This list is under construction.

You will need Acrobat Reader 7.x or better. You can download a free copy from Adobe Systems.

Copyright Notice: The documents distributed here have been provided as a means to ensure timely dissemination of scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.

Thompson, P. W. (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 (working
title)*, WISDOMe Monographs (Vol. 4). Laramie, WY: University of
Wyoming.

Weber, E., & Thompson, P. W.
(2014). Students' images of two-variable functions and their graphs. *Educational Studies in Mathematics*, 86.

Saldanha, L., & Thompson, P. W.
(2014). Conceptual issues in understanding the inner logic of statistical inference: Insights from two teaching experiments. *Journal of Mathematical Behavior*, 35, 1-30.

Thompson, P. W., Artigue, M., Torner, 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). New York: Springer.

Thompson, P. W. (2013, October). "Why
use *f*(*x*) when all we really mean is *y*?".
*OnCore, The Online Journal of the AAMT.*

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

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

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 Press.

Byerley, C., Hatfield, N., & Thompson, P. W. (2012). Calculus
Student Understandings of Division and Rate. In S. Brown, S.
Larsen, K. Marrongelle, & M. Oehrtman (Eds.), *Proceedings of
the 15th Annual Conference on Research in Undergraduate Mathematics
Education* (pp. 358-363). Portland, Oregon: SIGMAA/RUME.

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

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 Press.

Liu, Y., & Thompson, P. W. (2009). Teachers' understandings of proto-hypothesis testing. Pedagogies, 4(1).

Thompson, P. W. (2008). On professional judgment and the National Mathematics Panel Report. Educational Researcher, 38(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.

Thompson, P. W. (2008, July). *Conceptual
analysis of mathematical ideas: Some spadework at the foundation
of mathematics education*. Plenary paper delivered at the
32^{nd} Annual Meeting of the International Group for the
Psychology of Mathematics Education. In O.
Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. SÈpulveda
(Eds.), Proceedings of the Annual Meeting
of the International Group for the Psychology of Mathematics
Education, (Vol 1, pp. 45-64). MorÈlia,
Mexico: PME.

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. 117-131)*.* Washington, DC:
Mathematical Association of America.

Thompson, P. W. (2008, June). One approach to a coherent K-12 mathematics. Or, it takes 12 years to learn calculus. Paper presented at the Pathways to Algebra Conference, June 22-25, Mayenne, France.

Oehrtman, M. C., Carlson, M. P., & Thompson, P. W. (2008). Foundational reasoning abilities that promote coherence in students'
understandings of function. In M. P. Carlson & C.
Rasmussen (Eds.), *Making the connection: Research and practice in
undergraduate mathematics *(pp. 150-171). Washington, DC:
Mathematical Association of America.

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

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*.*

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

Saldanha, L., & Thompson, P. (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), pp. 270-297.

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.

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.

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.

Saldanha, L., & Thompson, P. (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.* Bahia, Brazil.

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

Thompson, P. W., & Saldanha, L. (2003). Fractions
and multiplicative reasoning. In J. Kilpatrick, G. Martin &
D. Schifter (Eds.), *Research companion to the Principles and
Standards for School Mathematics* (pp. 95-114). Reston, VA:
National Council of Teachers of Mathematics.

Saldanha, L. & Thompson, P. W. (2002). Conceptions
of sample and their relationships to statistical inference. *Educational
Studies in Mathematics,* *51,* 257?270.

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*. Dordrecth, The
Netherlands: Kluwer.

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*.
Athens, GA.

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. (2001). Holistic
perspectives on instructional design -- A review of __Symbolizing
and communicating in mathematics classrooms: Perspectives on
discourse, tools, and instructional design__. *Journal for
Research in Mathematics Education*, 32(3), 321-327.

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*.
Tuscon, 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*. Tuscon, Arizona.

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

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. W. (2000). Teaching
experiment methodology: Underlying principles and essential elements.
In R. Lesh & A. E. Kelly (Eds.), *Research design in
mathematics and science education* . Dordrecht, The Netherlands:
Kluwer.

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

Thompson, P. W. (1999). Remarks on representations, conventions, and common meanings. Panel for the PME-NA XXI Working Group on Representations, Cuernavaca, Mexico.

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*.
Cuernavaca, Mexico: Centro de Investigación y de Estudios Avanzados.

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.

Saldanha, L., & Thompson, P. W. (1998). Re-thinking
co-variation from a quantitative perspective: Simultaneous
continuous variation. In S. B. Berensah & W. N. Coulombe
(Eds.), *Proceedings of the Annual Meeting of the Psychology of
Mathematics Education - North America*. Raleigh, NC: North
Carolina State University.

Thompson, P. W., & Cobb, P. (1998). On
relationships between psychological and sociocultural perspectives.
In S. Berenson (Ed.). *Proceedings of the Proceedings of the
International Group for the Psychology of Mathematics Education,
Plenaries* (pp. 3-32). Raleigh, NC: North Carolina State
Universty Press.

Thompson, P. W. (1998, March 30). *Multiplicative
relationships among fraction, measurement, multiplication, and
division*. Patrick W. Thompson. [1999, March 17].

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

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

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.

Dugdale, S., Thompson, P. W., Harvey, W., Demana, F., Waits, B.,
Kieran, C., McConnell, J. W., & Christmas, P. (1995). Technology
and algebra curriculum reform: Current issues, potential directions,
and research questions. *Journal of Technology in
Mathematics, 14*(3), 325-358.

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., & Ball, D. L. (1995). Research and practice. *Journal
for Research in Mathematics Education, 26*(4), 300-303.

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., & 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, 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., & 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.

Thompson, P. W. (1994, April). *Bridges
between mathematics and science education*. Paper presented
at the Research blueprint for science education conference, New
Orleans, LA.

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

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. 179-234). Albany, NY: SUNY Press.

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

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.

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

Thompson, P. W. (1992). *Blocks
Microworld* *5.1*. Computer Program for Macintosh.
Santa Barbara, CA: Intellimation. (Click here
to see user documentation, which also describes and justifies design
decisions.)

Thompson, P. W. (1992). Notations,
conventions, and constraints: Contributions to effective uses of
concrete materials in elementary mathematics. *Journal for
Research in Mathematics Education, 23*(2), 123-147. (Click here
for full program documentation.)

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. (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. (1987, 1991). *Word Problem Analyst* *2.1*.
Computer Program for Macintosh. San Diego, CA: San Diego State
University.

Thompson, P. W., & Thompson, A. G. (1990). Salient
aspects of experience with concrete manipulatives. In *Proceedings
of the 14th Annual Meeting of the International Group for the
Psychology of Mathematics* Vol. 3 (pp. 337-343). Mexico City.

Thompson, P. W. (1990). *Over & Back* *1.0*. Computer
Program for Macintosh. San Diego, CA: San Diego State University.

Thompson, P. W. (1990). A theoretical model of quantity-based reasoning in arithmetic and algebraic. Center for Research in Mathematics & Science Education: San Diego State University.

Thompson, P. W. (1989). Artificial
intelligence, advanced technology, and learning and teaching algebra.
In C. Kieran & S. Wagner (Eds.), *Research issues in the
learning and teaching of algebra* (pp. 135-161). Hillsdale, NJ:
Erlbaum.

Thompson, P. W. (1989, July). *Mathematics
software*. Paper presented at the Apple Computer Higher
Education Conference on "Designing for Learning", Cuptertino, CA.

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

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 11th Annual Meeting of
International Group for Psychology of Mathematics Education* Vol.
1 (pp. 248-254). Montréal: University of Quebec, Montréal.

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. (1986). Logo
as a medium for thinking about thinking. In R. Noss & C.
Hoyles (Eds.), *Proceedings of the Second International Conference
on Logo and Mathematics Education* Vol. 1 (pp. 209-215). London:
London Institute of Education.

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

Dreyfus, T., & Thompson, P. W. (1985). Microwolds
and Van Hiele levels. In *Proceedings of the Ninth Annual
Meeting of the International Group for the Psychology of Mathematics
Education*. .

Thompson, P. W. (1985). Experience,
problem solving, and learning mathematics: Considerations in
developing mathematics curricula. In E. Silver (Ed.), *Teaching
and learning mathematical problem solving: Multiple research
perspectives* (pp. 189-243). Hillsdale, NJ: Erlbaum.

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

Thompson, P. W. (1985). Understanding
recursion: Process approximates Object. In S. Damarin (Ed.). *Proceedings
of the 7th Annual Meeting of the North American Group for the
Psychology of Mathematics Education* (pp. 357-362). Columbus, OH:
Ohio State University.

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

Thompson, P. W. (1984). Microworld environments for teaching
mathematics to future elementary school teachers. In *Proceedings
of the De Anza Conference on Computers in Higher Education* Vol.
1 (pp. 5-11). .

Thompson, P. W. (1982). *A theoretical framework for understanding
young children's concepts of whole-number numeration.*
Unpublished Doctoral dissertation, University of Georgia, Department
of Mathematics Education.

Steffe, L., Thompson, P., & Richards, J. (1982). Children's
counting in arithmetical problem solving. In T. Carpenter, T. Romberg,
& J. Moser (Eds.), *Addition and subtraction: A cognitive
perspective* (pp. 83-97). Hillsdale, NJ: Erlbaum.

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

Thompson, P. W. (1979, April). *The
teaching experiment in mathematics education research*.
Paper presented at the NCTM Research Presession, Boston, MA.