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Thompson, P. W., Artigue, M., Torner, G., & de Shalit, E.  (in press). Collaboration between mathematics and mathematics education. In M. Fried & T. Dreyfus (Eds.), Mathematics and mathematics education: Searching for common ground. New York: Springer.

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.

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

Thompson, P. W., 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.