Martin Simon
Professor of Mathematics Education
Phone: 212-998-5384
Email: msimon@nyu.edu
Office Hours: By appt.
- Departments:
- Programs:
Martin Simon's current research focuses on understanding the process by which students develop mathematical concepts through their mathematical activity, and how such learning can be fostered. Simon has also done extensive research on the development of mathematics teachers as they learn to teach mathematics with a conceptual focus. Simon has served as a professor of mathematics education at Penn State University and director of the Summer Math for Teachers program at Mount Holyoke College. He has served as principal investigator on five National Science Foundation projects, and was awarded the Distinguished Research Award by the Association of Teacher Educators in 2000, and a Career Achievement Award by the Penn State University College of Education in 2001. He earned his doctorate in mathematics education from the University of Massachusetts at Amherst in 1986.
Simon's current project, Measurement Approach to Rational Numbers (MARN), continues his research on how students learn mathematical concepts, while developing and researching an approach to teaching fractions and ratios building on measurement concepts.
Publications
- Simon, M.A. (2017). Explicating mathematical concept and mathematical conception as theoretical constructs. Educational Studies in Mathematics, 94.
- Simon, M.A., Kara, M., Placa, N., & Sandir, H. (2016). Categorizing and promoting reversibility of mathematical concepts. Educational Studies in Mathematics, 93(2), 137-153.
- Simon, M. A. (2016). An approach to design of mathematical task sequences: Conceptual learning as abstraction. PNA, 10(4), 270-279.
- Simon, M.A., Placa, N., Avitzur, A. (2016). Participatory and anticipatory stages of mathematical concept learning: Further empirical and theoretical development. Journal for Research in Mathematics Education, 47(1), 63-93.
- Simon, M. A. (2013). Issues in theorizing mathematics learning and teaching: A contrast between learning through activity and DNR research programs. The Journal of Mathematical Behavior, 32(3), 281-294.
- Simon, M. A. (2013). Promoting Fundamental Change in Mathematics Teaching: A Theoretical, Methodological, and Empirical Approach to the Problem. ZDM: The International Journal On Mathematics Education, 45(5), 573-582.
- Simon, M. A. (2012). Reasoning about intensive quantities in whole-number multiplication? A possible basis for ratio understanding. For the Learning of Mathematics, 32, 35-41.
- Simon, M. A. (2012). Extending the coordination of cognitive and social perspectives. PNA, 6, 43-49.
- Simon, M. A., Saldanha, L., McClintock, E., Karagoz Akar, G., Watanabe, T., & Ozgur Zembat, I. (2010). A developing approach to studying students’ learning through their mathematical activity. Cognition and Instruction, 28, 70-112.
- Simon, M. A. (2009). Amidst multiple theories of learning in mathematics education. Journal for Research in Mathematics Education, 40, 477 - 490.
- Simon, M. A. (2006). Key developmental understandings in mathematics: A direction for investigating and establishing learning goals. Mathematical Thinking and Learning, 8, 4, 359-371.
- Simon, M. A. (2004). Raising issues of quality in mathematics education research. Journal for Research in Mathematics Education, 35, 157-163.
- Simon, M. & Tzur, R. (2004) Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6, 91-104.
- Simon, M., Tzur, R., Heinz, K., & Kinzel, M (2004). Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction. Journal for Research in Mathematics Education, 35, 305-329.
- Tzur, R., Simon, M.A. (2004). Distinguishing two stages of mathematics conceptual learning. International Journal of Science and Mathematics Education, 2. (2), 287 – 304.
- Simon, M. A. (2001). National reform of mathematics teaching: The contrast between China and the United States. Contemporary Psychology APA review of Books, 46, 51-53.
- Tzur, R., Simon, M.A., Heinz, K., & Kinzel, M. (2001). An account of a teacher's perspective on learning and teaching mathematics: Implications for teacher development. Journal of Mathematics Teacher Education, 4, 227-254.
- Heinz, K., Kinzel, M., Simon, M. A., & Tzur, R. (2000). Moving students through steps of mathematical knowing: An account of the practice of an elementary mathematics teacher in transition. Journal of Mathematical Behavior, 19, 83-107.
- McNeal, B. & Simon, M. (2000). Mathematics culture clash: Negotiating new classroom norms with prospective teachers. Journal of Mathematical Behavior, 18, 475-509.
- Simon, M., Tzur, R., Heinz, K., Kinzel, M., & Smith, M. (2000). Characterizing a perspective underlying the practice of mathematics teachers in transition. Journal for Research in Mathematics Education, 31, 579-601.
- Simon, M. & Tzur, R. (1999). Explicating the teacher's perspective from the researchers' perspective: Generating accounts of mathematics teachers' practice. Journal for Research in Mathematics Education, 30, 252-264.
- Simon, M. A. (1998). Review of Teaching mathematics: Toward a sound alternative. Journal of Curriculum Studies, 30, 235-238.
- Sowder, J., Armstrong, B., Lamon, S., Simon, M. A., Sowder, L. & Thompson, A. (1998). Educating teachers to teach multiplicative structures in the middle grades. Journal of Mathematics Teacher Education, 1, 127-155.
- Simon, M. A. (1996). Beyond inductive and deductive reasoning: The search for a sense of knowing. Educational Studies in Mathematics, 30, 197-210.
- Simon, M. A. & Blume, G. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. Journal of Mathematical Behavior, 15, 3-31.
- Simon, M. A. & Brobeck, S. (1996). Challenges to mathematics reform in classrooms. Pennsylvania Educational Leadership, 15, 21-28.
- Simon, M. A. (1995). Investigating the development of multiplicative reasoning. Journal for Research in Mathematics Education, 26, 282-287.
- Simon, M. A. (1995). Elaborating models of mathematics teaching: A response to Steffe and D'Ambrosio. Journal for Research in Mathematics Education, 26, 160-162.
- Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114-145.
- Simon, M. A. (1994). Learning mathematics and learning to teach: Learning cycles in mathematics teacher education. Educational Studies in Mathematics, 26, 71-94.
- Simon, M. A. & Blume, G. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25, 472-494.
- Simon, M. A. & Blume, G. (1994). Mathematical modeling as a component of understanding ratio-as-measure: A study of prospective elementary teachers. Journal of Mathematical Behavior, 13, 183-197.
- Simon, M. A. (1993). A context for change: Themes related to mathematics education reform. In T. Wood (Ed.), Reforming children’s mathematical learning: Insights and issues. Journal for Research in Mathematics Education Monograph Series, Number 6, Reston, VA: National Council of Teachers of Mathematics.
- Simon, M. A. (1993). Focus on children’s mathematical learning in classrooms: Input and issues. In T. Wood (Ed.), Reforming children’s mathematical learning: Insights and issues. Journal for Research in Mathematics Education Monograph Series, Number 6, Reston, VA: National Council of Teachers of Mathematics.
- Simon, M. A. (1993). Prospective elementary teachers knowledge of division. Journal for Research in Mathematics Education, 24, 233-254.
- Simon, M. A. & Schifter, D. (1993). Toward a constructivist perspective: The impact of a mathematics teacher inservice program on students. Educational Studies in Mathematics, 25, 331-340.
- Schifter, D. & Simon, M. A. (1992). Assessing teachers' development of a constructivist view of learning. Teaching and Teacher Education, 8, 187-197.
- Simon, M. A. & Schifter, D. (1991). Toward a constructivist perspective: An intervention study of mathematics teacher development. Educational Studies in Mathematics, 22, 309-331.
- Simon, M. A. (1989). Intuitive understanding in geometry: The third leg. School Science and Mathematics, 89, 373-379.
- Simon, M. A. (1986). The teacher's role in increasing student understanding of mathematics, Educational Leadership, 43, #7, 40-43. (Reprinted in Exemplary Practice Series: Mathematics. Center on Evaluation, Development, Research, Phi Delta Kappa. Bloomington, IN: 1987.)
- Articles in Refereed Proceedings:
- Simon, M. A. (2015). Learning through activity: Analyzing and promoting mathematics conceptual learning.In K. Beswick, T. Muir, & J. Wells (Eds.) (2015). Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 51-65). Hobart, Australia: PME.
- Simon, M. A. (2014). An emerging theory for design of mathematical task sequences: Promoting reflective abstraction of mathematical concepts. In C. Nicol, S. Oesterle, P.,Liljedahl, & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education, Vol. 5 (pp. 193-199). Vancouver, Canada: PME.
- Simon, M., Placa, N., & Avitzur, A. (2014). Two stages of mathematics concept learning: Additional applications in analysis of student learning. In C. Nicol, S. Oesterle, P.,Liljedahl, & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education, Vol. 5 (pp. 201-207). Vancouver, Canada: PME.
- Simon, M.A. (2013). Promoting reversibility: Building on learning through activity. In A.M. Lindmeier & A. Heinze (Eds.)Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Vol. IV, (pp. 225-232), Kiel Germany: PME.
- Simon, M.A. (2013). Developing theory for design of mathematical task sequences: Conceptual learning as abstraction. In C. Margolinas (Ed), Task design in mathematics education. Proceedings of ICMI Study 22, (pp. 503-510). http://hal.archives-ouvertes.fr/docs/00/83/74/88/PDF/ICMI_STudy_22_proceedings_2013-FINAL_V2.pdf
- Placa, N. & Simon, M. A. (2012) Demonstrating the usefulness of the participatory-anticipatory distinction. In L. R. Van Zoest, J.-J. Lo, & J. L. Kratky (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, (pp. 1156 – 1162). Kalamazoo, MI: Western Michigan University.
- Simon, M.A., (2011). Studying mathematics conceptual learning: Student learning through their mathematical activity. In L. R. Wiest & T. Lamberg (Eds.), Proceedings of the Thirty-Third Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 31-43). Reno, NV: University of Nevada, Reno.
- Simon, M. (2010). Extending the coordination of cognitive and social perspectives. In Pinto, M. M. F. & Kawasaki, T. F. Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 177-183. Belo Horizonte Brazil: PME.
- Simon, M., Saldanha, L., McClintock, E., Karagoz Akar, G., Watanabe, T., & Zembat , I. (2007). Students’ learning through their own activity: Toward a basis for a scientific approach to task design and sequencing. In Lamberg, T., & Wiest, L. R. (Eds.), Proceedings of the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, pp. 311-318. Stateline (Lake Tahoe), NV: University of Nevada, Reno.
- Simon, M. (2007). Constraints on what teachers can learn from their practice: Teachers’ assimilatory schemes. In J-H Woo, H-C Lew, K-S Park, & D-Y Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, (pp. 137-141).
- Simon, M. (2007). Mathematics: A human potentail. In J-H Woo, H-C Lew, K-S Park, & D-Y Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, (pp. 109-114).
- Simon, M. (2006). Pedagogical concepts as goals for teacher education: Towards an agenda for research in teacher development. S. Alatorre, J.L. Cortina, M. Sáiz, & A. Méndez (Eds.)Proceedings of the Twenty Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 2, (pp. 730-735). Mérida, Mexico: Universidad Pedagógica Nacional.
- Simon, M. (2003). Logico-mathematical activity versus empirical activity: Examining a pedagogical distinction, In N. Pateman, B. J. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, (pp. 183-190). Honolulu, Hawaii:
- Simon, M. (2002). Focusing on critical understandings in mathematics. In D. Mewborn, P. Sztajn, D. White, H. Wiegel., R. Bryant, & K. Nooney (Eds.), Proceedings of the Twenty-fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol II, (pp. 991-998). Athens, GA: ERIC.
- Simon, M. A. (2000). Reconsidering mathematical validation in the classroom. In Proceedings of the twenty-fourth annual meeting of International Group for the Psychology of Mathematics Education. Hiroshima, Japan.
- Simon, M., Tzur, R., Heinz, K., & Kinzel, M. (2000). Articulating theoretical constructs for mathematics teaching, In Proceedings of the Twenty-second Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education. Tucson, AZ.
- Heinz, K., Simon, M., Kinzel, M. & Tzur, R. (1999). A perspective on the use of manipulatives: Making sense of a sixth-grade teacher’s use of base-ten blocks to promote understanding of the long division algorithm. In F. Hitt & M. Santos (eds.), Proceedings of the Twentieth-First Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 2, (pp. 737-743). Cuernavaca, Mexico.
- Simon, M., Tzur, R., Heinz, K., Smith, M., & Kinzel, M. (1999). On formulating the teacher's role in promoting mathematics learning. In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, (pp. 201-208), Haifa, Israel.
- Tzur, R., & Simon, M. (1999). Postulating relationships between levels of knowing and types of tasks in mathematics teaching: A constructivist perspective. In F. Hitt & M. Santos (eds.), Proceedings of the Twentieth-First Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education, Vol 2, (pp. 805-810). Cuernavaca, Mexico, Columbus, OH: ERIC.
- Simon, M., Tzur, R., Heinz, K., Kinzel, M., and Smith, M. (1998). Characterizing a perspective on mathematics learning of teachers in transition. In S. Berenson, K. Dawkins, M. Blanton, W. Coulombe, J. Kolb, K. Norwood, & L. Stiff (Eds.), Proceedings of the Twentieth Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 2, Columbus, OH: ERIC, pp. 768-774.
- Tzur, R., Simon, M. A., Heinz, K., & Kinzel, M. (1998). Meaningfully Connecting Mathematical Pieces: An Account of A Teacher in Transition. In A. Olivier & K Newstead (Eds.), Proceedings of the Twenty-Second Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, (pp. 145-152).
- Heinz, K., Kinzel, M., Simon, M. A., & Tzur, R. (1997). One teacher's solution to reforming mathematics teaching based on her evolving relationship to mathematics. In J. Dossey, J. Swafford, M. Parmantie, & A. Dossey (Eds.), Proceedings of the Nineteenth Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 2, (pp. 365-370), Bloomington/Normal, IL.
- McNeal, B. & Simon, M. A. (1997) Mathematics culture clash: Negotiating new classroom norms with prospective teachers. In J. Dossey, J. Swafford, M. Parmantie, & A. Dossey (Eds.), Proceedings of the Nineteenth Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education Vol. 2, (pp.487-493), Bloomington/Normal, IL.
- Simon, M. A. & Tzur, R. (1997). Generating theoretical accounts of mathematics teachers’ practices. In E. Pehkonen (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, (pp. 160- 165), Lahti, Finland.
- Simon, M. A. (1996). A methodology for research on mathematics teacher development: The teacher development experiment. In E. Jakubowski, D. Watkins, & H. Biske (Eds.), Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Panama City, FL.
- McNeal, B. & Simon, M. A. (1994). Development of classroom social norms and mathematical practices with preservice teachers. In D. Kirshner, Proceedings of the Sixteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 2, (pp. 231-237). Baton Rouge, LA.
- Myers, J. & Simon, M. A. (1993). Authorizing mathematical knowledge in a classroom community. In B. Pence (Ed.) Proceedings of the Fifteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Asilomar, CA.
- Simon, M. A. & Blume, G. (1993). Mathematical justification : A classroom teaching experiment with prospective teachers.In B. Pence (Ed.) Proceedings of the Fifteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Asilomar, CA.
- Simon, M. A. & Brobeck, S. (1993). Changing views of mathematics learning: A case study of a prospective elementary teacher. In B. Pence (Ed.) Proceedings of the Fifteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Asilomar, CA.
- Simon, M. A. & Mazza, W. (1993). From learning mathematics to teaching mathematics: A case study of a prospective teacher in a reform-oriented program. In B. Pence (Ed.) Proceedings of the Fifteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Asilomar, CA.
- Simon, M. A. & Blume, G. (1992). Understanding multiplicative structures: A study of prospective elementary teachers. In William Geeslin & Karen Graham (Eds.), Proceedings of the sixteenth annual meeting of the International Group for the Psychology of Mathematics Education, Vol. III (pp. 11-18), Durham, NH.
- Schifter, D. & Simon, M. A. (1991). Toward a constructivist perspective: Impact on students. In R. Underhill (Ed.), Proceedings of the thirteenth annual meeting Psychology of Mathematics Education, North American Chapter, Blacksburg, VA.
- Simon, M. A. (1991). Initial development of prospective elementary teachers’ conceptions of mathematics pedagogy. In F. Furlinghetti (Ed.), Proceedings of the fifteenth annual meeting of International Group for the Psychology of Mathematics Education, Assisi, Italy.
- Simon, M. A. (1990). Prospective elementary teachers’ knowledge of division. In G. Booker, P. Cobb, & T. Mendicuti (Eds.), Proceeding of the fourteenth annual meeting of the International Group for the Psychology of Mathematics Education, Mexico City, Mexico.
- Simon, M. A. (1988). Diagrams as an intermediate step in the development of algebraic representation. Proceedings of the tenth annual meeting of Psychology of Mathematics Education, North American Chapter, DeKalb, IL.
- Simon, M. A. (1988). Formative evaluation of a constructivist mathematics teacher inservice program. In A. Borbas (Ed.), Proceedings of the twelfth annual meeting of International Group for the Psychology of Mathematics Education, Veszprem, Hungary.
- Simon, M. A. (1986). Components of effective use of diagrams in math problem solving. In G. Lappan & R. Evan (Eds.), Proceedings of the eighth annual meeting of Psychology of Mathematics Education, North American Chapter.
- Simon, M. A. (1985). Diagram drawing: Effect on the conceptual focus of novice problem solvers. Proceedings of the seventh annual meeting of Psychology of Mathematics Education, North American Chapter, Columbus, OH.
- Chapters in Books:
- Simon, M. A. (in press). Challenges in mathematics teacher education from a (mostly) constructivist perspective. In A. Tyminsky & S. Kastenberg (Eds.), Building support for scholarly practices in methods. Charlotte, NC: IAP
- Simon, M. (2014). Hypothetical Learning Trajectories in Mathematics Education. In S. Lerman, (Ed.), Encyclopedia of Mathematics Education (pp. 272-275). Springer Netherlands.
- Dougherty, B., & Simon, M. (2014). Elkonin and Davydov Curriculum in Mathematics Education. In S. Lerman, (Ed.), Encyclopedia of Mathematics Education (pp. 204-207). Springer Netherlands.
- Simon, M. A. (2013). The need for theories of conceptual learning and teaching of mathematics. In K. Leatham & S. Williams (Eds.), Vital directions for mathematics education research (pp. 122-157). New York: Springer.
- Simon, M. (2008). The challenge of mathematics teacher education in an era of mathematics education reform. In B. Jaworski & T. Wood (Eds.), International handbook of mathematics teacher education: Vol.4. The mathematics teacher educator as a developing professional pp. 17-29. Rotterdam, the Netherlands: Sense Publishers.
- Simon, M. (2001). Refining conceptualizations of mathematics teaching through studying mathematics teacher development. In T. Wood, B. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics, 157-169. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Simon, M. A. (2000). Constructivism, mathematics teacher education, and research in mathematics teacher development. In L. Steffe & P. Thompson (Eds.), Radical constructivism in Action: Building on the Pioneering work of Ernst von Glasersfeld, pp. 213-230. London: Routledge Falmer.
- Simon, M. A. (2000). Research on mathematics teacher development: The teacher development experiment. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education, pp. 335-359. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Simon, M. A. (1997). Developing new models of mathematics teaching: An imperative for research on mathematics teacher development. In E. Fennema & B. Nelson. (Eds.), Mathematics teachers in transition, pp. 55-86. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Simon, M. A. (1996). Focusing on learning mathematics. In D. Schifter (ed.), Windows on the classroom: Teachers write about learning and teaching mathematics, pp. 37-43, New York: Teachers College Press.
- Simon, M. A. & Stimpson V. (1988). Developing algebraic representations using diagrams. In A. Coxford & A. Shulte, (Eds.) The ideas of algebra, K-12, Reston, VA: National Council of Teachers of Mathematics, 136-141.
- Simon, M. A. (1985). Diagram drawing in the math classroom: Eddie’s story. In Teaching mathematics. M. Driscoll and J. Confrey (Eds.), Northeast Regional Exchange, Inc.