to measure middle-school students' problem solving skills. This project started by developing a problem solving competency model based on a thorough review of the literature. Next, we identified relevant in-game indicators that would provide evidence about students'…
Learning from Examples versus Verbal Directions in Mathematical Problem Solving
ERIC Educational Resources Information Center
Lee, Hee Seung; Fincham, Jon M.; Anderson, John R.
This event-related fMRI study investigated the differences between learning from examples and learning from verbal directions in mathematical problem solving and how these instruction types affect the activity of relevant brain regions during instruction and solution periods within problem-solving trials. We identified distinct neural signatures…
Best Known Problem Solving Strategies in "High-Stakes" Assessments
ERIC Educational Resources Information Center
Hong, Dae S.
In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…
Reading-Enhanced Word Problem Solving: A Theoretical Model
ERIC Educational Resources Information Center
Capraro, Robert M.; Capraro, Mary Margaret; Rupley, William H.
There is a reciprocal relationship between mathematics and reading cognition. Metacognitive training within reading-enhanced problem solving should facilitate students developing an awareness of what good readers do when reading for meaning in solving mathematical problems enabling them to apply these strategies. The constructs for each cognitive…
Problem Solving: Getting to the Heart of Mathematics.
ERIC Educational Resources Information Center
Jarrett, Denise, Ed.
This publication features articles that illustrate how several Northwest teachers are using problem solving to achieve rigorous and imaginative learning in their classrooms. Articles include: (1) "Open-Ended Problem Solving: Weaving a Web of Ideas" (Denise Jarrett); (2) "Teenager or Tyke, Students Learn Best by Tackling Challenging Math" (Suzie…
Secondary 2 Students' Difficulties in Solving Non-Routine Problems
ERIC Educational Resources Information Center
Yeo, Kai Kow Joseph
As part of a study on mathematical problem solving of secondary 2 (13- to 14-years old) students in Singapore, 56 Secondary two students from ten secondary schools participated in this study. The purpose of this paper is to explore difficulties faced by 56 Secondary 2 students when solving problems. These interviews were analysed using the…
An Approach to Simulate Understanding Student Problem-Solving Behavior.
ERIC Educational Resources Information Center
Wang, Z. W.; Willoughby, T. L.
This paper describes a method of understanding student problem-solving behavior during computer-assisted instruction using trigonometry as the example domain. Instead of attempting to model the student's process for solving problems, techniques which infer the equivalence between two adjacent steps in the student's process are used to determine…
Students' Metaphors for Mathematical Problem Solving
ERIC Educational Resources Information Center
Yee, Sean P.
The purpose of this study was to determine the metaphors used by students to describe mathematical problem solving. This study focused on identifying how students interpret and perceive mathematical problem solving via conceptual metaphors (Lakoff and Johnson, 2003). These perceptions and interpretations were coded and analyzed qualitatively and…
Students' Use of Technological Features while Solving a Mathematics Problem
ERIC Educational Resources Information Center
Lee, Hollylynne Stohl; Hollebrands, Karen F.
The design of technology tools has the potential to dramatically influence how students interact with tools, and these interactions, in turn, may influence students' mathematical problem solving. To better understand these interactions, we analyzed eighth grade students' problem solving as they used a java applet designed to specifically accompany…
Monitoring Affect States during Effortful Problem Solving Activities
ERIC Educational Resources Information Center
D'Mello, Sidney K.; Lehman, Blair; Person, Natalie
We explored the affective states that students experienced during effortful problem solving activities. We conducted a study where 41 students solved difficult analytical reasoning problems from the Law School Admission Test. Students viewed videos of their faces and screen captures and judged their emotions from a set of 14 states (basic…
Improving Students' Ability To Problem Solve through Social Skills Instruction.
ERIC Educational Resources Information Center
Hopp, Mary Ann; Horn, Cheryl L.; McGraw, Kelleen; Meyer, Jenny
When elementary and middle level students lack effective problem-solving skills, they may make poor behavior choices in social conflicts, contributing to a negative learning and instructional environment. This action research project evaluated the impact of using social skills instruction to improve students' ability to solve problems related to…
Fostering Problem-Solving in a Virtual Environment
ERIC Educational Resources Information Center
Morin, Danielle; Thomas, Jennifer D. E.; Saadé, Raafat George
This article investigates students' perceptions of the relationship between Problem-Solving and the activities and resources used in a Web-based course on the fundamentals of Information Technology at a university in Montreal, Canada. We assess for the different learning components of the course, the extent of perceived problem-solving skills…
The Effects of Service Learning on Student Problem Solving
ERIC Educational Resources Information Center
Guo, Fangfang; Yao, Meilin; Wang, Cong; Yan, Wenfan; Zong, Xiaoli
Previous research indicated that service learning (SL) is an effective pedagogy to improve students' problem-solving ability and increase their classroom engagement. However, studies on SL are rare in China. This study examined the effects of SL on the problem solving of Chinese undergraduate students as well as the mechanism through which it…
Computers and Problem Solving for Sixth-Grade.
ERIC Educational Resources Information Center
Oughton, John M.
Presents a curriculum unit designed for average sixth-grade students intended to engage them in problem-solving experiences and to teach them problem-solving strategies. The curriculum consists of 20 sessions in which students engage in various activities using the following software packages: The Adventures of Jasper Woodbury, Rescue at Boone's…
Exploring Parental Influences on Children's Problem-Solving Skills.
ERIC Educational Resources Information Center
Derrington, Taletha; And Others
This study examined the impact of different styles of parental communication and teaching on children's problem solving, focusing on how parental teaching and communication styles affected children's performance on four problem-solving games involving deduction/categorization and planning. Thirty-two children ages 4 and 5 years and their families…
Role of Multiple Representations in Physics Problem Solving
ERIC Educational Resources Information Center
Maries, Alexandru
This thesis explores the role of multiple representations in introductory physics students' problem solving performance through several investigations. Representations can help students focus on the conceptual aspects of physics and play a major role in effective problem solving. Diagrammatic representations can play a particularly important role…
Social Problem Solving and Aggression: The Role of Depression
ERIC Educational Resources Information Center
Ozdemir, Yalcin; Kuzucu, Yasar; Koruklu, Nermin
The purpose of the present study was to examine direct and indirect relations among social problem-solving, depression, and aggression, as well as the mediating role of depression in the link between social problem-solving and aggression among Turkish youth. Data for the present study were collected from 413 adolescents. The participants' age…
A Descriptive Model of Information Problem Solving while Using Internet
ERIC Educational Resources Information Center
Brand-Gruwel, Saskia; Wopereis, Iwan; Walraven, Amber
This paper presents the IPS-I-model: a model that describes the process of information problem solving (IPS) in which the Internet (I) is used to search information. The IPS-I-model is based on three studies, in which students in secondary and (post) higher education were asked to solve information problems, while thinking aloud. In-depth analyses…
High School Students' Use of Meiosis When Solving Genetics Problems.
ERIC Educational Resources Information Center
Wynne, Cynthia F.; Stewart, Jim; Passmore, Cindy
Paints a different picture of students' reasoning with meiosis as they solved complex, computer-generated genetics problems, some of which required them to revise their understanding of meiosis in response to anomalous data. Students were able to develop a rich understanding of meiosis and can utilize that knowledge to solve genetics problems.…
Facilitating Flexible Problem Solving: A Cognitive Load Perspective
ERIC Educational Resources Information Center
Kalyuga, Slava; Renkl, Alexander; Paas, Fred
The development of flexible, transferable problem-solving skills is an important aim of contemporary educational systems. Since processing limitations of our mind represent a major factor influencing any meaningful learning, the acquisition of flexible problem-solving skills needs to be based on known characteristics of our cognitive architecture…
The Method To Acquire the Strategic Knowledge on Problem Solving.
ERIC Educational Resources Information Center
Takaoka, Ryo; Okamoto, Toshio
As a person learns, his problem solving ability improves and one reason for this is the increased acquisition of "macro-rules" which make problem solving more efficient. An intelligent computer assisted learning (ICAI) system is being developed which automatically acquires the useful knowledge from the domain experts; as experts give the learning…
Peer Instruction Enhanced Meaningful Learning: Ability to Solve Novel Problems
ERIC Educational Resources Information Center
Cortright, Ronald N.; Collins, Heidi L.; DiCarlo, Stephen E.
Students must be able to interpret, relate, and incorporate new information with existing knowledge and apply the new information to solve novel problems. Peer instruction is a cooperative learning technique that promotes critical thinking, problem solving, and decision-making skills. Therefore, we tested the hypothesis that peer instruction…
Prospective Teachers' Problem Solving Skills and Self-Confidence Levels
ERIC Educational Resources Information Center
Gursen Otacioglu, Sena
The basic objective of the research is to determine whether the education that prospective teachers in different fields receive is related to their levels of problem solving skills and self-confidence. Within the mentioned framework, the prospective teachers' problem solving and self-confidence levels have been examined under several variables.…
Solving Word Problems in the Primary Grades: Addition and Subtraction.
ERIC Educational Resources Information Center
Feinberg, Miriam M.
The purpose of this manual is to present a series of lessons on solving word problems, each focusing on a specific concept. The solving of story problems should be incorporated into the daily mathematics lesson so that children can maintain and increase their skills. The lessons are sequenced according to their complexity. Lessons one through…
Designing Computer Software for Problem-Solving Instruction.
ERIC Educational Resources Information Center
Duffield, Judith A.
Discusses factors that might influence the effectiveness of computer software designed to teach problem solving. Topics discussed include the structure of knowledge; transfer of training; computers and problem solving instruction; human-computer interactions; and types of software, including drill and practice programs, tutorials, instructional…
Measuring Problem Solving with Technology: A Demonstration Study for NAEP
ERIC Educational Resources Information Center
Bennett, Randy Elliot; Persky, Hilary; Weiss, Andy; Jenkins, Frank
This paper describes a study intended to demonstrate how an emerging skill, problem solving with technology, might be measured in the National Assessment of Educational Progress (NAEP). Two computer-delivered assessment scenarios were designed, one on solving science-related problems through electronic information search and the other on solving…
Problem Solving/Decision Making for Social and Academic Success.
ERIC Educational Resources Information Center
Elias, Maurice J.; Tobias, Steven E.
Based on the premise that systematic instruction in social decision-making and problem-solving skills is a developmental right of all children, this book provides an in-service training program for teaching a set of social decision-making and problem-solving steps that are essential for success in school, in the family, with friends, in the world…
Use of the Computer in Solving Mathematics Problems.
ERIC Educational Resources Information Center
Brooks, Sarah
Computer programing and problem-solving steps in mathematics are viewed to have related concepts. Some heuristics are compared with some suggestions for structured programing. The one fundamental difference between problem solving in general and when using the computer is seen as the computer solution must be finite. The computer is viewed as a…
Introduction to LogoWriter and Problem Solving for Educators.
ERIC Educational Resources Information Center
Yoder, Sharon Burrowes; Moursund, Dave
This book about Logo programming and problem solving is designed to introduce preservice and inservice teachers to problem solving in a Logo programming environment. Such a unit of study can be an important part of an introductory computers in education course for educators. Although Logowriter--a version of Logo--was developed by Logo Computer…
Engineering students' experiences and perceptions of workplace problem solving
NASA Astrophysics Data System (ADS)
Pan, Rui
In this study, I interviewed 22 engineering Co-Op students about their workplace problem solving experiences and reflections and explored: 1) Of Co-Op students who experienced workplace problem solving, what are the different ways in which students experience workplace problem solving? 2) How do students perceive a) the differences between workplace problem solving and classroom problem solving and b) in what areas are they prepared by their college education to solve workplace problems? To answer my first research question, I analyzed data through the lens of phenomenography and I conducted thematic analysis to answer my second research question. The results of this study have implications for engineering education and engineering practice. Specifically, the results reveal the different ways students experience workplace problem solving, which provide engineering educators and practicing engineers a better understanding of the nature of workplace engineering. In addition, the results indicate that there is still a gap between classroom engineering and workplace engineering. For engineering educators who aspire to prepare students to be future engineers, it is imperative to design problem solving experiences that can better prepare students with workplace competency.
Problem Solving and Collaboration Using Mobile Serious Games
ERIC Educational Resources Information Center
Sanchez, Jaime; Olivares, Ruby
This paper presents the results obtained with the implementation of a series of learning activities based on Mobile Serious Games (MSGs) for the development of problem solving and collaborative skills in Chilean 8th grade students. Three MSGs were developed and played by teams of four students in order to solve problems collaboratively. A…
The Utilization of Problem Solving for the Disabled.
ERIC Educational Resources Information Center
Cardon, Phillip L.; Scott, Michael L.
The problem-solving process has contributed greatly to the field of technology education and can be used to assist persons with disabilities. One problem-solving design that can help in working with persons with disabilities is the "Engineering for Success" design. This model groups technology education students with teachers of special education…
Problem Solving in Technology Education: A Taoist Perspective.
ERIC Educational Resources Information Center
Flowers, Jim
Offers a new approach to teaching problem solving in technology education that encourages students to apply problem-solving skills to improving the human condition. Suggests that technology teachers incorporate elements of a Taoist approach in teaching by viewing technology as a tool with a goal of living a harmonious life. (JOW)
Toward Group Problem Solving Guidelines for 21st Century Teams
ERIC Educational Resources Information Center
Ranieri, Kathryn L.
Effective problem-solving skills are critical in dealing with ambiguous and often complex issues in the present-day leaner and globally diverse organizations. Yet respected, well-established problem-solving models may be misaligned within the current work environment, particularly within a team context. Models learned from a more bureaucratic,…
Problem Solving, Reasoning, and Analytical Thinking in a Classroom Environment
ERIC Educational Resources Information Center
Robbins, Joanne K.
Problem solving, reasoning, and analytical thinking are defined and described as teachable repertoires. This paper describes work performed at a school serving special needs children, Morningside Academy, that has resulted in specific procedures developed over the past 15 years. These procedures include modifying "Think Aloud Pair Problem Solving"…
Students THINK: A Framework for Improving Problem Solving
ERIC Educational Resources Information Center
Thomas, Kelli R.
This article presents the results of research about students' and teachers' use of an interaction framework (THINK) to guide group communication about problem solving. Students who used the THINK framework demonstrated greater gains in problem-solving achievement than students who did not use the framework.
Extricating Justification Scheme Theory in Middle School Mathematical Problem Solving
ERIC Educational Resources Information Center
Matteson, Shirley; Capraro, Mary Margaret; Capraro, Robert M.; Lincoln, Yvonna S.
Twenty middle grades students were interviewed to gain insights into their reasoning about problem-solving strategies using a Problem Solving Justification Scheme as our theoretical lens and the basis for our analysis. The scheme was modified from the work of Harel and Sowder (1998) making it more broadly applicable and accounting for research…
Social Problem Solving and Health Behaviors of Undergraduate Students.
ERIC Educational Resources Information Center
Elliott, Timothy R.; And Others
Examines the relationship of social problem solving to health behaviors as reported by 126 undergraduate students. Findings revealed significant relationships between elements of social problem solving and wellness and accident prevention behaviors, and traffic and substance risk taking. However, correlations revealed differences between men and…
Connectedness Indicators and the Prediction of Problem Solving Success
ERIC Educational Resources Information Center
Yu-Shattuck, Sharon X.
In this study, it was hypothesized that problem solving success is dependent upon two related but district types of mathematical knowledge, content indicators and connectedness indicators. Results did indeed display that the problem solving success of 188 undergraduate students was related to these two indicators. The correlations of content…
Autobiographical Memory and Social Problem-Solving in Asperger Syndrome
ERIC Educational Resources Information Center
Goddard, Lorna; Howlin, Patricia; Dritschel, Barbara; Patel, Trishna
Difficulties in social interaction are a central feature of Asperger syndrome. Effective social interaction involves the ability to solve interpersonal problems as and when they occur. Here we examined social problem-solving in a group of adults with Asperger syndrome and control group matched for age, gender and IQ. We also assessed…
The Relationship between Students' Problem Solving Frames and Epistemological Beliefs
ERIC Educational Resources Information Center
Wampler, Wendi N.
Introductory undergraduate physics courses aim to help students develop the skills and strategies necessary to solve complex, real world problems, but many students not only leave these courses with serious gaps in their conceptual understanding, but also maintain a novice-like approach to solving problems. "Matter and Interactions"…
Problem-solving skills in high school biology: The effectiveness of the IMMEX problem-solving assessment software
NASA Astrophysics Data System (ADS)
Palacio-Cayetano, Joycelin
"Problem-solving through reflective thinking should be both the method and valuable outcome of science instruction in America's schools" proclaimed John Dewey (Gabel, 1995). If the development of problem-solving is a primary goal of science education, more problem-solving opportunities must be an integral part of K-16 education. To examine the effective use of technology in developing and assessing problem-solving skills, a problem-solving authoring, learning, and assessment software, the UCLA IMMEX Program-Interactive Multimedia Exercises-was investigated. This study was a twenty-week quasi-experimental study that was implemented as a control-group time series design among 120 tenth grade students. Both the experimental group (n = 60) and the control group (n = 60) participated in a problem-based learning curriculum; however, the experimental group received regular intensive experiences with IMMEX problem-solving and the control group did not. Problem-solving pretest and posttest were administered to all students. The instruments used were a 35-item Processes of Biological Inquiry Test and an IMMEX problem-solving assessment test, True Roots. Students who participated in the IMMEX Program achieved significant (p <.05) gains in problem-solving skills on both problem-solving assessment instruments. This study provided evidence that IMMEX software is highly efficient in evaluating salient elements of problem-solving. Outputs of students' problem-solving strategies revealed that unsuccessful problem solvers primarily used the following four strategies: (1) no data search strategy, students simply guessed; (2) limited data search strategy leading to insufficient data and premature closing; (3) irrelevant data search strategy, students focus in areas bearing no substantive data; and (4) extensive data search strategy with inadequate integration and analysis. On the contrary, successful problem solvers used the following strategies; (1) focused search strategy coupled
Behavioral flexibility and problem solving in an invasive bird
Behavioral flexibility is considered an important trait for adapting to environmental change, but it is unclear what it is, how it works, and whether it is a problem solving ability. I investigated behavioral flexibility and problem solving experimentally in great-tailed grackles, an invasive bird species and thus a likely candidate for possessing behavioral flexibility. Grackles demonstrated behavioral flexibility in two contexts, the Aesop's Fable paradigm and a color association test. Contrary to predictions, behavioral flexibility did not correlate across contexts. Four out of 6 grackles exhibited efficient problem solving abilities, but problem solving efficiency did not appear to be directly linked with behavioral flexibility. Problem solving speed also did not significantly correlate with reversal learning scores, indicating that faster learners were not the most flexible. These results reveal how little we know about behavioral flexibility, and provide an immense opportunity for future research to explore how individuals and species can use behavior to react to changing environments. PMID:27168984
Randomized controlled trial of a family problem-solving intervention.
Drummond, Jane; Fleming, Darcy; McDonald, Linda; Kysela, Gerard M
Adaptive problem solving contributes to individual and family health and development. In this article, the effect of the cooperative family learning approach (CFLA) on group family problem solving and on cooperative parenting communication is described. A pretest or posttest experimental design was used. Participant families were recruited from Head Start programs and exhibited two or more risk factors. Participant preschool children were screened to have two or more developmental delays. Direct behavioral observation measures were used to determine group family problem solving and cooperative parenting communication outcomes. Few group family problem-solving behaviors were coded, and they displayed little variability. However, intervention parents increased the length of time they played and extended the cooperative parent-child interactions. The evidence shows that CFLA has the potential to enhance parental-modeling of cooperative behavior while engaged in play activities with preschoolers. Direct measurement of group family problem solving was difficult. Solutions are suggested. PMID:15604228
Autobiographical memory and social problem-solving in Asperger syndrome.
Goddard, Lorna; Howlin, Patricia; Dritschel, Barbara; Patel, Trishna
Difficulties in social interaction are a central feature of Asperger syndrome. Effective social interaction involves the ability to solve interpersonal problems as and when they occur. Here we examined social problem-solving in a group of adults with Asperger syndrome and control group matched for age, gender and IQ. We also assessed autobiographical memory, on a cueing task and during social problem-solving, and examined the relationship between access to specific past experiences and social problem-solving ability. Results demonstrated a social problem-solving impairment in the Asperger group. Their solutions were less detailed, less effective and less extended in time. Autobiographical memory performance was also impaired with significantly longer latencies to retrieve specific memories and fewer specific memories retrieved in comparison to controls. PMID:16874561
Sautter, Rachael A; LeBlanc, Linda A; Jay, Allison A; Goldsmith, Tina R; Carr, James E
We examined whether typically developing preschoolers could learn to use a problem-solving strategy that involved self-prompting with intraverbal chains to provide multiple responses to intraverbal categorization questions. Teaching the children to use the problem-solving strategy did not produce significant increases in target responses until problem solving was modeled and prompted. Following the model and prompts, all participants showed immediate significant increases in intraverbal categorization, and all prompts were quickly eliminated. Use of audible self-prompts was evident initially for all participants, but declined over time for 3 of the 4 children. Within-session response patterns remained consistent with use of the problem-solving strategy even when self-prompts were not audible. These findings suggest that teaching and prompting a problem-solving strategy can be an effective way to produce intraverbal categorization responses. PMID:21709781
Problem Solving in Professional Adult Education.
ERIC Educational Resources Information Center
Commission of Professors of Adult Education.
The papers in the collection reflect areas of concern to adult educators, especially at the university level. The first of the collection's three sections deals with graduate program design and contains three papers: Problems of Graduate Program Design, Wilson B. Thiede, and two reaction papers by John Ohliger and Clive C. Veri. Section 2 on…
Evolutionary strategies for solving optimization problems
NASA Astrophysics Data System (ADS)
Ebeling, Werner; Reimann, Axel; Molgedey, Lutz
We will give a survey of applications of thermodynamically and biologically oriented evolutionary strategies for optimization problems. Primarily, we investigate the solution of discrete optimization problems, most of combinatorial type, using a certain class of coupled differential equations. The problem is to find the minimum on a large set of real numbers (the potential) Ui, defined on the integer set i = 1 ...s, where s is an extremely large nu mber. The stationary states of the system correspond to relative optima on the discrete set. First, several elementary evolutionary strategies are described by simple deterministic equations, leading to a high-dimensional system of coupled differential equations. The known equations for thermodynamic search processes and for simple models of biological evolution are unified by defining a two-parameter family of equations which embed both cases. The unified equations model mixed Boltzmann/Darwin- strategies including basic elements of thermodynamical and biological evolution as well. In a next step a master equation model in the occupation number space is defined. We investigate the transition probabilities and the convergence properties using tools from the theory of stochastic processes. Several examples are analyzed. In particular we study the optimization of theoretical model sequences with simple valuation rules. In order to demonstrate that the strategies developed here may also be used to investigate realistic problems we present an example application to RNA folding (search for a minimum free energy configuration).
Student Ecosystems Problem Solving Using Computer Simulation.
ERIC Educational Resources Information Center
Howse, Melissa A.
The purpose of this study was to determine the procedural knowledge brought to, and created within, a pond ecology simulation by students. Environmental Decision Making (EDM) is an ecosystems modeling tool that allows users to pose their own problems and seek satisfying solutions. Of specific interest was the performance of biology majors who had…
Professional Development: How Young Children Solve Problems
ERIC Educational Resources Information Center
Shure, Myrna B.
There are lots of ways to handle behavior problems in the classroom. Some teachers send difficult children to time out, others tell them what and what not to do, and many explain why. But these techniques have one thing in common: they all do the thinking for the child. In this article, the author discusses how to help children handle conflicts…
Sociodrama: Group Creative Problem Solving in Action.
ERIC Educational Resources Information Center
Riley, John F.
Sociodrama is presented as a structured, yet flexible, method of encouraging the use of creative thinking to examine a difficult problem. An example illustrates the steps involved in putting sociodrama into action. Production techniques useful in sociodrama include the soliloquy, double, role reversal, magic shop, unity of opposites, and audience…
Solving Connected Subgraph Problems in Wildlife Conservation
NASA Astrophysics Data System (ADS)
Dilkina, Bistra; Gomes, Carla P.
We investigate mathematical formulations and solution techniques for a variant of the Connected Subgraph Problem. Given a connected graph with costs and profits associated with the nodes, the goal is to find a connected subgraph that contains a subset of distinguished vertices. In this work we focus on the budget-constrained version, where we maximize the total profit of the nodes in the subgraph subject to a budget constraint on the total cost. We propose several mixed-integer formulations for enforcing the subgraph connectivity requirement, which plays a key role in the combinatorial structure of the problem. We show that a new formulation based on subtour elimination constraints is more effective at capturing the combinatorial structure of the problem, providing significant advantages over the previously considered encoding which was based on a single commodity flow. We test our formulations on synthetic instances as well as on real-world instances of an important problem in environmental conservation concerning the design of wildlife corridors. Our encoding results in a much tighter LP relaxation, and more importantly, it results in finding better integer feasible solutions as well as much better upper bounds on the objective (often proving optimality or within less than 1% of optimality), both when considering the synthetic instances as well as the real-world wildlife corridor instances.
Solving the 10 Most Common Carpet Problems.
ERIC Educational Resources Information Center
Hilton, Michael
Identifies the 10 most common carpet problems in school facilities and offers solutions. These include: transition areas, moisture, spot removal, recurring spots, cleaning agents, allergens, wicking, biological contamination, equipment selection, and cleaning methods. Ensuring a successful maintenance program results in satisfactory appearance,…
Modeling crowdsourcing as collective problem solving
Guazzini, Andrea; Vilone, Daniele; Donati, Camillo; Nardi, Annalisa; Levnajić, Zoran
Crowdsourcing is a process of accumulating the ideas, thoughts or information from many independent participants, with aim to find the best solution for a given challenge. Modern information technologies allow for massive number of subjects to be involved in a more or less spontaneous way. Still, the full potentials of crowdsourcing are yet to be reached. We introduce a modeling framework through which we study the effectiveness of crowdsourcing in relation to the level of collectivism in facing the problem. Our findings reveal an intricate relationship between the number of participants and the difficulty of the problem, indicating the optimal size of the crowdsourced group. We discuss our results in the context of modern utilization of crowdsourcing. PMID:26552943
Modeling crowdsourcing as collective problem solving
NASA Astrophysics Data System (ADS)
Guazzini, Andrea; Vilone, Daniele; Donati, Camillo; Nardi, Annalisa; Levnajić, Zoran
Crowdsourcing is a process of accumulating the ideas, thoughts or information from many independent participants, with aim to find the best solution for a given challenge. Modern information technologies allow for massive number of subjects to be involved in a more or less spontaneous way. Still, the full potentials of crowdsourcing are yet to be reached. We introduce a modeling framework through which we study the effectiveness of crowdsourcing in relation to the level of collectivism in facing the problem. Our findings reveal an intricate relationship between the number of participants and the difficulty of the problem, indicating the optimal size of the crowdsourced group. We discuss our results in the context of modern utilization of crowdsourcing.
Modeling crowdsourcing as collective problem solving.
Guazzini, Andrea; Vilone, Daniele; Donati, Camillo; Nardi, Annalisa; Levnajić, Zoran
Crowdsourcing is a process of accumulating the ideas, thoughts or information from many independent participants, with aim to find the best solution for a given challenge. Modern information technologies allow for massive number of subjects to be involved in a more or less spontaneous way. Still, the full potentials of crowdsourcing are yet to be reached. We introduce a modeling framework through which we study the effectiveness of crowdsourcing in relation to the level of collectivism in facing the problem. Our findings reveal an intricate relationship between the number of participants and the difficulty of the problem, indicating the optimal size of the crowdsourced group. We discuss our results in the context of modern utilization of crowdsourcing. PMID:26552943
Cognitive functioning in mathematical problem solving during early adolescence
NASA Astrophysics Data System (ADS)
Collis, Kevin F.; Watson, Jane M.; Campbell, K. Jennifer
Problem-solving in school mathematics has traditionally been considered as belonging only to the concrete symbolic mode of thinking, the mode which is concerned with making logical, analytical deductions. Little attention has been given to the place of the intuitive processes of the ikonic mode. The present study was designed to explore the interface between logical and intuitive processes in the context of mathematical problem solving. Sixteen Year 9 and 10 students from advanced mathematics classes were individually assessed while they solved five mathematics problems. Each student's problem-solving path, for each problem, was mapped according to the type of strategies used. Strategies were broadly classified into Ikonic (IK) or Concrete Symbolic (CS) categories. Students were given two types of problems to solve: (i) those most likely to attract a concrete symbolic approach; and (ii) problems with a significant imaging or intuitive component. Students were also assessed as to the vividness and controllability of their imaging ability, and their creativity. Results indicated that the nature of the problem is a basic factor in determining the type of strategy used for its solution. Students consistently applied CS strategies to CS problems, and IK strategies to IK problems. In addition, students tended to change modes significantly more often when solving CS-type problems than when solving IK-type problems. A switch to IK functioning appeared to be particularly helpful in breaking an unproductive set when solving a CS-type problem. Individual differences in strategy use were also found, with students high on vividness of imagery using IK strategies more frequently than students who were low on vividness. No relationship was found between IK strategy use and either students' degree of controllability of imagery or their level of creativity. The instructional implications of the results are discussed.
Escaping mental fixation: incubation and inhibition in creative problem solving.
Koppel, Rebecca H; Storm, Benjamin C
The inhibition underlying retrieval-induced forgetting has been argued to play a crucial role in the ability to overcome interference in memory and cognition. Supporting this conjecture, recent research has found that participants who exhibit greater levels of retrieval-induced forgetting are better at overcoming fixation on the Remote Associates Test (RAT) than are participants who exhibit reduced levels of retrieval-induced forgetting. If the ability to inhibit inappropriate responses improves the ability to solve fixated RAT problems, then reducing the fixation caused by inappropriate responses should reduce the correlation between retrieval-induced forgetting and problem solving. We tested this hypothesis by inserting an incubation period between two 30-second problem-solving attempts: half of the participants were given an incubation period (distributed condition), half were not (continuous condition). In the continuous condition retrieval-induced forgetting correlated positively with problem-solving performance during both the initial and final 30 seconds of problem solving. In the distributed condition retrieval-induced forgetting only correlated with problem-solving performance during the first 30 seconds of problem solving. This finding suggests that incubation reduces the need for inhibition by reducing the extent to which problem solvers suffer fixation. PMID:23607286
Impacts of Learning Inventive Problem-Solving Principles: Students' Transition from Systematic Searching to Heuristic Problem Solving
ERIC Educational Resources Information Center
Barak, Moshe
This paper presents the outcomes of teaching an inventive problem-solving course in junior high schools in an attempt to deal with the current relative neglect of fostering students' creativity and problem-solving capabilities in traditional schooling. The method involves carrying out systematic manipulation with attributes, functions and…
The Effects of a Problem Solving Intervention on Problem Solving Skills of Students with Autism during Vocational Tasks
ERIC Educational Resources Information Center
Yakubova, Gulnoza
Problem solving is an important employability skill and considered valuable both in educational settings (Agran & Alper, 2000) and the workplace (Ju, Zhang, & Pacha, 2012). However, limited research exists instructing students with autism to engage in problem solving skills (e.g., Bernard-Opitz, Sriram, & Nakhoda-Sapuan, 2001). The…
A Study of the Problem Solving Abilities of Seventh Grade Students Who Receive Anchored Problem Solving Instruction.
ERIC Educational Resources Information Center
Griesser, Sara Anne
Current mathematics education emphasizes the importance of a problem solving mindset in the classroom. Students need to know how they are going to use what they are learning in real life. The purpose of this study was to determine the effect of anchored problem solving instruction on middle school students' mathematical abilities. The researcher…
The Effects of Pair Problem Solving Technique Incorporating Polya's Problem Solving Strategy on Undergraduate Students' Performance in Chemistry
ERIC Educational Resources Information Center
Bilgin, Ibrahim
The purpose of this study was to investigate the effects of pair problem solving technique incorporating Polya's problem solving strategy on undergraduate students' performance in conceptual and algorithmic questions in chemistry. The subjects of this study were 89 students enrolled from two first year chemistry classes. The experimental group was…
Effects of the Problem Solving and Subject Matter Approaches on the Problem Solving Ability of Secondary School Agricultural Education
ERIC Educational Resources Information Center
Olowa, O. W.
The approach used by teachers is very important to the success of the teaching process. This is why this study seeks to determine which teaching approaches--problem solving and subject-matter, would best improve the problem solving ability of selected secondary agricultural education students in Ikorodu Local Government Area. Ten classes and 150…
Swinging into thought: directed movement guides insight in problem solving.
Thomas, Laura E; Lleras, Alejandro
Can directed actions unconsciously influence higher order cognitive processing? We investigated how movement interventions affected participants' ability to solve a classic insight problem. The participants attempted to solve Maier's two-string problem while occasionally taking exercise breaks during which they moved their arms either in a manner related to the problem's solution (swing group) or in a manner inconsistent with the solution (stretch group). Although most of the participants were unaware of the relationship between their arm movement exercises and the problem-solving task, the participants who moved their arms in a manner that suggested the problem's solution were more likely to solve the problem than were those who moved their arms in other ways. Consistent with embodied theories of cognition, these findings show that actions influence thought and, furthermore, that we can implicitly guide people toward insight by directing their actions. PMID:19648458
Problem solving performance and learning strategies of undergraduate students who solved microbiology problems using IMMEX educational software
NASA Astrophysics Data System (ADS)
Ebomoyi, Josephine Itota
The objectives of this study were as follows: (1) Determine the relationship between learning strategies and performance in problem solving, (2) Explore the role of a student's declared major on performance in problem solving, (3) Understand the decision making process of high and low achievers during problem solving. Participants (N = 65) solved problems using the Interactive multimedia exercise (IMMEX) software. All participants not only solved "Microquest," which focuses on cellular processes and mode of action of antibiotics, but also "Creeping Crud," which focuses on the cause, origin and transmission of diseases. Participants also responded to the "Motivated Strategy Learning Questionnaire" (MSLQ). Hierarchical multiple regression was used for analysis with GPA (Gracie point average) as a control. There were 49 (78.6%) that successfully solved "Microquest" while 52 (82.5%) successfully solved "Creeping Crud". Metacognitive self regulation strategy was significantly (p < .10) related to ability to solve "Creeping Crud". Peer learning strategy showed a positive significant (p < .10) relationship with scores obtained from solving "Creeping Crud". Students' declared major made a significant (p < .05) difference on the ability to solve "Microquest". A subset (18) volunteered for a think aloud method to determine decision-making process. High achievers used fewer steps, and had more focused approach than low achievers. Common strategies and attributes included metacognitive skills, writing to keep track, using prior knowledge. Others included elements of frustration/confusion and self-esteem problems. The implications for educational and relevance to real life situations are discussed.
Solving SAT Problem Based on Hybrid Differential Evolution Algorithm
NASA Astrophysics Data System (ADS)
Liu, Kunqi; Zhang, Jingmin; Liu, Gang; Kang, Lishan
Satisfiability (SAT) problem is an NP-complete problem. Based on the analysis about it, SAT problem is translated equally into an optimization problem on the minimum of objective function. A hybrid differential evolution algorithm is proposed to solve the Satisfiability problem. It makes full use of strong local search capacity of hill-climbing algorithm and strong global search capability of differential evolution algorithm, which makes up their disadvantages, improves the efficiency of algorithm and avoids the stagnation phenomenon. The experiment results show that the hybrid algorithm is efficient in solving SAT problem.
A dependency-based modelling mechanism for problem solving
NASA Technical Reports Server (NTRS)
London, P.
The paper develops a technique of dependency net modeling which relies on an explicit representation of justifications for beliefs held by the problem solver. Using these justifications, the modeling mechanism is able to determine the relevant lines of inference to pursue during problem solving. Three particular problem-solving difficulties which may be handled by the dependency-based technique are discussed: (1) subgoal violation detection, (2) description binding, and (3) maintaining a consistent world model.
An amoeboid algorithm for solving linear transportation problem
NASA Astrophysics Data System (ADS)
Gao, Cai; Yan, Chao; Zhang, Zili; Hu, Yong; Mahadevan, Sankaran; Deng, Yong
Transportation Problem (TP) is one of the basic operational research problems, which plays an important role in many practical applications. In this paper, a bio-inspired mathematical model is proposed to handle the Linear Transportation Problem (LTP) in directed networks by modifying the original amoeba model Physarum Solver. Several examples are used to prove that the provided model can effectively solve Balanced Transportation Problem (BTP), Unbalanced Transportation Problem (UTP), especially the Generalized Transportation Problem (GTP), in a nondiscrete way.
Earth rotation: Solved and unsolved problems
NASA Astrophysics Data System (ADS)
Cazenave, A.; Paquet, P.
A workshop dedicated to earth rotation problems was held in Bonas, France, June 11-13, 1985. It was organized by the North Atlantic Treaty Organization (NATO) Scientific Affairs Division and the Council of Europe and was attended by 39 participants from eight different countries.In the last 10 years, extremely precise measurements of the earth's rotation parameters and new global geophysical data have become available, allowing major advances to be made in the understanding of the various irregularities affecting the earth's rotation. The aim of this workshop was to bring together scientists who have made important contributions in this field during the last decade, both at the observational and geophysical interpretation levels. The first session was dedicated to the definition, implementation, and maintenance of the terrestrial and celestial reference systems.
Towards solving the pulsar timing sampling problem
NASA Astrophysics Data System (ADS)
van Haasteren, Rutger; Ellis, Justin; Vallisneri, Michele; Nanograv Collaboration
Bayesian data analysis of Pulsar Timing Array (PTA) has proved to be a computationally challenging problem, with scaling relations that are super-linear in both the number of pulsars and the number of model parameters. Thus far, our best models cannot be used when analyzing full (international) pulsar timing array datasets in the search for gravitational waves, and shortcuts always need to be made. A promising approach in the literature, based on Hamiltonian sampling techniques, has been shown to be infeasible in realistic datasets due to phase transition behavior of the likelihood. We have introduced a coordinate transformation that mitigates this phase transition behavior, and makes Hamiltonian sampling efficient. This makes a full (stochastic) gravitational-wave search in pulsar timing data feasible with our most up-to-date models. This method scales almost linearly with the number of pulsars. Supported by NASA through Einstein fellowship PF3-140116.
Fedorov's attempt to solve the nutation problem
NASA Astrophysics Data System (ADS)
Yatskiv, Ya. S.
First of all a brief history of the investigation of nutation carried out before Fedorov's first studies of this problem is presented. Afterwards the main attention is paid to the Fedorov's determination of corrections to nutation coefficients from latitude observations and to the Fedorov's theory of nutation of a perfectly elastic Earth. Fedorov showed that elastic deformations do not virtually affect the motion of the axis of angular momentum in space, i.e. the nutation of this axis. At the same time they diminish the coefficients of the expression of forced nearly diurnal motion of the pole, the so-called Oppolzer terms. Therefore Fedorov compared the expression of these terms for a perfectly elastic Earth with observations and stated: - the Earth as a whole is not a perfectly elastic body: - the theory of nutation of the Earth consisting of an elastic mantle and a fluid core has not been developed to a degree such that it is possible to test this theory by observations.
Methodologies for examining problem solving success and failure.
DeCaro, Marci S; Wieth, Mareike; Beilock, Sian L
When designing research to examine the variables underlying creative thinking and problem solving success, one must not only consider (a) the demands of the task being performed, but (b) the characteristics of the individual performing the task and (c) the constraints of the skill execution environment. In the current paper we describe methodologies that allow one to effectively study creative thinking by capturing interactions among the individual, task, and problem solving situation. In doing so, we demonstrate that the relation between executive functioning and problem solving success is not always as straightforward as one might initially believe. PMID:17434416
Surveying Turkish high school and university students' attitudes and approaches to physics problem solving
NASA Astrophysics Data System (ADS)
Balta, Nuri; Mason, Andrew J.; Singh, Chandralekha
Students' attitudes and approaches to physics problem solving can impact how well they learn physics and how successful they are in solving physics problems. Prior research in the U.S. using a validated Attitude and Approaches to Problem Solving (AAPS) survey suggests that there are major differences between students in introductory physics and astronomy courses and physics experts in terms of their attitudes and approaches to physics problem solving. Here we discuss the validation, administration, and analysis of data for the Turkish version of the AAPS survey for high school and university students in Turkey. After the validation and administration of the Turkish version of the survey, the analysis of the data was conducted by grouping the data by grade level, school type, and gender. While there are no statistically significant differences between the averages of various groups on the survey, overall, the university students in Turkey were more expertlike than vocational high school students. On an item by item basis, there are statistically differences between the averages of the groups on many items. For example, on average, the university students demonstrated less expertlike attitudes about the role of equations and formulas in problem solving, in solving difficult problems, and in knowing when the solution is not correct, whereas they displayed more expertlike attitudes and approaches on items related to metacognition in physics problem solving. A principal component analysis on the data yields item clusters into which the student responses on various survey items can be grouped. A comparison of the responses of the Turkish and American university students enrolled in algebra-based introductory physics courses shows that on more than half of the items, the responses of these two groups were statistically significantly different, with the U.S. students on average responding to the items in a more expertlike manner.
Human problem solving performance in a fault diagnosis task
NASA Technical Reports Server (NTRS)
Rouse, W. B.
It is proposed that humans in automated systems will be asked to assume the role of troubleshooter or problem solver and that the problems which they will be asked to solve in such systems will not be amenable to rote solution. The design of visual displays for problem solving in such situations is considered, and the results of two experimental investigations of human problem solving performance in the diagnosis of faults in graphically displayed network problems are discussed. The effects of problem size, forced-pacing, computer aiding, and training are considered. Results indicate that human performance deviates from optimality as problem size increases. Forced-pacing appears to cause the human to adopt fairly brute force strategies, as compared to those adopted in self-paced situations. Computer aiding substantially lessens the number of mistaken diagnoses by performing the bookkeeping portions of the task.
Cognitive Backgrounds of Problem Solving: A Comparison of Open-Ended vs. Closed Mathematics Problems
ERIC Educational Resources Information Center
Bahar, Abdulkadir; Maker, C. June
Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of elementary…
Assessing Student Written Problem Solutions: A Problem-Solving Rubric with Application to Introductory Physics
ERIC Educational Resources Information Center
Docktor, Jennifer L.; Dornfeld, Jay; Frodermann, Evan; Heller, Kenneth; Hsu, Leonardo; Jackson, Koblar Alan; Mason, Andrew; Ryan, Qing X.; Yang, Jie
Problem solving is a complex process valuable in everyday life and crucial for learning in the STEM fields. To support the development of problem-solving skills it is important for researchers and curriculum developers to have practical tools that can measure the difference between novice and expert problem-solving performance in authentic…
Developing Metacognitive and Problem-Solving Skills through Problem Manipulation
ERIC Educational Resources Information Center
Parker Siburt, Claire J.; Bissell, Ahrash N.; Macphail, Richard A.
In a collaborative effort between the our university's department of chemistry and the academic resource center, we designed a model for general chemistry recitation based on a problem manipulation method in which students actively assess the skills and knowledge used to answer a chemical problem and then manipulate the problem to create a new…