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# Math Assessment Plan and Course Outcomes ### Mission and Goals

The mission of the Developmental Math Program is to prepare students for success in college-level classes (Developmental Math Program Review). The mission of the College-level Math Program is to give students the mathematical skills and literacy required by their chosen field of study.

### Overview

Assessment of student achievement aims at ensuring that students who pass TMCC math classes possess appropriate mathematical skills and understandings. The collection of retention data aims at increasing the number of students who complete TMCC math courses and sequences.

The department assesses its effectiveness by means of three measures: course retention, successful transition from developmental to collegiate-level classes, and student performance on course-specific learning outcomes.

### Course Retention

Definition and assessment cycle. Course retention is the ratio of student "completers" in a course (defined as having received an A, B, C, or D grade) to the total number of students enrolled in the course. The department strives to increase this ratio from year to year for all its math courses, and in particular for its developmental courses, because attrition—the rate at which students sign up for classes without passing them—is wasteful of time and resources for everyone involved. The assessment cycle is short: retention data is provided to the department on a yearly basis by TMCC's Institutional Research Office.

Assessment of the measure. Course retention figures must be evaluated with care. An instructor who passes 70% of his students in a given course is not a better instructor than one who passes 50% of her students in that course, if only 40% of his students pass the subsequent course in the sequence while 60% of hers pass that subsequent course. Retention figures must therefore be judged over sequences of classes, and retention data is collected for the entire department rather than instructor by instructor.

Closing the loop. Many factors contribute to student attrition. A college's admission and registration policies (e.g., allowing underprepared students to carry large course loads, allowing students who have not passed the prerequisite class into the next class in a sequence, etc.) can unduly place at-risk students in math classes. Students by their own behaviors (e.g., not coming to class and/or not doing the homework) can set themselves up for failure. Poor pedagogical practices (e.g., material covered insufficiently, lack of support, inflexible class policies, etc.) and lack of quality control within the department (e.g., inconsistencies in course delivery and student assessment) can needlessly burden students already struggling to master the material. The department therefore works internally in faculty and policy development and externally with administration and student services to tackle the retention problem on all fronts.

### Successful Transition from Developmental to Collegiate-level Math

Definition and assessment cycle. This measure is computed as follows: a cohort of students who have successfully completed Math 96 (the last developmental math class before college-level math classes) are given three years to successfully complete their first college-level math class (either Math 120 or Math 126); the number of these students who complete either Math 120 or Math 126 is then divided by the number of students in the cohort. Increasing the successful transition from developmental to collegiate-level math is of critical interest to the college because many students fail to graduate due to being short just one math class (hence the dictum "Math is the class that keeps Community College students from graduating"). The assessment cycle for this measure is short: successful transition from developmental to collegiate-level math data is provided to the department on a yearly basis by TMCC's Institutional Research office.

Assessment of the measure. This measure would more accurately gauge how well the department is preparing its developmental students academically for success in college-level math classes if, instead of comparing the number of students in the cohort who complete either Math 120 or Math 126 within three years to the total number of students in the cohort, it compared the number of students in the cohort who complete either Math 120 or Math 126 within three years of having completed Math 96 to the number of students in the cohort who register for Math 120 or Math 126 at TMCC within three years. This modification of the measure would leave out of the sample space students who leave the college or otherwise don't register within three years for a TMCC college-level math class.

Closing the loop. An ACT national survey that included more than one thousand colleges nation-wide placed "inadequate preparation for college work" at the top of the student characteristics contributing the most to student attrition in two-year public colleges ("What Works in Student Retention – Two-Year Public Colleges," ACT 2004). The department considers that its best strategy to help students complete a college-level math class after going through its developmental sequence is to strengthen this sequence so that students going through the sequence will be well-prepared for college-level work.

### Student Performance on Course-specific Student Learning Outcomes

Definition and assessment cycle. The lead faculty for each math course gathers student performance data on specific questions embedded in the final exams given for each class; the results are shared with all instructors who teach the class. The assessment cycle is short: data is collected and shared every year.

Assessment of the measure. This measure directly follows Standard 4.A.3 of the NWCCU. The importance of making sure that students in a given class achieve the learning outcomes for that class cannot be over-emphasized.

Closing the loop. Each semester, each lead instructor makes recommendations for all faculty based on student performance on the questions embedded in all final exams. ### Math Course Outcomes

#### Math 96

• Outcome 1: Students will solve nonlinear equations using analytic methods.
• Outcome 2: Students will use mathematics concepts in real world situations.
• Outcome 3: Students will simplify and perform operations with nonlinear expressions.

#### Math 100

• Outcome 1: Students will apply ratio and proportion to problems in health sciences.
• Outcome 2: Students will convert between metric, household, and Apothecary units.
• Outcome 3: Students will compute dosages.

#### Math 105R

• Outcome 1: Students will use proportions to solve basic problems in radiology.
• Outcome 2: Students will convert between metric and English system units.
• Outcome 3: Students will apply basic algebra and geometry to problems in radiological science.

#### Math 106

• Outcome 1: Students will demonstrate knowledge of the basic concepts of Euclidean geometry.
• Outcome 2: Students will do basic geometrical constructions with a straight edge and ruler.
• Outcome 3: Students will construct simple geometric proofs.

#### Math 107

• Outcome 1: Students will use percentages to solve real estate problems.
• Outcome 2: Students will compute taxes and commissions on a property sale.
• Outcome 3: Students will compute the appreciation and deprecation in property values.

#### Math 108

• Outcome 1: Students will use units correctly and convert between metric and standard units of measurement.
• Outcome 2: Students will use ratio and proportion and simple algebra to solve applied technical problems.
• Outcome 3: Students will apply trigonometry and basic geometry to applied technical problems.

#### Math 120

• Outcome 1: Students will demonstrate the ability to solve financial math problems.
• Outcome 2: Students will demonstrate the ability to solve exponential growth and decay problems.
• Outcome 3: Students will demonstrate the ability to solve basic problems in probability and statistics.

#### Math 122

• Outcome 1: Students will understand numbers, way of representing numbers, relationships among numbers, and number systems.
• Outcome 2: Students will use mathematical models to represent and understand quantitative relationships.
• Outcome 3: Students will communicate their mathematical thinking coherently and clearly to students, peers, and others.

#### Math 123

• Outcome 1: Students will relate geometric ideas to number and measurement ideas.
• Outcome 2: Students will measure/calculate length, perimeter, capacity, weight, area, volume, time, temperature and angle measures.
• Outcome 3: Students will perform Euclidean constructions.

#### Math 126

• Outcome 1: Students will demonstrate the ability to algebraically analyze functions.
• Outcome 2: Students will demonstrate the ability to graphically analyze functions.
• Outcome 3: Students will demonstrate the ability to model real-life scenarios using functions.

#### Math 127

• Outcome 1: Students will demonstrate the ability to solve equations involving trigonometric values.
• Outcome 2: Students will demonstrate the ability to prove trigonometric identities.
• Outcome 3: Students will be able to solve Polar Equations.

#### Math 152

• Outcome 1: Students will demonstrate the ability to use quantitative analysis.
• Outcome 2: Students will demonstrate the ability to use statistical concepts to analyze "real world" issues.
• Outcome 3: Students will demonstrate the ability to summarize and interpret date.

#### Math 181

• Outcome 1: Compute and interpret average rate of change over an interval and instantaneous rate of change for a function at a point.
• Outcome 2: Compute limits of functions as the independent variable approaches some finite value or infinity.
• Outcome 3: Interpret the derivative of a function graphically, numerically and analytically.

#### Math 182

• Outcome 1: Students will gain the ability to evaluate indefinite and definite integrals by selecting and correctly applying appropriate integration techniques(s).
• Outcome 2: Students will be able to develop an appropriate integral form to solve a specific applied problem in geometry, physics, or probability.
• Outcome 3: Students will be able to utilize appropriate theory and computational techniques to construct Taylor series with its interval of convergence for use in a variety of applications such as approximating values of a function, creating series for new functions, and studying the behavior of a function.

#### Math 190

• Outcome 1: Students will simplify circuit diagrams using the rules for capacitors and resistors.
• Outcome 2: Students will use Boolean algebra to design and simplify logic circuits.
• Outcome 3: Students will apply complex numbers to computing the impedance of a circuit.

#### Math 283

• Outcome 1: Students will demonstrate the ability to compute derivatives and integrals of real valued and vector valued functions of several variables.
• Outcome 2: Students will demonstrate the ability to interpret geometrically the derivatives and integrals of real valued and vector valued functions of several variables.
• Outcome 3: Students will demonstrate the ability to apply the techniques of multivariable calculus to problems in mathematics, the physical sciences, and engineering.

#### Math 285

• Outcome 1: Students will demonstrate the ability to formulate models of natural phenomena using differential equations.
• Outcome 2: Students will demonstrate the ability to solve a variety of differential equations analytically and numerically.
• Outcome 3: Students will demonstrate the ability to interpret a differential equation qualitatively.
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