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Thompson, P. W. (in press) A Journey from a Question in Mathematics to a Theory of Calculus Learning and Teaching. In Yan, X. K., Mamalo, A., & Kantorovich, I,. (Eds.) *Where is the Math in your MathEd Research? Personal responses of leading educators* (Chapter 17). Springer.

Thompson, P. W. (in press). *Figurative and operative imagery: Essential aspects of reflection in the development of schemes and meanings.* In Dawkins, P., Hackenberg, A., and Norton, A. (Eds.), *Piaget's genetic epistemology in mathematics education research*. New York: Springer.

Karagöz Akar, G., Özgür Zembat, I., Selahattin, A., & Thompson, P. W. (Eds.) *Quantitative reasoning in mathematics and science education*(pp. 1-16). Zürich: Springer Cham.

Thompson, P. W. (2022). Quantitative reasoning as an educational lens. In Karagöz Akar, G., Özgür Zembat, I., Selahattin, A., & Thompson, P. W. (Eds.) *Quantitative reasoning in mathematics and science education*, (pp. 5-20). Zürich: Springer Cham.

Thompson, P. W., & Harel, G. (Eds.) (2021) Calculus learning and teaching around the world. *ZDM Mathematics Eduction*, 53.

Thompson, P. W., & Harel, G. (2021). Ideas foundational to calculus learning and their links to students’ difficulties.* ZDM Mathematics Education, 53*(3), 507-519

Frank, K. & Thompson, P. W. (2021). School students’ preparation for calculus in the United States. *ZDM Mathematics Education, 53*(3), 549-562

Thompson, P. W. (2020; online first). Musing on musings. Review of Vinner, S. (2018). *Mathematics, education, and other endangered species.** Mathematical Thinking and Learning.*

Yoon, H., & Thompson, P. W. (2020). Secondary teachers' meanings for function notation in the United States and South Korea. *Journal of Mathematical Behavior, online*

Thompson, P. W. (2019). Making the Fundamental Theorem of Calculus Fundamental to *Students'* Calculus. Plenary paper for the *Conference on Calculus in Upper Secondary and Beginning University Mathematics*, Kristiansand, Norway, 6-9 August 2019.

I normally post papers only when they are published. But I do not anticipate publishing this one and I've received many requests for it.

The presentation created for this paper is at my presentations page

Thompson, P. W. (2019, Spring). Animations: Windows into a dynamic mathematics. *OnCore: Journal of the Arizona Association of Teachers of Mathematics*, pp. 48-51.

Thompson, P. W., & Ashbrook, M. (2019) *Calculus:
Newton meets technology.* Part of Project DIRACC: Developing and
Investigating a Rigorous Approach to Conceptual Calculus.

Thompson, P. W., & Milner, F. (2018). Teachers’
meanings for function and function notation in South Korea and the
United States. In H.-G. Weigand, W. McCallum, M. Menghini, M.
Neubrand & G. Schubring (Eds.), *The Legacy of Felix Klein* (pp. 55-66).
Berlin: Springer.

Byerley, C., & Thompson, P. W. (2017). Teachers'
meanings for measure, slope, and rate of change. *Journal of
Mathematical Behavior, 48*, 168-193*.*

Thompson, P. W., Hatfield, N. J., Yoon, H., Joshua, S.,
& Byereley, C. (2017). Covariational
reasoning among U.S. and South Korean secondary mathematics teachers.
*Journal of Mathematical Behavior, 48*, 95-111.

Thompson, P. W., & Carlson, M. P. (2017). Variation,
covariation, and functions: Foundational ways of thinking
mathematically. In J. Cai (Ed.), *Compendium for research in
mathematics education *(pp. 421-456). Reston, VA: National Council of Teachers of Mathematics.

Thompson, P. W. (2016). Researching
mathematical meanings for teaching. In L. D. English & D.
Kirshner (Eds.), *Handbook of international research in mathematics
education* (pp. 435-461). New York: Taylor & Francis.

Thompson, P. W., & Dreyfus, T. (2016). A
coherent approach to the Fundamental Theorem of Calculus using
differentials. In R. Biehler & R. Hochmuth (Eds.), *Proceedings
of the Conference on Didactics of Mathematics in Higher Education as a
Scientific Discipline* (pp. 355-359). Hannover, Germany: KHDM.

Yoon, H., Byerley, C., & Thompson, P. W. (2015). Teachers'
meanings for average rate of change in U.S.A. and Korea. In T.
Fukawa-Connelly, N. E. Infante, K. Keene & M. Zandieh (Eds.), *Proceedings
of the 18th Meeting of the MAA Special Interest Group on Research in
Undergraduate Mathematics Education*, pp. 335-348. Pittsburgh, PA:
RUME.

Musgrave, S., Hatfield, N., & Thompson, P. W. (2015).
Calculus students' meaning for difference.
In T. Fukawa-Connelly, N. E. Infante, K. Keene & M. Zandieh (Eds.), *Proceedings
of the 18th Meeting of the MAA Special Interest Group on Research in
Undergraduate Mathematics Education*, pp. 809-814. Pittsburgh, PA:
RUME.

Moore, K. C., & Thompson, P. W. (2015). Shape
thinking and students' graphing activity. In T. Fukawa-Connelly, N.
E. Infante, K. Keene & M. Zandieh (Eds.), *Proceedings of the 18th
Meeting of the MAA Special Interest Group on Research in Undergraduate
Mathematics Education*, pp. 782-789. Pittsburgh, PA: RUME.

Joshua, S., Musgrave, S., Hatfield, N., & Thompson,
P. W. (2015). Conceptualizing and
reasoning with frames of reference. In T. Fukawa-Connelly, N. E.
Infante, K. Keene & M. Zandieh (Eds.),

Musgrave, S., Hatfield, N., & Thompson, P. W. (2015).
Teachers' meanings for the substitution
principle. In T. Fukawa-Connelly (Ed.),

Thompson, P. W. (2015). Mathematical
meanings of Korean and USA mathematics teachers for mathematical ideas
they teach. *Research in Mathematical Education*, *19*(3),
1-6. (Introduction to plenary address at the KSME Int'l Conference on
Mathematical Education, Nov 5, 2015.)

Byerley, C., & Thompson, P. W. (2014). Secondary
teachers' relative size schemes. In P. Liljedahl & C. C. Nicol
(Eds.), *Proceedings of the 38th Meeting of the International Group
for the Psychology of Mathematics Education*, (Vol 2, pp. 217-224).
Vancouver, BC: PME.

Musgrave, S., & Thompson, P. W. (2014). Function
notation as idiom. In P. Liljedahl & C. C. Nicol (Eds.), *Proceedings
of the 38th Meeting of the International Group for the Psychology of
Mathematics Education*, (Vol 4, pp. 281-288). Vancouver, BC: PME.
Retrieved from http://bit.ly/1p08TCG

Thompson, P. W, Carlson, M. P., Byerley, C., &
Hatfield, N. (2014). 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, pp. 1-24).
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* (1), 67-85.

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 32nd
Annual Meeting of the International Group for the Psychology of
Mathematics Education. In O. Figueras, J. L. Cortina, S. Alatorre, T.
Rojano & A. SČpulveda (Eds.), *Proceedings of the Annual Meeting of
the International Group for the Psychology of Mathematics Education*(Vol
1, pp. 45-64). MorČlia, 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. Berenson & 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.