Area of Research Activity

Learning, teaching, curriculum, and professional development in the areas of:

- Algebraic reasoning in elementary and secondary mathematics

- Development of quantitative reasoning in mathematics and science

- Development of teachers’ and students’ understanding of calculus

- Relationships among probabilistic, statistical, and quantitative reasoning

- Technology in learning and teaching mathematics

Education

University of Georgia, 1977 - 1982, Ed.D. Mathematics Education (Dissertation title: A Theoretical Framework for Understanding Young Children’s Concepts of Whole Number Numeration, L. P. Steffe, Advisor.)

University of Georgia, 1975 - 1977, M.Ed. Mathematics Education

Central Washington State College, 1968 - 1972, B.Sc. Mathematics (Cum Laude)

Experience

Professor of Mathematics Education, Arizona State University (2005-Present)

Director of Research, Center for Research on Education in Science, Mathematics, Engineering and Technology; Arizona State University (2005-2008)

Professor of Mathematics Education, Vanderbilt University (1997-2005)

Chair, Department of Teaching and Learning, Peabody College, Vanderbilt University (2000 - 2003)

Founder and co-director, Vanderbilt Program for Talented Youth, (1998-2000)

Professor of Mathematical Sciences, Emeritus, San Diego State University (1999-present)

Director, Joint Ph.D. in Mathematics and Science Education, San Diego State University and University of California, San Diego (1995-1997)

Professor of Mathematical Sciences, San Diego State University (1992-1997)

Associate Professor of Mathematical Sciences, San Diego State University (1990-1992)

Associate Professor of Mathematics, Illinois State University (1985-1990)

Assistant Professor of Mathematical Sciences, San Diego State University (1982-1985)

Lecturer, Department of Mathematical Sciences, San Diego State University (1980-1982)

Research Associate, Department of Mathematics Education, University of Georgia (1977-1980)

Program Mathematics Educator, West African Regional Mathematics Programme, USAID (1973-1975)

Peace Corp Volunteer, Uganda and Sierra Leone (1972-1973)

Honors and Affiliations

Honors

Featured Speaker, International Science, Mathematics, and Technology Education Conference, Bangkok (January, 2013)

Finalist, ASU Parents’ Association Professor of the Year (2011)

Fellow, American Educational Research Association (Elected 2010)

Senior Scholars in Mathematics Education Lecture, Brigham Young University (December 2008)

Featured Guest, Mathematics Education Student Association (November, 2008)

Honored Guest, Japan Society of Mathematics Education, Hiroshima University (September, 2007)

Visiting Scholar, Singapore National Institute of Education (July, 2006)

University of Georgia College of Education Distinguished Alumni Award for Professional Achievement (2006)

Maseeh Lecture, Portland State University (2006)

Fullbright Senior Specialist, Israel. (2004)

Fullbright Senior Specialist, Israel, (2002).

Spencer Mentor for Dissertation Fellow Awardees, Spencer Foundation (2000)

Runner-up, Article of the Year, Journal for Research in Mathematics Education (1994)

Initiative Award. Recognized by Illinois State University for outstanding work in initiating significant research programs. (1987)

Recognition Award for contributions to research in the Illinois State University Laboratory School. (1987)

Leadership Award, San Diego and Imperial Counties Teacher Education and Computer Center. Awarded for outstanding contributions to the improvement of mathematics teaching and learning. (1984)

Offices

Elected

At-large member of the Executive Board, International Group for the Psychology of Mathematics Education – North American Chapter, 1998-2001.

Co-chair, Special Interest Group for Research in Mathematics Education of the American Educational Research Association, 1988-1990

Appointed

Research Advisory Committee of the National Council of Teachers of Mathematics (1993-1996; Chair, 1995-1996)

Co-chair Division C, Section 2 Program Committee of the American Educational Research Association, 1992

National Committees and Advisory Boards

College Board SAT Mathematics Subject Tests Writing Committee (2011-present)

Writing Team, Common Core Career and College Readiness Standards (2009-2010)

Institute for Mathematics Education, University of Arizona (Executive Board, 2007-present)

James J. Kaput Center for Research and Innovation in Mathematics Education (Advisory Board, 2007-present)

Mathematical Association of America, Working Group for Algebra as a Gateway to a Technological Future. (2006)

American Statistical Association, Committee to Establish Guidelines for Statistics in Mathematics Education Research (2004-2006)

National Research Council Committee on Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations (2002-2004)

College Entrance Examining Board, Committee for the Organization of the Graduate Record Exam Quantitative Reasoning Measure (1993-1994)

National and International Plenary Lectures

Thompson, P. W. (2012, April) Mathematics and Mathematics Education. Invited presentation at the International Conference on Mathematics in Mathematics Education, Tel Aviv, Israel.

Thompson, P.W. (2012, January) The Professional Development of Secondary Mathematics Teachers: A Triburte to Judy Sowder. Keynote address at the Conference to Honor the Career of Judith Threadgill-Sowder.

Thompson, P. W. (2010, November). Research as professional development: The role of research in reforming mathematics instruction at two-year colleges. Keynote address given at the annual meeting of the American Mathematical Association of Two-Year Colleges.

Thompson, P. W. (2010, September). Quantitative reasoning and mathematical modeling. Keynote address given at the Invitational Planning Conference for the Wyoming Institute for the Study and Development of Mathematical Education, Laramie, WY.

Thompson, P. W. (2010, March). School mathematics is largely useless for learning physics. But it needn’t be. Keynote address given at the annual meeting of the American Physical Society, Portland, OR.

Thompson, P. W. (2009, April). Rate of change and the fundamental theorem of calculus. Keynote address at the Institute for Mathematics and Education Workshop on Calculus Learning, Tucson, AZ.

Thompson, P. W. (2008, December). In the absence of meaning. Senior Scholars in Mathematics Education Lecture on the Future of Mathematics Education, Brigham Young University.

Thompson, P. W. (2008, November). A unified vision of learning and teaching mathematics K-16. Featured lecture, Mathematics Education Student Association, University of Georgia.

Thompson, P. W. (2008, July). Conceptual analysis of mathematical ideas: Some spadework at the foundations of mathematics education. Plenary paper presented at the Annual Meeting of the International Group for the Psychology of Mathematics Education, Morelia, Mexico.

Thompson, P. W. (2007, September). Constructivism in mathematics education. Japan Society of Mathematics Education, Hiroshima.

Thompson, P. W. (2007, September). A new perspective on mathematical literacy. Japan Society of Mathematics Education, Hiroshima.

Thompson, P. W. ( 2007, February). Epistemology, ontology, and method. Paper delivered at the International Workshop on Guided construction of knowledge in classrooms, Hebrew University, Jerusalem.

Thompson, P. W. (2006, March). Where is the mathematics in mathematics education. Invited address in the Maseeh Lecture Series, Portland State University, Portland, Oregon.

Thompson, P. W. (2006, February). Democracy and mathematics: The legacy of Jim Kaput in mathematics education research. Invited address, Mathematical Association of America Annual Conference on Research in Undergraduate mathematics Education, Rutgers University, Piscataway, NJ.

Thompson, P. W. (2005, February). What it means to understand what it means to understand a mathematical idea deeply. Invited opening address, Mathematical Association of America Annual Conference on Research in Undergraduate Mathematics Education, Phoenix, Arizona.

Thompson, P. W. (2004, June). Cross-talk and miscommunication in teaching mathematics. Invited plenary address given at the Maine Symposium on Research in Mathematics and Science Education, University of Maine, Orono, Maine.

Thompson, P. W. (2004, May). The concept of tool in mathematics teaching. Fullbright lecture given at the Weizmann Institute of Technology, Rehovot, Israel.

Thompson, P. W. (2004, May). The many faces of multiplicative reasoning. Fullbright lecture given at the University of Tel Aviv, Tel Aviv, Israel.

Thompson, P. W. (2004, May). The tangled web of probabilistic reasoning. Fullbright lecture given at the Technion University, Haifa, Israel.

Thompson, P. W. (2002, June). Making sense of interviews. Invited plenary address given at the Conference on The Role of Research in Science and Mathematics Education Reform, Orono, Maine.

Thompson, P. W. (2001, September). What is the probability that Al Gore will be elected President in 2004 given that he lost the 2000 election? Or, why probabilistic reasoning is so hard. Invited opening address, Mathematical Association of America Annual Conference on Research in Undergraduate Mathematics Education, Chicago, Illinois.

Thompson, P. W. (1999). Representations and evolution: A discussion of Duval’s and Kaput’s papers. In F. Hitt (Ed.). Proceedings of the Twenty-first Annual Meeting of the Psychology of Mathematics Education, North America, Plenary Volume. Cuernavaca, Mexico: Centro de Investigación y de Estudios Avanzados.

Thompson, P. W., & Cobb. P. (October, 1998). On relationships between psychological and sociocultural perspectives in mathematics education. Invited plenary address given at the Annual Meeting of the International Group for the Psychology of Mathematics Education – North America. Raleigh, NC.

Thompson, P. W. (1996, November). If you say it, will they hear? Or, the relevance to teaching mathematics of research on mathematics learning and comprehension. Invited featured session at the Annual Meeting of the American Mathematical Association of Two Year Colleges, Long Beach, CA.

Thompson, P. W., & Sfard, A. (October, 1994). Problems of reification: Representations and mathematical objects. Invited plenary address given at the Annual Meeting of the International Group for the Psychology of Mathematics Education – North America. Baton Rouge, LA.

Thompson, P. W. (1994, March) Concepts of Function, Concepts of Rate, and Newton’s Fundamental Theorem of Calculus. Invited plenary address at the Center for Investigations in Mathematics Education, Mexico City.

Thompson, P. W. (1993, January). Students, functions, and the undergraduate mathematics curriculum. Invited plenary address given at the Joint Meeting of the American Mathematical Society and the Mathematical Association of America. San Antonio, TX.

Thompson, P. W. (1984, April). Computer environments for diagnosing concept formation. Invited plenary address given at the Annual Meeting of the Research Council on Diagnostic and Prescriptive Mathematics, San Francisco.

Journal Editorial Activity

Editor

Research in Collegiate Mathematics Education (co-editor, 2006-2008; editor, 2008-present)

Cognition and Instruction (associate editor; 2002-2007)

Journal for Research in Mathematics Education (Appointed 2002; withdrew for health reasons)

Editorial Boards

International Journal of Science and Mathematics Education (2010-2013)

Open Mathematical Education Notes—Online journal of the Scientific Society of Mathematicians of Banja Luka, Bosnia (2010-2013)

Educational Researcher (2000-2003)

Educational Studies in Mathematics (1992-1996; 2000-2004)

International Journal of Computers in Mathematics Learning (1999-present)

Peabody Journal of Education (1997-2005)

Journal of Artificial Intelligence in Education (1989-1992)

Journal of Computers in Mathematics and Science Teaching (1992-1995)

Reviewer

Australian Research Council

Canadian Research Council

Cognition and Instruction

European Journal of Learning and Instruction

Journal for Research in Mathematics Education

Journal of the Learning Sciences

Mathematics Teacher

National Science Foundation:

Applications of Advanced Technology

Research on Learning and Evaluation

Research on Teaching and Learning

Teacher Professional Continuum

Research in Undergraduate Mathematics Education

Spencer Foundation

Memberships in Professional Organizations

American Educational Research Association

Association of Mathematics Teacher Educators

National Council of Teachers of Mathematics

Mathematical Association of America

International Group for the Psychology of Mathematics Education

Publications

Books

Thompson, P. W., Harel, G., & Thomas, M. O. J. The Didactics of Calculus. (in preperation).

Confrey, J., Thompson, P. W., Grouws, D., Saari, D., Castillo-Chavez, C., Schmidt, W., Mahone, C., Valez, W. (2004). On evaluating curricular effectiveness: Judging the quality of K-12 mathematics evaluations. Washington, DC: National Academies Press.

Edited Books

Hitt, F., Holton, D., Thompson, P. W. (Eds.) (2010) Research in Collegiate Mathematics Education VII (Issues in Mathematics Education, Vol. 16). Washington, DC: American Mathematical Society.

Steffe, L. P., & Thompson, P. W. (Eds.), (2000). Radical constructivism in mathematics and science education: Essays in honor of Ernst von Glasersfeld. London: Falmer Press.

Articles in Refereed Journals

Thompson, P. W, Byerley, C., & Hatfield, N. (in press). A conceptual approach to calculus made possible by technology. Computers in the Schools.

Weber, E., Tallman, M., Byerley, C., & Thompson, P. W. (in press). Introducing the derivative via calculus triangles. Mathematics Teacher.

Liu, Y., & Thompson, P. W. (2009). Mathematics teachers' understandings of proto-hypothesis testing. Pedagogies, 4(2), 126-138.

Thompson, P. W. (2008). On professional judgment and the National Mathematics Panel report. Educational Researcher, 37(9), 582-587.

Silverman, J., & Thompson, P. W. (2008). Toward a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11, 499-511.

Thompson, P. W., Carlson, M. P., & Silverman, J. (2007). The design of tasks in support of teachers’ development of coherent mathematical meanings. Journal of Mathematics Teacher Education, 10, 415-432.

Liu, Y., & Thompson, P. W. (2007). Teachers’ understandings of probability. Cognition and Instruction, 25(2-3), 113-160.

Saldanha, L. A. and Thompson, P. W. (2007). 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, 2(3), 270-297.

Saldanha, L., & Thompson, P. W. (2002). Students’ conceptions of samples and their relationship to statistical inference. Educational Studies in Mathematics, 51(3), 257-270.

Thompson, P. W. (2001). 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.

Thompson, P. W. (2000). What is required to understand fractal dimension? Mathematics Educator, 10(2), 33-35.

Steffe, L. P., & Thompson, P. W. (2000). Interaction or intersubjectivity? A reply to Lerman. Journal for Research in Mathematics Education, 31(2), 191-209.

Thompson, A. G., & Thompson, P. W. (1996, January). Talking about rates conceptually, Part II: Mathematical knowledge for teaching. Journal for Research in Mathematics Education, 27(1), 2-24.

Dugdale, S., Thompson, P. W., et. al (1995). Technology and algebra curriculum reform: Current issues, potential directions, and research questions. Journal of Technology in Mathematics, 14(3), 325-358.

Kaput, J. J., & Thompson, P. W. (1994). Technology in mathematics education research: The first 25 years in JRME. Journal for Research in Mathematics Education, 25(6), 676-684.

Thompson, P. W. (1994). Students, functions, and the undergraduate mathematics curriculum. In E. Dubinsky, A. H. Schoenfeld, & J. J. Kaput (Eds.), Research in Collegiate Mathematics Education, 1 (Issues in Mathematics Education Vol. 4, pp. 21-44). Providence, RI: American Mathematical Society.

Thompson, P. W., & Thompson, A. G. (1994). Talking about rates conceptually, Part I: A teacher’s struggle. Journal for Research in Mathematics Education, 25(3), 279-303.

Thompson, P. W. (1994). Images of rate and operational understanding of the Fundamental Theorem of Calculus. Educational Studies in Mathematics, 26(2-3), 229-274.

Thompson, P. W. (1994). Concrete materials and teaching for mathematical understanding. Arithmetic Teacher, 41(9), 556-558.

Thompson, P. W. (1993). Quantitative reasoning, complexity, and additive structures. Educational Studies in Mathematics, 25(3), 165-208.

Thompson, P. W. (1993). Yes, Virginia, some children do grow up to be mathematicians. [Review of Advanced Mathematical Thinking, D. Tall (Ed.)]. Journal for Research in Mathematics Education, 24(3), 279-284.

Thompson, P. W. (1992). Notations, conventions, and constraints: Contributions to the effective use of concrete materials in elementary mathematics. Journal for Research in Mathematics Education, 23(2), 123-147.

Thompson, P. W. (1990). Review of Interactive Physics, The Mathematics Teacher, 83(2).

Thompson, P. W., & Dreyfus, T. (1988, March). Integers as transformations. Journal for Research in Mathematics Education, 19, 115-133.

Thompson, P. W. (1985). A Piagetian approach to transformation geometry via microworlds. Mathematics Teacher, 78 (6), 465-472.

Thompson, P. W. (1984). Content versus method. College Mathematics Journal, 15 (5), 394-395.

Thompson, P. W. (1982). Were lions to speak, we wouldn’t understand. Journal of Mathematical Behavior, 3 (2), 147-165.

Chapters in Books

Thompson, P. W. (in press). Advances in research on quantitative reasoning. In R. Mayes, R. Bonillia, L. L. Hatfield & S. Belbase (Eds.), Quantitative reasoning: Current state of understanding, WISDOMe Monographs (Vol. 2). Laramie, WY: University of Wyoming.

Thompson, P. W. (in press). In the absence of meaning. In K. Leatham (Ed.), Vital directions for research in mathematics education. New York: Springer.

Thompson, P. W. (2011). Quantitative reasoning and mathematical modeling. In L. L. Hatfield, S. Chamberlain & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education, WISDOMe Monographs (Vol. 1, pp. 33-57). Laramie, WY: University of Wyoming.

Thompson, P. W. (2010). Foreword. Introduction to Steffe, L. P., & Olive, J. Children’s Fraction Knowledge (pp. i-iv). New York: Springer.

Oehrtman, M. C., Carlson, M. P., & Thompson, P. W. (2008). Foundational reasoning abilities that promote coherence in students’ function understanding. In M. P. Carlson & C. Rasmussen (Eds.), Making the connection: Research and practice in undergraduate mathematics (pp. 27-42). Washington, DC: Mathematical Association of America.

Thompson, P. W., & Silverman, J. (2008). The concept of accumulation in calculus. In M. Carlson & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics (pp. 43-52). Washington, DC: Mathematical Association of America.

Thompson, P. W., Liu, Y., & Saldanha, L. A. (2007). Intricacies of statistical inference and teachers’ understandings of them. In M. Lovett & P. Shaw (Eds.), Thinking with data (pp. 207-231). Mahwah, NJ: Erlbaum.

Smith, J. P., & Thompson, P. W. (2007). Quantitative reasoning and the development of algebraic reasoning. In J. J. Kaput, D. W. Carraher & M. L. Blanton (Eds.), Algebra in the early grades (pp. 95-132). New York: Erlbaum.

McCallum, W., Thompson, P. W., Harel, G., Blaire, R., Dance, R., Nolan, E., et al. (2007). Intermediate algebra. In V. J. Katz (Ed.), Algebra: Gateway to a technological future (pp. 19-27). Washington, DC: Mathematical Association of America.

Thompson, P. W., & Saldanha, L. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick & G. Martin (Eds.), Research companion to the NCTM Standards. Washington, DC: National Council for Teachers of Mathematics.

Thompson, P. W. (2002). Didactic objects and didactic models in radical constructivism. In K. Gravemeijer, R. Lehrer, B. van Oers, L. Verschaffel (Eds.), Symbolizing and modeling in mathematics education. Dordrecht, The Netherlands: Kluwer

Thompson, P. W. (2000). Radical constructivism: Reflections and directions. In L. P. Steffe & P. W. Thompson (Eds.), Radical constructivism in action: Building on the pioneering work of Ernst von Glasersfeld (pp. 412-448). London: Falmer Press.

Steffe, L. P. & Thompson, P. (2000). Teaching experiment methodology: Underlying principles and essential elements. In Kelly, A. & Lesh, R. (Eds.) Research design in mathematics and science education. Amsterdam, Netherlands: Kluwer

Thompson, P. W. (1996). Imagery and the development of mathematical reasoning. In L. P. Steffe, B. Greer, P. Cobb, P. Nesher, & G. Goldin (Eds.), Theories of learning mathematics (pp. 267-283). Hillsdale, NJ: Erlbaum.

Thompson, P. W. (1995). Notation, convention, and quantity in elementary mathematics. In J. Sowder & B. Schapelle (Eds.), Providing a foundation for teaching middle school mathematics (pp. 199–221). Albany, NY: SUNY Press.

Thompson, P. W. (1995). Constructivism, cybernetics, and information processing: Implications for research on mathematical learning. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 123–134). Hillsdale, NJ: Erlbaum.

Thompson, A. G., Philipp, R. A., Thompson, P. W., & Boyd, B. A. (1994). Calculational and conceptual orientations in teaching mathematics. In A. Coxford (Ed.) 1994 Yearbook of the NCTM (pp. 79-92). Reston, VA: NCTM.

Thompson, P. W. (1994). The development of the concept of speed and its relationship to concepts of rate. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 181-236). Albany, NY: SUNY Press.

Thompson, P. W. (1991). To experience is to conceptualize: Discussions of epistemology and experience. In L. P. Steffe (Ed.) Epistemological foundations of mathematical experience (pp. 260-281). New York: Springer-Verlag.

Thompson, P. W. (1989) Artificial intelligence, advanced technology, and learning and teaching algebra. In C. Kieren & S. Wagner (Eds.) Research issues in the learning and teaching of algebra. Reston, VA: National Council of Teachers of Mathematics, 135-161. [Pre-printed in Learning and Technology, 1988, 2(5&6).]

Thompson, A. G., & Thompson, P. W. (1989). Affect and problem solving in an elementary school mathematics classroom. In D. B. McLeod & V. A. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 162-176). New York: Springer-Verlag.

Thompson, P. W. (1987). Mathematical microworlds and intelligent computer-assisted instruction. In G. Kearsley (Ed.) Artificial Intelligence and Education (pp. 83-109). New York: Addison-Wesley.

Thompson, P. W. (1985). Experience, problem solving, and learning mathematics: Considerations in developing mathematics curricula. In E. A. Silver (Ed.), Learning and teaching mathematical problem solving: Multiple research perspectives (pp. 189-236). Hillsdale, NJ: Erlbaum.

Thompson, P. W. (1985). Mathematical microworlds. In G. Kearsley & I. Begg (Eds.), Moving intelligent CAI into the real world. Burroughs, Canada Technical Report (pp. 32-67).

Thompson, P. W. (1985). Computers in research on mathematical problem solving. In E. A. Silver (Ed.), Learning and teaching mathematical problem solving: Multiple research perspectives (pp. 417-436). Hillsdale, NJ: Erlbaum.

Steffe, L. P., Thompson, P. W., & Richards, J. (1982). Children’s counting in arithmetical problem solving. In T. C. Carpenter, T. Romberg, & J. Moser (Eds.), Children’s arithmetic: A cognitive perspective (pp. 83-98). Hillsdale, NJ: Lawrence Erlbaum.

Articles in Refereed Proceedings

Byerley, C., Hatfield, N., & Thompson, P. W. (in press). Calculus students’ understandings of division and rate. In Proceedings of the 15th Annual Conference on Research in Undergraduate Mathematics Education. Portland, OR.

Thompson, P. W., & Miller, C. (2006). Through the looking glass: Perspectives on the evolution of learning communities through the lens of intersubjectivity. In. S. Alatorre, J. L. Cortina, M. Sáiz, & A. Méndez (Eds.). Proceedings of the Twenty-eighth Annual Meeting of the International Group for the Psychology of Mathematics Education, Muriel, Mexico: PME.

Saldanha, L., & Thompson, P. (2006). Investigating statistical unusualness in the context of resampling. Proceedings of the International Congress on Teaching Statistics. Salvadore, Brazil.

Thompson, P. W., & Liu, Y. (2005). Understandings of margin of error. In S. Wilson (Ed.), Proceedings of the Twenty-seventh Annual Meeting of the International Group for the Psychology of Mathematics Education, Roanoke, VA. Vicksburg, VA: Virginia Tech.

Liu, Y., & Thompson, P. W. (2005). Teachers’ understanding of hypothesis testing. In S. Wilson (Ed.), Proceedings of the Twenty-seventh Annual Meeting of the International Group for the Psychology of Mathematics Education, Roanoke, VA. Vicksburg, VA: Virginia Tech.

Silverman, J., & Thompson, P. W. (2005). Investigating the relationship between mathematical understanding and teaching mathematics. In S. Wilson (Ed.), Proceedings of the Twenty-seventh Annual Meeting of the International Group for the Psychology of Mathematics Education, Roanoke, VA. Vicksburg, VA: Virginia Tech.

Liu, Y., & Thompson, P. W. (2004). Teachers’ personal and pedagogical understanding of probability and statistical inference. In D. McDougal (Ed.), Proceedings of the Twenty-sixth Annual Meeting of the International Group for the Psychology of Mathematics Education. Toronto: PME-NA.

Liu, Y., & Thompson, P. W. (2002). Randomness: Rethinking the foundations of probability. In D. Mewborn (Ed.), Proceedings of the Twenty-fourth Annual Meeting of the International Group for the Psychology of Mathematics Education—North America. Athens, GA: PME-NA.

Saldanha, L. & Thompson, P. W. (2002). Students’ scheme-based understanding of sampling distributions and its relationship to statistical inference. In D. Mewborn (Ed.), Proceedings of the Twenty-fourth Annual Meeting of the International Group for the Psychology of Mathematics Education. Athens, GA.

Thompson, P. W. & Saldanha, L. (2000). Conceptual issues in understanding sampling distributions and margins of error. Proceedings of the Twenty-second Annual Meeting of the International Group for the Psychology of Mathematics Education. Tucson, Arizona.

Thompson, P. W. & Saldanha, L. (2000). Epistemological analyses of mathematical ideas: A research methodology. Proceedings of the Twenty-second Annual Meeting of the International Group for the Psychology of Mathematics Education. Tucson, Arizona.

Cortina, J., Saldanha, L., & Thompson, P. W. (1999). Multiplicative conceptions of arithmetic mean. In F. Hitt (Ed.). Proceedings of the Twenty-first Annual Meeting of the International Group for the Psychology of Mathematics Education. Cuernavaca, Mexico: Centro de Investigación y de Estudios Avanzados.

Thompson, P. W., & Cobb, P. (1998). On relationships between psychological and sociocultural perspectives in mathematics education. In S. Berenson & & K. Dawkins (Eds.)., Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education — North America, Plenary Sessions Vol. 1 (pp. 1–26). Raleigh, NC: North Carolina State University.

Saldanha, L. & Thompson, P. W. (1998) Re-thinking covariation from a quantitative perspective: Simultaneous continuous variation. In S. Berenson & & K. Dawkins (Eds.)., Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education — North America Vol. 1 (pp. 298-304). Raleigh, NC: North Carolina State University.

Thompson, P. W., & Sfard, A. (1994). Problems of reification: Representations and mathematical objects. In D. Kirshner (Ed.), Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education — North America, Plenary Sessions Vol. 1 (pp. 1–32). Baton Rouge, LA: Lousiana State University.

Fraivillig, J. L., Fuson, K. C., & Thompson, P. W. (1993). Microworld support of children’s understanding of multidigit addition. In S. Ohlson, P. Brna, & H. Pain (Eds.), Proceedings of the World Conference on AI in Education Vol. 1. Edinburgh, Scotland: University of Edinburgh.

Thompson, P. W. (1991). Getting ahead, with theories: I have a theory about this. In R. Underhill & C. Brown (Eds.), Proceedings of the Annual Meeting of the Psychology of Mathematics Education, North America, Plenary Lectures Vol. 1 (pp. 240-245). Blacksburgh, VA: Virginia Tech.

Thompson, P. W., & Thompson, A. G. (1990, July). Salient aspects of experiences with concrete manipulatives. In Proceedings of the 14^th Annual Meeting of the Psychology of Mathematics Education, Mexico City.

Thompson, P. W. (1988). Quantitative concepts as a foundation for algebra. In M. Behr (Ed.) Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education Vol. 1 (pp. 163-170). Dekalb, IL.

Thompson, P. W., & Thompson, A. G. (1987). Computer presentations of structure in algebra. In N. Herscovics & C. Kieran (Eds.), Proceedings of the 11^th Annual Meeting of International Group for Psychology of Mathematics Education Vol. 1 (pp. 248-254). Montréal: University of Quebec, Montréal.

Thompson, P. W. (1986). Logo as a medium for thinking about thinking. Proceedings of the Second International Conference on Logo and Mathematics Education, 1, 209-215.

Thompson, P. W. (1985). Understanding recursion: Process ≈ product. Proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education, 1, 357-362.

Dreyfus, T., & Thompson, P. W. (1985). Microworlds and Van Hiele levels. Proceedings of the Ninth Annual Meeting of the International Group for the Psychology of Mathematics Education, 1, 5-11.

Thompson, P. W. (1984). Microworld environments for teaching mathematics to future elementary school teachers. Proceedings of the De Anza Conference on Computers in Higher Education, 1, 123-129.

Reports

Thompson, P. W., Castillo-Chavez, C., Culbertson, R. J., Flores, A., Greely, R., Haag, S., et al. (2007). Failing the future: Problems of persistence and retention in science, techhnology, engineering, and mathematics majors at Arizona State University. Tempe, AZ: Office of the Provost.

Published Software

Thompson, P. W. (1992). Blocks Microworld. A program for students to explore numeration systems and to construct notational methods for numerical operations. Published by Intellimation Library for the Macintosh.

Thompson, P. W. (1986). MOTIONS: A microworld for exploring transformation geometry. Published by Cosine, Inc., W. Lafayette, IN. and Control Data Publishing, Australia.

Thompson, P. W. (1984). INTEGERS: A microworld for integers and introductory algebra. Published by Cosine, Inc., W. Lafayette, IN. and Control Data Publishing, Australia.

Thompson, P. W. (1984). TREE DIAGRAM: A microworld for exploring discrete probability. Published by Cosine, Inc., W. Lafayette, IN. and Control Data Publishing, Australia.

Thompson, P. W. (1984). NUMBER AIDS: A number theoretic toolkit. Published by Cosine, Inc., W. Lafayette, IN. and Control Data Publishing, Australia.

Thompson, P. W. (1984). GLUE BOXES: A microworld for elementary arithmetic. Published by Cosine, Inc., W. Lafayette, IN. and Control Data Publishing, Australia.

Thompson, P. W. (1984). CIRCUITS: A microworld for exploring the logic of equivalence. Published by Cosine, Inc., W. Lafayette, IN. and Control Data Publishing, Australia.

Thompson, P. W. (1984). INSIDE LOGO: A microworld for exploring the inner workings of Logo. Published by Cosine, Inc., W. Lafayette, IN. and Control Data Publishing, Australia.

Other publications

Thompson, P. W. (2005). Letter to the editor, The New York Times.

Thompson, P. W. (2004). Letter to the editor, The New York Times.

Thompson, P. W. (2004). Letter to the editor, The Tennessean.

Thompson, P. W. (1992). Letter to the editor, The Mathematics Teacher, 85(?).

Thompson, P. W. (1988). Letter to the editor, The Mathematics Teacher, 81 (4).

Thompson, P. W. (1985). Letter to the editor, The Mathematics Teacher, 78 (4).

Thompson, P. W. (1984). Computers in mathematics education at San Diego State University. Newsletter of the Consortium for Computers in Mathematical Sciences Education.

Thompson, P. W. (1984). A microworld for integers. Newsletter of the Consortium for Computers in Mathematical Sciences Education.

Invited Testimony

Thompson, P. W. (2007, April). Invited testimony given to the President’s National Mathematics Panel. Aurora, Il.

Refereed Papers and Presentations

Thompson, P. W. (2010, April). Rethinking mathematical knowledge for teaching. Paper presented at the Research Presession to the annual meeting of the National Council of Teachers of Mathematics, San Diego, CA.

Thompson, P. W. (2010, April). Toward a foundation of mathematics education. Paper presented at the annual meeting of the American Educational Research Association, Denver, CO.

Thompson, P. W. (2009, April). The role of meaning in the reform of school arithmetic and algebra. Paper presented at the annual Research Presession of the National Council of Teachers of Mathematics, Washington, DC.

Thompson, P. W. (2009, April). Exercising professional judgment in mathematics curriculum reform. Paper presented at the Annual Meeting of the American Educational Research Association, San Diego, CA.

Thompson, P. W. (2008, April). Affecting teachers’ images of what and who they teach. Paper presented at the Research Presession to the Annual Meeting of the National council of Teachers of Mathematics, Salt Lake City, UT. (Also, organizer of research symposium by the same name.)

Thompson, P. W. (2007, April). The design of tasks to promote coherence in classroom mathematics. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, IL.

Thompson, P. W., & Carlson, M. P. (2006, June). Affecting teachers’ learning communities by affecting their mathematical knowledge. Paper presented at the China-U.S. Educational Leadership Conference, Beijing, China.

Thompson, P. W. (2006, April). Measurement: The lost strand in elementary mathematics. Discussant for the symposium Constructing Data, Modeling Worlds. Annual Meeting of the American Educational Research Association, San Francisco, CA.

Liu, Y. & Thompson, P. W. (2006, April). Teachers’ understandings of probability and their implications for teacher professional development. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA.

Thompson, P., & Carlson, M. P. (2006, April). Mathematical thinking and intersubjective operations: A lens on the creation of mathematical learning communities. Paper presented at the Research Presession of the Annual Meeting of the National Council of Teachers of Mathematics. St. Louis, MO.

Thompson, P. W. (2005, October). Affecting teachers’ practices through their mathematical knowledge. Presentation given at the Twenty-Seventh Annual Meeting of the Psychology of Mathematics Education—North America. Roanoke, VA.

Thompson, P. W. (2005, April). On evaluating curricular effectiveness: Judging the quality of mathematics K-12 curriculum evaluations. Presentation given at the Research Presession of the Annual Meeting of the National Council of Teachers of Mathematics. Ahaheim, CA.

Thompson, P. W. (2005, April). Creating data, modeling worlds, changing practices. Presentation given at the Research Presession of the Annual Meeting of the National Council of Teachers of Mathematics. Anaheim, CA.

Thompson, P. W. (2005, April. Discussant for symposium, Unexpected Findings About How Young Students Learn Algebra. Presentation given at the Research Presession of the Annual Meeting of the National Council of Teachers of Mathematics. Anaheim, CA.

Carlson, M. P., & Thompson, P. W. (2005, April). The reflexive relationship between individual cognition and classroom practices: A covariation framework and problem solving research informs calculus instruction. Paper presented at the Annual Meeting of the American Educational Research Association, Montreal, Quebec.

Thompson, P. W. (2005, March). Issues in algebra learning, teaching, and curricula. Invited address given at the annual meeting of the Appalachian Mathematics and Science Project, Lexington, KY.

Thompson, P. W., Saldanha, L. A., & Liu, Y. (2004, April). Why statistical inference is hard to understand. Paper presented at the annual meeting of the American Educational Research Association, San Diego.

Thompson, P. W., Milner, R., & Liu, Y. (2004, April). Teacher reflection and reflective abstraction: Viewing mathematics teachers’ struggles from two perspectives. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA.

Thompson, P. W. (2004, April). Discussant, Symposium on mathematics learning. American Educational Research Association, San Diego, CA.

Thompson, P. W., & Liu, Y. (2002, April). What is the probability my car is red? Tensions in the development of probabilistic reasoning. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.

Thompson, P. W. (2002, April) Methodology: A Quest for Knowledge. Discussant for the Symposium on Teaching Experiments as Research Methodologies, Research Presession to the Annual Meeting of the National Council of Teachers of Mathematics, Las Vegas, NV.

Thompson, P. W. (2001, August). Helping students find meaning in measures of association. Presentation given at the Annual Joint Meeting of the Statistical Associations, Atlanta, GA.

Thompson, P. W. (2001, April). Students’ probabilistic reasoning. Symposium presentation given at the American Educational Research Association Annual Meeting, Seattle, WA.

Thompson, P. W. (2001, April). Do computers make a difference in students’ mathematical learning? Symposium presentation given at the American Educational Research Association Annual Meeting, Seattle, WA.

Thompson, P. W. (2001, January). Multiplicative reasoning as a foundation for probabilistic and statistical reasoning. Poster presentation given at the National Science Foundation Directors Meeting.

Thompson, P. W. (2000, April). The essential role of quantitative reasoning in the development of algebraic competence. (And organizer of symposium by the same title.) Research Presession of the Annual Meeting of the National Council of Teachers of Mathematics, Chicago, IL.

Thompson, P. W. (1998, March). Discussant for A New Vision of Calculus, research symposium at the Research Presession of the Annual Meeting of the National Council of Teachers of Mathematics, Washington, DC.

Thompson, P. W. (1998, April). Symbols and tools as occasions to talk. Presentation given as part of Perspectives on the Role of Tools and Artifacts in Mathematical Learning, a research symposium held at the Annual Meeting of the American Educational Research Association.

Thompson, P. W., & Thompson, A. G. (1992, April). Images of rate. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco.

Thompson, P. W. (1991, March). Quantitative reasoning, complexity, and additive structures. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago.

Thompson, P. W. (1991, March). Representations, principles, and constraints: Contributions to the effective use of concrete manipulatives in elementary mathematics. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago.

Thompson, P. W. (1989, March). A cognitive model of quantity-based algebraic reasoning. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco.

Thompson, P. W. (1988, March). Preparing school students for algebra: Are textbook publishers and teacher education programs part of the solution or part of the problem? Paper presented at the Research Presession to the Annual Meeting of the National Council of Teachers of Mathematics, Chicago.

Thompson, P. W. (1982, March). Children’s schemata for understanding and solving problems of whole number numeration. Paper presented at the Annual Meeting of the American Educational Research Association, New York.

Thompson, P. W. (1982, March). Cognitive objectives for instruction in whole number numeration. Paper presented at the Annual Meeting of the American Educational Research Association, New York.

Invited Papers and Addresses

Thompson, P. W. (2010, November). Calculus reform. Invited presentation given to the First Year Mathematics Faculty, Arizona State University, Tempe, AZ.

Thompson, P. W. (2010, August). Professional development by researching one’s teaching. Invited presentation to the Department of Mathematics, Scottsdale Community College.

Thompson, P. W. (2010, April). The mathematics in mathematics education research. Invited presentation at the Research Presession to the annual meeting of the National Council of Teachers of Mathematics, San Diego, CA.

Thompson, P. W. (2009, November). Mathematical knowledge for teaching: The central problem in mathematics education reform. Invited presentation, College of Education, University of North Carolina, Chapel Hill, NC.

Thompson, P. W. (2009, August). The Didactic Triad in mathematics teacher professional development. Invited presentation given at the University of Michigan College of Education, Ann Arbor, MI.

Thompson, P. W. (2008, September). What is “higher” about higher cognition in school students? Invited presentation at the National Science Foundation Workshop on higher cognition in adolescents and young adults.

Thompson, P. W. (2008, July). Learning without understanding and its implications for the mathematics that teachers teach. Invited presentation at Mathfest 2008, Madison, WI. (Also, invited organizer of the symposium Implications for teaching of research on learning mathematics.)

Thompson, P. W. (2008, May). The problem of scaling up versus the problem of researching the scaling process. Invited presentation given to the Education and Human Services Directorate, National Science Foundation, Washington, D. C.

Thompson, P. W., Castillo-Garsow, C., & Moore, K, & Carlson, M. P. (2007, June). Quantitative reasoning as a foundation for “algebra as modeling”. Invited paper presented at the Pathways to Algebra Conference, Evron, France.

Thompson, P. W. (2008, May). Quantity and magnitude as a foundation for algebraic reasoning throughout the grades. Invited workshop given at the Mathematical Sciences Research Institute, Berkeley, CA.

Thompson, P. W. (2007, February). Epistemology, ontology, and method. Invited paper presented at the International Workshop on Guided Construction of Knowledge in Classrooms, Hebrew University, Jerusalem, Israel.

Thompson, P. W. (2006, July). A cognitive foundation for affecting the ways professional learning communities work. Invited presentation given at the National Institute of Education, Singapore.

Carlson, M. P., & Thompson, P. W. (2005, October). Assessing conceptual knowledge of function in secondary mathematics. Invited presentation at the U.S. Department of Education and National Science Foundation Joint Conference for State Mathematics and Science Partnership Directors. Washington, DC.

Thompson P. W. (2005, January). Statistics in education research: Issues from mathematics and science education. Invited presentation given to the American Statistical Association Meeting on Using Statistics in Mathematics and Science Education Research, Washington DC.

Thompson, P. W., Liu, Y., Saldanha, L. A. (2004, June). Intricacies of statistical inference and teachers’ understandings of them. Invited paper presented at the Carnegie Symposium on Cognition, Carnegie Mellon University, Pittsburgh, PA.

Thompson, P. W. (2001, August). Understanding sampling distributions and margin of error. Presentation given at the 2^nd Conference on Statistics Reasoning, Teaching, and Literacy, Armidale, Australia.

Thompson, P. W. (2001, August). Helping students find meaning in measures of association. Presentation given at the Joint Statistical Meetings, Atlanta, GA.

Thompson, P. W. (2001, July). Investigating students’ understanding of big ideas: The case of distributions of sample statistics. Presentation given at the Park City Mathematics Institute, Park City, UT.

Thompson, P. W. (2001, February). Epistemological analysis: Creating epistemic subjects. Presentation given at the Wisconsin Education Research Center, Madison, WI.

Thompson, P. W. (2000, January). High school students’ understandings of sampling distributions. Invited presentation given to the Department of Mathematical and Computer Sciences, San Diego State University.

Thompson, P. W. (1999, May). Making warranted claims from small samples: Types of generalizations from small samples. Invited address given at the National Science Foundation Project Directors’ Meeting, Washington, DC.

Thompson, P. W. (1999, October). Tensions and dilemmas in designing a mathematics education Ph.D. program. Presentation given to the Conference on the future of mathematics education Ph.D. programs. University of Missouri, Columbia, MO.

Thompson, P. W. (1999, October). Some remarks on conventions, representations, and the danger of attributing too much to evident agreement Invited paper presented to the Working Group on Representations, PME-XXI, Cuernavaca, Mexico.

Thompson, P. W. (1998, October). Multiplicative reasoning as a cultural artifact. Invited address given to the Mathematics Education Research Group, University of Colorado, Boulder.

Thompson, P. W. (1998, June). Didactic Objects and Didactic Models in Radical Constructivism . Invited paper presented at the International Conference on Symbolizing and Modeling in Mathematics Education, Freudenthal Institute, University of Utrecht, Utrecht, The Netherlands.

Thompson, P. W. (1998, May). Multiplicative Reasoning and the Development of post-additive Numbers and Operations. White paper developed for the National Council of Teachers of Mathematics as background for their Standards 2000 project.

Thompson, P. W. (1998, January). Mutliplicative foundations of probabalistic reasoning. Invited address given to the Department of Mathematics, East Carolina University.

Thompson, P. W. (1997, November). Chaos, fractals, and art. Seventh grade, Grassland Elementary School, Williamson County, Tennessee.

Thompson, P. W. (1996, July). Technology and Curriculum Reform: Designing for emergence, or Making students, curricula, and instruction meet where none of them is, or You can’t teach them what you want them to learn. Keynote Address given to the Working Group on Technology and Curriculum Reform, International Congress of Mathematical Education, Seville, Spain.

Thompson, P. W. (1996, April). What does it mean to really understand rate? Invited presentation given at the Annual Meeting of the National Council of Teachers of Mathematics, San Diego.

Thompson, P. W., Thompson, A. G., Philipp, R., Clement, L., & Bernhard, J. (1996, April). Reform in mathematics teaching: Its many aspects and difficulties. Presentation given at the Research Presession to the Annual Meeting of the National Council of Teachers of Mathematics, San Diego.

Thompson, P. W. (1995, October). Making sense of what students learn from instruction: Perspectives from mathematics education research. Invited presentation given at the Annual Meeting of the Norhern California Section of the Mathematical Association of America, San Luis Obispo, Ca.

Thompson, P. W. (1995, May). What is a fractal and how do you make one? Sixth-grade, Dailard Elementary School, San Diego.

Thompson, P. W. (1995, February). Fundamental difficulties and insights in learning the calculus. Department of Mathematics Education, University of Georgia, Athens, GA.

Thompson, P. W. (1994, June). Algebraic transformations of the elementary mathematics curriculum. National Center for Research in Mathematical Sciences Education, University of Wisconsin, Madison.

Thompson, P. W. (1993, October). Imagery, process, function, rate: Helping students see what Newton saw. Invited special presentation given at the Annual Meeting of the International Group for the Psychology of Mathematics Education, North American Chapter, Asilomar, CA.

Thompson, P. W. (1992, February). Research on algebra and its implications for textbook reform. Presentation made to the Joint Conference of the American Association of Publishers and the National Council of Teachers of Mathematics.

Thompson, P. W. (1992, August). Imagery and the development of mathematical reasoning. Paper presented at the Seventh International Congress on Mathematical Education, Quebec City, Canada.

Thompson, P. W. (1992, August). Computers in teaching and learning mathematics. Invited presentation given at the Technology Colloquium Series of the Seventh International Congress of Mathematical Education, Québec City, Québec, Canada.

Thompson, P. W. (1991, December). Coping with a conceptual curriculum. Paper presented at the 2^nd NCTM Standards Research Catalyst Conference, Miami.

Thompson, P. W., & Thompson, A. G. (1991, May). The Quantitative Reasoning Project. Presentation made to the Wisconsin Center for Research on Learning and Teaching Mathematics Working Group on Quantities, San Diego.

Thompson, P. W. (1990, October).What is quantitative reasoning and why is it important for understanding algebra? Invited presentation made at the University of Hawaii Research and Development Center, Honolulu.

Thompson, P. W. (1990, October). Why do we expect so little of our students? Plenary address given at the Annual Meeting of the Hawaii Council of Teachers of Mathematics, Honolulu.

Thompson, P. W. (1990, October). One dimensional areas and volume. Paper presented at the NSF Director’s Meeting, Washington, D. C.

Thompson, P. W. (1990, April). Quantitative reasoning and algebra. Colloquium presented to the Department of Mathematical Sciences, San Diego State University.

Thompson, P. W. (1989, July). Design issues in mathematics software. Paper presented at the conference Designing for Learning, Apple Computer, Cupertino, CA.

Thompson, P. W. (1989, April). Notes on technology and curriculum reform. Working paper distributed at the symposium New Technology’s Challenges to Curriculum, Pedagogy, and Evaluation, Research Presession to the Annual Meeting of the National Council of Teachers of Mathematics, Orlando.

Thompson, P. W. (1988, March).Two views of algebra. Colloquium presented at the Center for Research in Mathematics and Science Education, San Diego State University.

Thompson, P. W. (1988, February). Achieving competence in introductory algebra by building competence in arithmetical problem solving. Presentation given at Success for Everyone, a conference on diagnosis and remediation in high school mathematics topics, University of Illinois at Chicago.

Thompson, P. W. (1987, October). Symbolic computation in mathematics teacher education. presentation given to the Illinois Council of Teachers of Mathematics, Urbana.

Thompson, P. W. (1987, March). Artificial intelligence, advanced technology, and learning and teaching algebra. Paper presented at the Research Agenda Conference on Algebra, University of Georgia, Athens.

Thompson, P. W. (1987, February). “Direct Engagement” Software in Teaching Mathematics. Paper presented at Computers in Education VII, Chicago.

Thompson, P. W. (1987, December).Transitions to Algebra. Invited lecture given to the Department of Mathematical Sciences, Northern Illinois University.

Thompson, P. W. (1986, March). Mathematical microworlds and intelligent computer-assisted instruction. Invited presentation at the Army Research Institute’s Conference on ICAI and military training.

Thompson, P. W. (1986, April). Creating a technology of mathematics education: Or, there is nothing more practical than a good theory. Rutgers University President’s Lecture Series, Center for Mathematics and Science Education, Rutgers University, New Brunswick.

Thompson, P. W. (1985, February). Microworlds: A bridge between computer-assisted instruction and intelligent computer-assisted instruction. Paper presented at the Invitational Workshop on Intelligent Computer-Assisted Instruction, San Diego.

Thompson, P. W. (1985, April). Microworld inquiries into sixth-graders’ concepts of integers. Paper given at the Research Presession to the Annual Meeting of the National Council of Teachers of Mathematics, San Antonio, TX.

Software Developed for Research on Mathematics Learning and Teaching

Over & Back....................... A program for students to use in exploring the concepts of speed and average speed.

Blocks Microworld................. A program that allows students to explore concepts of numeration and the operations of addition, subtraction, multiplication, and division in either of two representational systems for whole numbers and decimals (on Dienes’ blocks or on digits of numerals) and which reflects the student’s actions in the other representational system. Students can work in any base from two to ten.

Word Problem Analyzer........ An implementation of a cognitive model for quantity-based arithmetic and algebraic reasoning. The program lets users represent arithmetic and algebra word problems in terms of their quantitative structures, and it solves a problem (i.e., infers arithmetical operations or derives equations) as soon as the described situation is well-represented.

Expressions/Equations.......... A program that allows students to manipulate arithmetical and algebraic expressions and equations by acting directly on their operational structure (as depicted in expression trees).

Grant Activity

Research Grants

Principal Investigator (with Marilyn Carlson), National Science Foundation: Project Aspire: Defining and Assessing Mathematical Knowledge for Teaching Mathematics. ($1.95 million, September 2011 – August 2014).

Principal Investigator (with Marilyn Carlson). National Science Foundation: Developing a Professional Learning Community Model for Secondary Precalculus Teachers: A Model for Teacher Professional Growth ($4.5 million, May, 2004-April, 2010).

Co-Principal Investigator (with R. Lehrer, L. Schauble, R. Hall). National Science Foundation Grant: Modeling Data, Creating Worlds. ($1.8 million, January 2004-December 2006).

Principal Investigator, National Science Foundation Grant: Multiplicative reasoning as a foundation for the teaching and learning of stochastic reasoning. ($670,000, January 1999 – June 2004). (Accompanied by a $12,000 gift of software from Data Description and Key Curriculum Press).

Co-Principal Investigator (with J. Lobato and J. Bowers), National Science Foundation Instructional Laboratory Improvement grant, $345,000.(1996)

Co-Principal Investigator (with J. Sowder), National Science Foundation Grant: Reforming the preparation and professional development of elementary and middle school mathematics teachers. ($550,000; 1994-1998)

Principal Investigator, National Science Foundation Grant: Quantitative Concepts as a Foundation for Algebra. ($826,000; 1989-1994).

Principal Investigator, Apple Computer Office of External Research: Improving Students’ Concepts in Algebra ($33,000 equipment; 1987-1989).

Principal Investigator, National Science Foundation Grant: Cognitive Effects of Multiple Representation of Mathematical Concepts. ($87,000; 1987-1988, $12,000; 1988-1989).

Principal Investigator, San Diego State University Foundation Grant: Modeling students’ cognitions in understanding integers. (1984).

Faculty Associate, NSF Grant, E. A. Silver (Director), San Diego State University: Synthesis of cognitive science and mathematics education literatures on mathematical problem solving. (1980-1982).

Instructional Grants

Co-Principal Investigator, National Science Foundation: Reforming the preparation and professional development of elementary and middle school mathematics teachers (J. Sowder and A. Thompson, Co-PIs; $650,000; 1994-1998).

Co-Principal Investigator (with J. Lobato & J. Bowers). National Science Foundation Grant: Enhancing Prospective Teachers’ Mathematical Understanding Through Computer-Based Modeling. ($100,00 equipment grant; 1997-1999)

Principal Investigator, Illinois State University Instructional Development Project Grant: Improving undergraduates’ understanding of numerical algorithms. (1986).

Major Course and Program Development

Arizona State University

Calculus redesign (present)

Bachelor of Arts in Education, Secondary Mathematics Education (2010)

Bachelor of Arts, Mathematics, with Mathematics Education Concentration (2009)

Ph. D. in Mathematics Education, School of Mathematical and Statistical Sciences (2009)

Teaching

Arizona State University

Extended analysis of functions 1

Extended analysis of functions 2

Research in Undergraduate Mathematics Education I

Research in Undergraduate Mathematics Education II

Research in Undergraduate Mathematics Education III

Research in Undergraduate Mathematics Education IV

Advanced Methods of Teaching Secondary School Mathematics

Piaget’s Genetic Epistemology

Calculus I

Technology and Mathematical Visualization

Vanderbilt University

Cognition, computers, and mathematics curriculum

Research on multiplicative reasoning

Piaget’s Genetic Epistemology.

Methods of teaching secondary mathematics

Methods of teaching elementary mathematics

Computers, teaching, and mathematical visualization.

Seminar on mathematics student teaching

Secondary mathematics student teaching

Technology and Conditions for Teaching and Learning.

San Diego State University

Teacher preparation courses

Transformation geometry

Computers and calculators in elementary/junior high mathematics

Computer-extended secondary mathematics

Logo in mathematics

Graduate courses

Research in mathematics education

Seminar on Multiplicative Reasoning

Construction of computerized mathematical environments

Seminars in artificial intelligence and Lisp programming

Research on learning and teaching algebra

Graduate Students

Doctoral Students

Advisor

Ana Lagaramirez (Ph.D. 2011). Dissertation title: Mathematical Knowledge for Teaching: Exploring a Teacher's Sources of Effectiveness

Carlos Castill-Garsow (Ph.D. 2010). Dissertation title: Teaching the Verhulst Model: A Teaching Experiment in Covariational Reasoning and Exponential Growth

Scott Courtney (Ph.D. 2010). Dissertation title: Exploring Teachers' Capacity to Reflect on Their Practice: An Investigation Into the Development of Mathematical Knowledge for Teaching

Edward (Ted) Coe (PhD., 2007). Dissertation title: Modeling teachers’ ways of thinking about rate of change.

Yan Liu (PhD, 2006). Dissertation title: Teachers’ understandings of probability and statistical inference and their implications for professional development (Otto Bassler award for Outstanding Dissertation)

Jason Silverman (PhD, 2006) Dissertation title: An investigation of content knowledge for teaching: Understanding its development and its influence on pedagogy

Luis Saldanha (PhD, 2005). Dissertation title: Is this sample unusual?”: An investigation of students exploring connections between sampling distributions and statistical inference. (Otto Bassler award for Outstanding Dissertation)

Eric Weber

Linda Agoune

Cameron Byerley

Neil Hatfield

Dissertation Committee

Stacey Bowling

Ah Young (Ph.D., 2010)

Kevin Moore (Ph.D., 2010)

April Strom (Ph.D., 2008)

Nanci Smith (Ph.D., 2008)

Jana Viskovska (Ph. D., 2008)

Nicole Engelke (Ph.D., 2007)

Lynn Chrystal Dean (PhD, 2005)

Jose Cortina (PhD, 2005)

Samuel Katz (EdD, 2004)

Randall Bouldin (PhD, 2004)

Maggie McGatha (Ph.D, 2003)

Lynn Hodge (PhD, 2003)

Inge Poole (PhD, 2003)

Kirsten Ellenbogen (PhD, 2002)

Masters Students

Hsinyi Huang Smith (MNS Mathematics, 2009). Thesis title: Teaching and learning function transformations.

Ashlee John (MNS Mathematics, 2009). Thesis title: Parametric functions in Algebra II: Implications of a covariational approach to teaching functions.

Shanon Bishop (MNS Mathematics, 2009). Thesis title: Parametric functions in Algebra II: Implications of a covariational approach to teaching functions.

Christopher Lowber (MA Math Education, 2003, Comprehensive exam)

Tiffany Dale (MA Math Education, 1999). Comprehensive exam.

James Love (MS Computer Science, 1985). Thesis title: A computer microworld for teaching operations on structured data.

Eun Jong Kim (MS Math Education, 1995). Thesis title: A computer environment for helping students to understand the structure of expressions.

Eric Knuth (MS Math Education, 1995). Comprehensive exam.

Elizabeth Nagel (MS Math Education, 1994). Thesis title: Effects of graphing calculators on college algebra students’ understanding of functions and graphs.

Donna Troy (MS Mathematics Education, 1993). Thesis title: Future teachers’ imagery while reasoning quantitatively.

Barbara Boyd (MS Math Education, 1992; co-advised with Alba Thompson). Thesis title: The relationship between mathematics subject matter knowledge and instruction: A case study.

Service

Professional Service

Organizing Committees for Conferences

Workshop on Calculus Reform, Institute for Mathematics and Education, University of Arizona (2008-2010)

Pathways to Algebra, Evron, France, 2008.

American Educational Research Association Division C (mathematics), 1995

Conference on Constructivism in Mathematics and Science Education, Atlanta, April 1994

NCTM Regional Meeting, San Diego, April 1985

San Diego Council of Teachers of Mathematics, February 1984

Advisory Boards

(lost track of recent advisory boards)

Purdue University , Calumet, NSF project on learning differential equations. (1999, 2000)

University of Georgia, NSF project on children’s reasoning about fractions (1998, 1999, 2000)

University of Michigan, INTASC analysis of teacher videotapes (1999)

East Carolina University, consultant on developing a PhD program in mathematics education (1998)

A Conference on the Future of Ph. D. Programs in Mathematics Education. NSF Funded project, Robert Reys, Director. (1998-2000)

University of Colorado (1998)

Maxwell Laboratories. Advise on the design and development of multi-media software for teaching secondary science and mathematics. (1994-1996)

NSF Grant, Vanderilt University (Paul Cobb, Director). Advise on design of teaching experiments to investigate children’s emerging use of symbols in their mathematical reasoning. (1995-1996)

NSF Grant, U. Georgia (Leslie P. Steffe, Director). Advise on theoretical constructs used to develop models of children’s understanding of fractional quantities and rational numbers. (1995-1996)

NSF Grant, U. Massachussetts (James J. Kaput, Director). Advise on conceptual foundations of interface design for SIMCALC—calculus simulations for mathematics learning. (1993)

Member, NCTM’s Research Catalyst Group: Develop research programs to investigate aspects of implementation of NCTM’s Curriculum and Evaluation Standards. (1993)

Science Applications International Corporation. Advise on qualification proposal to the National Security Administration for development of educational software. (1992)

NSF Grant, Purdue University (Paul Cobb, Director). To advise on the use of computers in research on socialization in 3^rd-grade mathematics classrooms. (1989)

NSF Grant, A. G. Thompson & C. A. Thornton (Co-directors). To develop new courses and new software for a model middle-school teacher training program. (1986-1989)

Cosine, Inc., an educational software company. Advised on issues of design, implementation, and marketing. (1983-1985)

San Diego City Schools Program for the Gifted and Talented. Developed evaluation instrument for an instructional program to teach mathematical problem solving. (1982-1983)

NSF Grant, M. G. Kantowski (Director), University of Florida. Advised on the design and evaluation of software for teaching and learning mathematical problem solving. (1979-1981)

University Service

Arizona State University

University

Chair, Freshman Science, Technology, Engineering, and Mathematics Improvement Committee. An ad hoc committee of the Vice President and Provost. (2007-2008)

Department of Mathematics and Statistics

Member, Graduate Committee (2005-present)

Vanderbilt University

University

Member, University Academic Computing and Information Technology Committee (2004-2006)

Co-founder and co-director, Vanderbilt Program for Talented Youth (1998-2000)

Member, Chancellor’s Council on Teacher Education (2000-2003)

College

Member, Peabody Curriculum Committee (2004-2007)

Chair, Ad Hoc Committee on Technology. (2002-2003)

Member, Budget Resource Committee, a subcommittee of the Faculty Senate. (1997-1998)

Member, Research committee; a subcommittee of the Faculty Senate (2000-2002)

Department

Chair, Search Committee for Department of Teaching and Learning Chair and Professor of Teacher Education (1998-2000)

Member, Department mentoring committee (1999-2000)

Chair, Search Committee for Department of Teaching and Learning Chair and Professor of Teacher Education (1998-1999)

Member, Department graduate admissions committee (1999-2000)

Chair, Department of Teaching and Learning Search Committee for Mathematics Education (1998-2000)

San Diego State University

Director, Ph.D. Program in Mathematics and Science Education, Joint-doctoral program of San Diego State University and University of California, San Diego (1995-1997).

Director, Master of Science in mathematics education, Illinois State University (1989).

Chair, Calculus Reform Committee, Department of Mathematics (1991-1992).

Organizer and leader, College of Sciences Course Study Program (a program of “internal sabbaticals” funded by the Dean’s office to support faculty research of student learning in college science and mathematics courses; 1994).

Member, College of Sciences Teacher Preparation Committee (1993-1995).

Director, University Developmental Math Lab (1980-1982).

Community Service

President and Founder, Ralph P. Dailard School Foundation. (1993-1994; Treasurer, 1994-1995)

Member, Governance Team for Ralph P. Dailard Elementary School, San Diego Unified School District. (1993-1995)

Member, School Site Council of Ralph P. Dailard Elementary School, San Diego Unified School District. (1993-1995)

Organizer, Committee for the integration of computers and instruction, Ralph P. Dailard Elementary School, San Diego Unified School District. (1993-1995)

Member, Reconfiguration Task Force, San Diego Unified School District (1995)