Vita

January, 2014

Patrick W.
Thompson

Professor, Mathematics Education

Arizona State University

School of Mathematical & Statistical Sciences

P. O. Box 871804

Tempe, AZ 85287-1804

E-mail: Pat.Thompson@asu.edu

Web site: http://Pat-Thompson.net/

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 teachersÕ and studentsÕ understanding of calculus

- Relationships among probabilistic, statistical, and quantitative reasoning

- Technology in mathematics education

University of Georgia, 1977 - 1982, Ed.D. Mathematics
Education (Dissertation title: *A
Theoretical Framework for Understanding Young ChildrenÕs 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)

Professor of Mathematics Education, *School of Mathematical and Statistical
Sciences,* *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,* Peabody College,* *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, *Department of Mathematical Sciences, 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, *Department of Mathematical Sciences, San
Diego State University (1992-1997)*

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

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

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

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

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

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

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

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

Featured Guest, Mathematics Education Student Association (September, 2012)

Finalist, ASU ParentsÕ 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 (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)

Thompson, P.
W. (2014, January). *Mathematics Education
Reform and the Common Core State Standards.* Banquet address, San Diego
County Chapter of Mathematics for America, San Diego, CA.

Thompson, P.
W. (2013, June). *Schemes for Thinking
about Magnitudes.* Keynote address given at the Conference on Epistemic
Algebra Students, Athens, GA.

Thompson, P.
W. (2013, February). *Under the Radar:
Foundational Meanings that Math Professors (Mistakenly) Assume Students Have.*
Plenary address given at the annual meeting of the MAA Special Interest Group
on Research in Undergraduate Mathematics Education.

Thompson, P.
W. (2013, January). *Fostering StudentsÕ
Critical and Creative Thinking in Mathematics.* Featured address given at
the International Science, Mathematics, and Technology Conference, Bangkok,
Thailand.

Thompson, P.
W. *Advances In Quantitative Reasoning*.
(2012, May). Plenary presentation given at the Conference on Quantitative
Reasoning and Mathematical Modeling: A Driver for STEM Integrated Education,
Savannah, GA.

Thompson, P.
W. (2012, April) *Mathematics and
Mathematics Education.* Plenary panel at the International Conference on
Mathematics and Mathematics Education, Ben-Gurion University, Israel.

Thompson, P.W.
(2012, January) *The Professional
Development of Secondary Mathematics Teachers: A Tribute 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 NeednÕt 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*. 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 DuvalÕs And KaputÕs Papers*. Plenary discussant at* *the Twenty-first Annual Meeting of the
Psychology of Mathematics Education, North America*. *Cuernavaca, Mexico.

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. (1996, July). *Technology And
Curriculum Reform: Designing For Emergence, Or Making Students, Curricula, And
Instruction Meet Where None Of Them Is, Or You CanÕt 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., & 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 NewtonÕs 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.

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

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

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,
2007-2012*)

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)

Research in Collegiate Mathematics Education (co-editor, 2006-2008; editor, 2008-2012)

Cognition and Instruction (associate editor; 2002-2007)

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

International Journal of Science and Mathematics
Education (*2010-present*)

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

Educational Researcher (*2000-2003*)

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

International Journal of Computers in Mathematics
Learning (*1999-2010*)

Peabody Journal of Education (*1997-2005*)

Journal of Artificial Intelligence in Education (*1989-1992*)

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

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

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

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

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.

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.

Weber, E.,
& Thompson, P. W. (submitted). Students' images of two-variable functions
and their graphs. *Educational Studies in
Mathematics.*

Weber, E.,
& Thompson, P. W. (submitted). Students' schemes for rate of change in two
and three dimensions. *Journal for
Research in Mathematics Education.*

Moore, K. C.,
Weber, E., & Thompson, P. W. (submitted). Static and emergent shape
thinking *Journal for Research in
Mathematics Education.*

Moore, K. C.,
Weber, E., & Thompson, P. W. (submitted). Shape thinking and studentsÕ
graphing activity. *Psychology of
Mathematics Education.*

Thompson, P.
W., & Draney, K. (submitted). A methodology for investigating teachersÕ
mathematical meanings for teaching. *Psychology
of Mathematics Education.*

Byerley, C.,
& Thompson, P. W (submitted). Secondary teachersÕ relative size schemes. *Psychology of Mathematics Education.*

Yoon, H.,
Hatfield, N., & Thompson, P. W. (submitted). TeachersÕ meanings for
function notation. *Psychology of
Mathematics Education.*

Musgrave, S.,
& Thompson, P. W. (submitted). Function notation as idiom. *Psychology of Mathematics Education.*

Saldanha, L., & Thompson, P. W. (in press). Conceptual
issues in understanding the inner logic of statistical inference: Insights from
two teaching experiments. *Journal of
Mathematical Behavior.*

Thompson, P. W. (2013). Constructivism in mathematics
education. *Encyclopedia of mathematics
education [online].* Berlin: Springer. doi: 10.1007/SpringerReference_313210
2013-05-10 00:00:07 UTC.

Thompson, P. W. (2013, September). ÒWhy use *f*(*x*)
when all we really mean is *y*?Ó. *OnCore—The Online Journal of the
Arizona Association of Mathematics Teachers*.

Thompson, P. W, Byerley, C., & Hatfield, N. (2013).
A conceptual approach to calculus made possible by technology. *Computers in
the Schools*, *30*, 124-147.

Weber, E., Tallman, M., Byerley, C., & Thompson,
P. W. (2012). Introducing the derivative via calculus triangles. *Mathematics Teacher*, *104*(4), 274-278.

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 teachersÕ development of coherent
mathematical meanings. *Journal of
Mathematics Teacher Education,* **10**,
415-432.

Liu, Y., & Thompson, P. W. (2007). TeachersÕ
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 studentsÕ 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). StudentsÕ
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 teacherÕs 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
wouldnÕt understand. *Journal of
Mathematical Behavior*, *3 *(2),
147-165.

Thompson, P. W., Carlson, M. P., Byerley, C., &
Hatfield, N. (in press). Schemes for thinking with magnitudes: A hypothesis
about foundational reasoning abilities in algebra. In K. C. Moore, L. P. Steffe
& L. L. Hatfield (Eds.), *Epistemic
algebra students: Emerging models of students' algebraic knowing*. WISDOMe
Monographs (Vol. 4). Laramie, WY: University of Wyoming.

Thompson, P. W., Artigue, M., Tšrner, G., & de
Shalit, E. (2014). Collaboration between mathematics and mathematics education.
In M. Fried & T. Dreyfus (Eds.), *Mathematics
and mathematics education: Searching for common ground* (pp. 313-333).
Berlin: Springer.

Thompson, P. W. (2013). In the absence of meaning. In
K. Leatham (Ed.), *Vital directions for research in mathematics education *(pp. 57-93). New York: Springer.

Thompson, P. W. (2012). 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, pp. 143-148). Laramie, WY: University of Wyoming.

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. *ChildrenÕs
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 studentsÕ
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 teachersÕ 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). ChildrenÕs counting in arithmetical problem solving. In T. C.
Carpenter, T. Romberg, & J. Moser (Eds.), *ChildrenÕs arithmetic: A cognitive perspective* (pp. 83-98).
Hillsdale, NJ: Lawrence Erlbaum.

Byerley, C., Hatfield, N., & Thompson, P. W. (2012).
Calculus studentsÕ understandings of division and rate*.* In *Proceedings
of the 15th Annual Conference on Research in Undergraduate Mathematics
Education* (pp. 3358-363).
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. S‡iz, &
A. MŽndez (Eds.). *Proceedings of the
Twenty-eighth Annual Meeting of the International Group for the Psychology of
Mathematics Education*, Muriel, Mexico.

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). TeachersÕ
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). TeachersÕ
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). StudentsÕ
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 Investigaci—n 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 childrenÕs 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). MontrŽal: University of Quebec, MontrŽal.

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 Å 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.

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.

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.

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. (2007, April). Invited testimony given to the PresidentÕs National Mathematics Panel. Aurora, Il.

Thompson, P. W. (2014, April). *Connecting Data with Chance Through Modeling: A Commentary.*
Symposium discussant at the annual Research Presession of the National Council
of Teachers of Mathematics, New Orleans, LA.

Thompson, P. W. (2013, April). *Recognizing Proportional Relationships: A Commentary.* Symposium
discussant at the annual Research Presession of the National Council of
Teachers of Mathematics, Denver, CO.

Thompson, P. W. (2012, April). *Fractions, Units, and the Common Core State Standards for Mathematics*.
Symposium discussant at the annual Research Presession of the National Council
of Teachers of Mathematics, Philadelphia, PA.

Thompson, P. W. (2012, April). *Current Thinking on Trig Concepts Worth Knowing: This is Not
SOH-CAH-TOA.* Symposium discussant at the annual Research Presession of the
National Council of Teachers of Mathematics, Philadelphia, PA.

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 TeachersÕ 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 TeachersÕ 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). *TeachersÕ 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 TeachersÕ 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
TeachersÕ 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). *StudentsÕ 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 StudentsÕ 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). *ChildrenÕs 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.

Thompson, P. W. (2013, November). *Weak Meanings Lead To Weak Learning.* Invited colloquium given at
the School of Mathematical and Statistical Sciences, Arizona State University,
Tempe, AZ.

Thompson, P. W. (2013, September). *Why Function Notation Is Important And Why
It Is Hard To Understand.* Invited presentation given at the annual meeting
of the Arizona Association of Teachers of Mathematics, Tempe, AZ.

Thompson, P. W. (2013, January). *Assessing Teachers Mathematical Meanings for Teaching Secondary
Mathematics: Implications for Math and Science Partnerships*. Invited
presentation at the NSF Learning Network Conference, Washington, D.C.

Thompson, P. W., & Hatfield, N. (2012, March). *Technology and Calculus Reform.* Invited
address given at the Central Regional Meeting of the Mathematical Association
of America (presented by N. Hatfield).

Thompson, P. W. (2012, October). *A Calculus Course That Focuses On Students' Understanding Of The Fundamental
Theorem Of Calculus*. Invited colloquium for the Department of Mathematics,
Virginia Tech.

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. (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 OneÕs Own 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 ÒHigherÓ 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 ÒAlgebra As ModelingÓ.* 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 TeachersÕ 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 StudentsÕ 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 StudentsÕ 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 DirectorsÕ 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, 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, QuŽbec City, QuŽbec, 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
DirectorÕs 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
TechnologyÕs 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). ÒDirect EngagementÓ 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 InstituteÕs 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 PresidentÕs 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-gradersÕ concepts of integers.*
Paper given at the Research Presession to the Annual Meeting of the National
Council of Teachers of Mathematics, San Antonio, TX.

*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 DienesÕ blocks
or on digits of numerals) and which reflects the studentÕs 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).

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 StudentsÕ
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 studentsÕ
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).

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 TeachersÕ Mathematical Understanding Through Computer-Based Modeling. ($100,00 equipment grant; 1997-1999)

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

Calculus redesign (present)

Technology and Mathematical Visualization (present)

Bachelor of Science, Mathematics, with Concentration in Mathematics Education (2011)

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

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

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

PiagetÕs Genetic Epistemology

Calculus I

Technology and Mathematical Visualization

Cognition, computers, and mathematics curriculum

Research on multiplicative reasoning

PiagetÕs 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.

Transformation geometry

Computers and calculators in elementary/junior high mathematics

Computer-extended secondary mathematics

Logo in mathematics

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

Eric Weber (Ph.D. 2012). Dissertation title: Students'
Understandings of Two-Variable Functions and Rate of Change

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 teachersÕ ways of thinking about rate of change.

Yan Liu (PhD, 2006). Dissertation title: TeachersÕ 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?Ó: An investigation of students exploring connections between sampling distributions and statistical inference. (Otto Bassler award for Outstanding Dissertation)

Linda Agoune

Cameron Byerley

Neil Hatfield

Hyunkyoung Yoon

Michael Tallman

Stacey Bowling

Aviva Halani (Ph.D., 2013)

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)

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 studentsÕ understanding of functions and graphs.

Donna Troy (MS Mathematics Education, 1993). Thesis
title: *Future teachersÕ 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.

Mathematics
in Undergraduate Study Programs: Challenges for Research and for the Dialogue
between Mathematics and Didactics of Mathematics, *Mathematisches Forschungsinstitut Oberwolfach (December, 2014)*

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*

(lost track of recent advisory boards)

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

University of Georgia, NSF project on childrenÕs 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 childrenÕs 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 childrenÕs 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, NCTMÕs Research Catalyst Group: Develop research programs to investigate aspects of implementation of NCTMÕs 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)

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

Member, Graduate Committee (2005-2013)

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

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

Member, ChancellorÕs Council on Teacher Education (2000-2003)

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)

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)

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 Òinternal
sabbaticalsÓ funded by the DeanÕs 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).

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)