Pat Thompson researches teaching and learning mathematics. Current projects are an investigation of high school mathematics teachers’ mathematical meanings for teaching, an investigation of the teaching and learning of calculus, and the creation of a new calculus curriculum. All three projects build on his theoretical and empirical work on quantitative reasoning as a foundation for algebra and calculus. His theory of quantitative reasoning addresses the cognitive foundations of reasoning concretely and abstractly about situations, which entails understanding ways that individuals create mathematical models by using various representational systems in conceiving and expressing quantities and relationships among them. Thompson’s theories are being used by many researchers around the world, both in their own research and in the design of curricular and instructional materials.
Thompson, P. W., & Milner, F. (in press). Teachers’ meanings for function and function notation in South Korea and the United States. In H.-G. Weigand, W. McCallum, M. Menghini, M. Neubrand & G. Schubring (Eds.), The Legacy of Felix Klein - looking back and looking ahead [tentative]. Berlin: Springer.
Moore, K. C., & Thompson, P. W. (in press). Ideas of calculus, and graphs as emergent traces. Paper presented at the 13th International Congress on Mathematical Education, Hamburg, Germany.
Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 421-456). Reston, VA: National Council of Teachers of Mathematics.
Thompson, P. W., & Dreyfus, T. (2016). A coherent approach to the Fundamental Theorem of Calculus using differentials. In R. Göller, R. Biehler & R. Hochsmuth (Eds.), Proceedings of the Conference on Didactics of Mathematics in HIgher Education as a Scientific Discipline, pp. 355-359). Hannover, Germany: KHDM.
Thompson, P. W. (2016). Researching mathematical meanings for teaching. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (pp. 435-461). New York: Taylor & Francis.
Yoon, H., Byerley, C., & Thompson, P. W. (2015). Teachers’ meanings for average rate of change in U.S.A. and Korea. In T. Fukawa-Connelly, N. E. Infante, K. Keene & M. Zandieh (Eds.), Proceedings of the 18th Meeting of the MAA Special Interest Group on Research in Undergraduate Mathematics Education (Vol 1, pp. 335-348). Pittsburgh, PA: RUME.
Thompson, P. W. (2015). Mathematical meanings of Korean and USA mathematics teachers for mathematical ideas they teach. In O. N. Kwon (Ed.), Proceedings of the Korean Society of Mathematics Education International Conference on Mathematics Education, pp. 1-6). Seoul, Korea: Seoul National University.
Musgrave, S., Hatfield, N., & Thompson, P. W. (2015). Teachers' meanings for the substitution principle. In T. Fukawa-Connelly (Ed.), Proceedings of the 18th Meeting of the MAA Special Interest Group on Research in Undergraduate Mathematics Education, pp. 801-808). Pittsburgh, PA: RUME.
Musgrave, S., Hatfield, N., & Thompson, P. W. (2015). Calculus students' meaning for difference. In T. Fukawa-Connelly, N. E. Infante, K. Keene & M. Zandieh (Eds.), Proceedings of the 18th Meeting of the MAA Special Interest Group on Research in Undergraduate Mathematics Education, pp. 809-814). Pittsburgh, PA: RUME.
Moore, K. C., & Thompson, P. W. (2015). Shape thinking and students' graphing activity. In T. Fukawa-Connelly, N. E. Infante, K. Keene & M. Zandieh (Eds.), Proceedings of the 18th Meeting of the MAA Special Interest Group on Research in Undergraduate Mathematics Education, pp. 782-789). Pittsburgh, PA: RUME.
Joshua, S., Musgrave, S., Hatfield, N., & Thompson, P. W. (2015). Conceptualizing and reasoning with frames of reference. In T. Fukawa-Connelly, N. E. Infante, K. Keene & M. Zandieh (Eds.), Proceedings of the 18th Meeting of the MAA Special Interest Group on Research in Undergraduate Mathematics Education, pp. 31-44). Pittsburgh, PA: RUME.
Saldanha, L., & Thompson, P. W. Conceptual issues in understanding the inner logic of statistical inference: Insights from two teaching experiments. Journal of Mathematical Behavior (2014).
Weber, E., & Thompson, P. W. Students' images of two-variable functions and their graphs. Educational Studies in Mathematics (2014).
Thompson, P. W., Carlson, M. P., Byerley, C., & Hatfield, N. Schemes for thinking with magnitudes: A hypothesis about foundational reasoning abilities in algebra. Epistemic algebra students: Emerging models of students' algebraic reasoning. WISDOMe Monographs (2014).
Byerley, C., & Thompson, P. W. Secondary teachers' relative size schemes. Psychology of Mathematics Education (2014).
Musgrave, S., & Thompson, P. W. Function notation as idiom. Psychology of Mathematics Education (2014).
Thompson, P. W., & Draney, K. A methodology of investigating teachers' mathematical meanings for teaching. Psychology of Mathematics Educaton (2014).
Yoon, H., Hatfield, N., & Thompson, P. W. Teachers' meanings for function notation. Psychology of Mathematics Education (2014).
Thompson, P. W. Constructivism in mathematics education. Encyclopedia of Mathematics Education [online] (2013).
Thompson, P. W. Byerley, C. Hatfield, N. A conceptual approach to calculus made possible by technology. Computers in the Schools (2013).
Thompson, P. W. "Why use f(x) when all we really mean is y?". Oncore: The Online Journal of the AAMT (2013).
Thompson, P. W. In the absence of meaning. Vital directions in mathematics education research (2013).
Thompson, P. W., Artigue, M., Törner, G., & de Shalit, E. Collaboration between mathematics and mathematics education. Mathematics and mathematics education: Searching for common ground (2013).
Weber, E., Tallman, M., Byerley, C., Thompson, P. W. Introducing the derivative via calculus triangles. The Mathematics Teacher (2012).
Thompson, P. W. Advances in research on quantitative reasoning. Quantitative reasoning: Current state of understanding. WISDOMe Monographs (Vol. 2) (2012).
Byerley, C. Hatfield, N. Thompson, P. W. Calculus student understandings of division and rate. Mathematical Association of America, Special Interest Group on Research in Undergraduate Mathematics Education (2012).
Thompson, P. W. Quantitative reasoning and mathematical modeling. New perspectives and directions for collaborative research in mathematics education (2011).
Hitt, Fernando Holton, Derek Thompson, Patrick W. Research in Collegiate Mathematics Education VII (Issues in Mathematics Education, Vol. 16). (2010).
Thompson, P. W. Foreword. Children's fraction knowledge (2010).
Y Liu, Patrick Thompson. Mathematics teachers' understandings of proto-hypothesis testing. Pedagogies (2009).
Silverman, Jason Thompson, Patrick W. Toward a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education (2008).
Thompson, Patrick W. On professional judgment and the National Mathematics Panel report. Educational Researcher (2008).
Oehrtman, Mike Carlson, Marilyn P Thompson, Patrick W. Foundational reasoning abilities that promote coherence in students' function understanding. Making the Connection: Research to Practice in Undergraduate Mathematics (2008).
Thompson, Patrick W. Carlson, Marilyn P. Silverman, Jason. The concept of accumulation in calculus. Making the Connection: Research to Practice in Undergraduate Mathematics (2008).
Thompson, Patrick W. Conceptual analysis of mathematical ideas: Some spadework at the foundations of mathematics education. International Group for the Psychology of Mathematics Education (2008).
Saldanha, Luis Thompson, Patrick W. Exploring connections between sampling distributions and statistical inference: An analysis of students' engagement and thinking in the context of instruction involving repeated sampling. International Electronic Journal of Mathematics Education (2007).
Y Liu, Patrick Thompson. Teachers' understandings of probability. Cognition and Instruction (2007).
McCallum, William Thompson, Patrick W. Harel, Guershon Blaire, R. Dance, R. Nolan E. Intermediate algebra. Algebra: Gateway to a technological future (2007).
Smith, John P. Thompson, Patrick W. Quantitative reasoning and the development of algebraic reasoning. Algebra in the early grades (2007).
Thompson, Patrick W (Author) ,Liu, Yan (Author) . Intricacies of statistical inference and teachers' understanding of them. Thinking with data (2007).
Thompson, Patrick W. Liu, Yan Saldanha, Luis. Intricacies of statistical inference and teachers' understandings of them. Thinking with data (2007).
Saldanha, L, Thompson, Patrick. Investigating statistical unusualness in the context of resampling. (2006).
Thompson, Patrick, Miller, C. Through the looking glass: Perspectives on the evolution of learning communities through the lens of intersubjectivity. (2006).
Liu, Y, Thompson, Patrick. Understanding margin of error. S. Wilson (2005).
Silverman, J, Thompson, Patrick. Investigating the Relationship Between Pre-Service Teachers' Understandings of Mathematics and their Developing Pedagogy. S. Wilson (2005).
Thompson, Patrick, Liu, Y. Teachers' understanding of hypothesis testing. (2005).
Confrey, Jere Thompson, Patrick W Castillo-Chavez, Carlos Sarri, Don Grouws, Douglas. On evaluating curricular effectiveness: Judging the quality of K-12 mathematics evaluations. (2004).
Confrey, Jere Thompson, P. W. Castillo-Chavez, Carlos Saari, Donald Grouws, Douglas. On evaluating curricular effectiveness: Judging the quality of K-12 mathematics evaluations. (2004).
Liu, Y, Thompson, Patrick. Teachers' personal and pedagogical understanding of probability and statistical inference. PME-NA (2004).
. . Research companion to the NCTM Standards (2003).
L Saldanha, Patrick Thompson. Students' conceptions of samples and their relationship to statistical inference. Educational Studies in Mathematics (2002).
. . Symbolizing and modeling in mathematics education (2002).
Liu, Y, Thompson, Patrick. Randomness: Rethinking the foundations of probability. PME-NA (2002).
Saldanha, L, Thompson, Patrick. Students' scheme-based understanding of sampling distributions and its relationship to statistical inference. (2002).
Patrick Thompson. Holistic perspectives on instructional design [Review of Symbolizing and Communicating in Mathematics Classrooms, P. Cobb, E. Yackel, & K. McClain (Eds.)]. Journal for Research in Mathematics Education (2001).
L Steffe, Patrick Thompson. Interaction or intersubjectivity? A reply to Lerman. Journal for Research in Mathematics Education (2000).
Patrick Thompson. What is required to understand fractal dimension?. Mathematics Educator (2000).
Steffe, L P, Thompson, Patrick W. Radical constructivism in mathematics and science education: Essays in honor of Ernst von Glasersfeld. (2000).
. . Research design in mathematics and science education (2000).
Thompson, Patrick W. Radical constructivism: Reflections and directions. Radical constructivism in action: Building on the pioneering work of Ernst von Glasersfeld (2000).
Thompson, Patrick, Saldanha, L. Conceptual issues in understanding sampling distributions and margins of error. (2000).
Thompson, Patrick, Saldanha, L. Epistemological analyses of mathematical ideas: A research methodology. (2000).
Thompson,Patrick W*. Promoting Excellence in Arizona Middle School Mathematics: Increasing Student Achievement through Systemic Instructional Change. MARICOPA COMMUNITY COLLEGE(3/15/2012 - 2/28/2017).
Thompson,Patrick W*, Ramirez,Nora G. RSC-MSP Training Agreement. CNTY OF MARICOPA-SUPT OF SCHL(2/1/2006 - 1/31/2007).
Thompson, P. W. Hidden Obstacles to Mathematics Education Reform. Association for Public and Land-grant Universities Mathematics Teacher Education Partnerships (Jun 2015).
Thompson, P. W. Making the Fundamental Theorem of Calculus Fundamental to Calculus. International Conference on Mathematics in Undergraduate Study Programs (Dec 2014).
Thompson, P. W. Mathematics Education Reform and the Common Core State Standards. Banquet for Meeting of the Mathematics for America San Diego Chapter (Jan 2014).
Thompson, P. W., Carlson, M. P., Byerley, C., & Hatfield, N. Schemes for thinking about magnitudes. Conference on Epistemic Algebra Students (Jun 2013).
Thompson, P. W. Recognizing proportional relationships: A commentary. Symposium on How Teachers Make Sense of Proportional Situations, NCTM Res Presession (Apr 2013).
Thompson, P. W. Under the Radar: Foundational Meanings that Math Professors (Mistakenly) Assume Students Have. Annual Meeting of the MAA Special Interest Group on Research in Undergraduate Mathematics Education (Feb 2013).
Thompson, P. W. Fostering Students' Critical and Creative Thinking in Mathematics. International Science, Mathematics, and Technology Education Conference (Jan 2013).
Thompson, P. W. A calculus course that focuses on students' understanding of the Fundamental Theorem of Calculus. Invited colloquium for the Department of Mathematics, Virginia Tech (Oct 2012).
Thompson, P. W. High school teachers' mathematical meanings for teaching secondary mathematics. Invited colloquium for the University of Arkansas mathematics department (Oct 2012).
Thompson, P. W. Mathematical MEANINGS for teaching secondary mathematics vs. mathematical KNOWLEDGE for teaching secondary mathematics. Invited colloquium for the Mathematics Education Student Association (Sep 2012).
Thompson, P. W. Assessing high school mathematics teachers' mathematical meanings for teaching secondary mathematics. Invited colloquium for the Mathematics Education Student Association (Sep 2012).
Thompson, P. W. Advances in quantitative reasoning. Conference on Quantitative Reasoning and Mathematical Modeling: A Driver for STEM Integrated Educati (May 2012).
Thompson, P. W. Fractions, units, and the Common Core State Standards. Symposium on Students Fractional Knowledge and the Common Core State Standards, NCTM Res Presession (Apr 2012).
Thompson, P. W. Current thinking on trig concepts worth knowing: This is NOT SOH-CAH-TOA. Symposium on Current Research on the Teaching and Learning of Trigonometry, NCTM Res Presession (Apr 2012).
Thompson, P. W. Finding the common ground. Symposium on Mathematics and Mathematics Education: Toward the Common Ground (Apr 2012).
Thompson, P. W. Byerley, C. Hatfield, N. Muhanraj, H. An approach to calculus made possible by technology. MAA Southwestern Section Joint Meeting (Mar 2012).
Thompson, P. W. A tribute to Judy Sowder. Conference in Honor of Judith Sowder's Retirement (Jan 2012).
Thompson, Patrick W. Quantitative reasoning and mathematical modeling. Invitational planning conference for the Wyoming Institute for the Study and Development of Mathemat (Sep 2011).
Thompson, P. W. Mathematical knowledge for teaching. Annual meeting of the American Educational Research Association (Apr 2011).
Thompson, P. W. A project in Calculus 1. First Year Mathematics Colloquium Series (Apr 2011).
Thompson, P. W. Researching a quantitative approach to learning calculus. Invited Presentation to the Steinhardt School of Culture, Education and Human Development (Apr 2011).
Thompson, Patrick W. Research as professional development: The role of research in reforming mathematics instruction at two-year colleges. American Mathematical Association of Two-Year Colleges (Nov 2010).
Thompson, Patrick W. Rethinking mathematical knowledge for teaching. Research Presession to the annual meeting of the National Council of Teachers of Mathematics (Apr 2010).
Thompson, Patrick W. Miller, Christina Lage-Ramirez, Ana Courtney, Scott. Mathematical Knowledge for Teaching: Its Meaning and Sources. Symposium at the Research Presesession of the annual meeting of the NCTM (Apr 2010).
Thompson, Patrick W. Toward a foundation of mathematics education. Annual Meeting of the American Educational Research Association (Apr 2010).
Thompson, Patrick W. School mathematics is largely useless for learning physics. But it needn't be. Annual Meeting of the American Physical Society (Mar 2010).
Thompson, Patrick W. Millier, Christina. Teaching Mathematics; Teaching Students; Teaching Mathematics to Students: Teachers Trajectories toward Mathematical Knowledge for Teaching. Annual Conference of the National Science Foundation DR-k12 program (Sep 2009).
Thompson, Patrick W. Rate of change and the fundamental theorem of calculus. Institute for Mathematics and Education Workshop on Calculus Learning (Apr 2009).
Thompson, Patrick W. Commentary on the National Mathematics Panel Report. Research Presession to the annual meeting of the National Council of Teachers of Mathematics (Apr 2009).
Thompson, Patrick W. What is "higher" about higher cognition in school students?. National Science Foundation Workshop on Higher Cognition in Adolescents (Sep 2008).
Thompson, Patrick W. Learning without understanding and its implications for the mathematics that teachers teach. Mathematical Association of American MathFest (Jul 2008).
Thompson, Patrick W. Castillo-Garsow, Carlos Moore, Kevin. One approach to a coherent K-12 mathematics. Or, it takes 12 years to learn calculus. Pathways to Algebra Conference (Jun 2008).
Thompson, Patrick W. The problem of scaling up versus the problem of researching the scaling process. Education and Human Services, National Science Foundation (May 2008).
Thompson, Patrick W. Castillo-Garsow, Carlos Miller, Chris Lage Ramirez, Ana McClain, Kay. Affecting teachers' images of what and whom they teach. Research Presession to the Annual Meeting of the National Council of Teachers of Mathematics (Apr 2008).
Thompson, Patrick. Constructivism in Mathematics Education. Presentation to the Japan Society of Mathematics Education (Oct 2007).
Thompson, Patrick. Teaching for Mathematical Literacy. Presentation to the Japan Society of Mathematics Education (Oct 2007).
Thompson, Patrick. Presentation to the National Mathematics Panel. Invited Testimony to the President's National Mathematics Panel (Apr 2007).
Thompson, Patrick, Bloom, Irene, Bowling, Stacey, Castillo-Garsow, Carlos. Affecting Secondary Mathematics Teachers Instructional Practices By Affecting Their Mathematical Knowledge. Conference on Research in Undergraduate Mathematics Education (Feb 2007).
Thompson, Patrick, Carlson, M. Mathematical thinking and intersubjective operatins: A lens on the creation of mathematical learning communities. Research Presession to the Annual Meeting of the National Council of Teachers of Mathematics (Apr 2006).
Thompson, Patrick. Measurement: The lost strand in elementary mathematics. Annual Meeting of the American Educational Research Association (Apr 2006).
Liu, Y, Thompson, Patrick. Teachers' undestandings of probabiltiy and their implications for teacher professinoal development. Annual Meeting of the American Educational Research Association (Apr 2006).
Thompson, Patrick. Where is the mathematics in mathematics education?. 2006 Maseeh Lecture, Portland State University (Mar 2006).
Thompson, Patrick. Democracy and mathematics: The legacy of Jim Kaput in mathematics education research. Conference of the Mathematical Association of America's Special Interest Group on Research on Underg (Feb 2006).
Thompson, Patrick. Affecting mathematics teachers' practices through their mathematical knowledge. 27th Annual Meeting of the International Group for the Psychology of Mathematics Education (Oct 2005).
Thompson, Patrick. Creating data, modeling worlds, changing practices. Research Presession to the Annual Meeting of the National Council of Teachers of Mathematics (Apr 2005).
Thompson, Patrick. Discussant, Symposium on unexpected findings about how young students learn algebra. Research Presession to the Annual Meeting of the National Council of Teachers of Mathematics (Apr 2005).
Carlson, M, Thompson, Patrick. The reflexive relationship between individual cognition and classroom practices: A covariation framework and problem solving research informs calculus instruction. Annual Meeting of the American Educational Research Association (Apr 2005).
Thompson, Patrick. On evaluating curricular effectiveness: Judging the quality of mathematics K-12 curriculum evaluations. Research Presession to the Annual Meeting of the National Council of Teachers of Mathematics (Apr 2005).
Thompson, Patrick. Issues in algebra learning, teaching, and curricula. Annual Meeting of the Appalachian Mathematics and Science Project (Mar 2005).