Prof. Tommy Dreyfus

Tommy Dreyfus specializes in mathematics education. His research interests include processes of learning abstract mathematical ideas in classrooms, students' meanings for the fundamental concepts of calculus, and the learning and teaching of proof. In teaching, he aims to convey how mathematical meaning grows out of the connectivity of concepts, processes, and representations of mathematical objects

טומי דרייפוס מתמחה בחינוך מתמטי. תחומי מחקריו כוללים תהליכי המשגה והפשטה בכיתה, משמעויות של תלמידים עבור מושגי היסוד של החדוו״א, וההוראת והלמידה של הוכחות. בהוראתו הוא שואף לגרום לתלמידים להתנסות ביצירת משמעות מתמטית מתוך הקישוריות של מושגים, תהליכים, וייצוגים של אובייקטים מתמטיים.

Education

Diploma (theoretical physics), Swiss Federal Institute of Technology, 1969

High school teaching certificate in mathematics and physics, Swiss Federal Institute of Technology, 1969

Dr. ès sciences (physics), University of Geneva, Switzerland, 1975

Award

2019 Felix Klein medal (awarded by the Internationa; Commission for Mathematics Instruction

Professional experience

Hebrew University of Jerusalem, Israel: Lady Davis Postdoctoral Fellow, 1975 – 1977

Weizmann Institute of Science, Israel: Julius Baer Postdoctoral Fellow, 1977 – 1978

Center for Technological Education, Holon, Israel, Department of Exact Sciences: Lecturer (1978 – 1982), Senior Lecturer (1982 – 1988), Associate Professor (1988 – 1995), Professor (1995 – 2001)

Tel Aviv University, Constantiner School of Education, Department of Education in Mathematics, Science and Technology: Professor (2001 – 2014), Professor Emeritus (since 2014)

Visiting professorships

• Swiss Federal Institute of Technology, Zurich, Switzerland (1981)
• San Diego State University, CA, USA (1983-1985, 2014)
• Autonomous University of Barcelona, Spain (1988)
• University of Fribourg, Switzerland (1990/91)
• Concordia University, Montreal, Canada (1996/97)
• University of Bremen, Germany (2007)
• University of Auckland, New Zealand (2008)
• Arizona State University, USA (2015)
• New York University, USA (2015)

Research projects

Abstraction in Context: Consolidation of Constructed Knowledge in the course of Successive Activities (2002 – 2005, with Rina Hershkowitz and Baruch Schwarz, funded by the ISF)

Abstraction in Context: The Teacher's Role in Processes of Constructing and Consolidating (2005 – 2008, with Rina Hershkowitz and Baruch Schwarz, funded by the ISF)

Effective mathematical knowledge construction in interest-dense situations (2008 – 2011, with Angelika Bikner-Ahsbahs and Ivy Kidron, funded by the GIF)

Students' constructions of mathematical justifications as processes of abstraction in context (2009 – 2012, with Ivy Kidron, funded by the ISF)

Coordinating the development of individual and collective learning of mathematics in the classroom (2012 – 2015, with Michal Tabach, funded by the ISF

Knowledge shifts in the mathematics classroom: The roles of students and teacher (2015 – 2019, with Michal Tabach, funded by the ISF)

Meanings for fundamental calculus concepts in high school  (2019 – 2023, with Anatoli Kouropatov, funded by the ISF)

Rate of Change and Accumulation in Calculus (seminar)

Constructing abstract mathematical knowledge (seminar)

Justification and proof in mathematics education

Concepts of the calculus

The shape of space – selected topics in topology

Introduction to chaos and fractals

The real numbers

Opechowski, W., & Dreyfus, T. (1971). Classification of magnetic structures. Acta Crystallographica A27, 470-484.

Dreyfus, T. (1978). The determinant of the scattering matrix and its relation to the number of eigenvalues. Journal of Mathematical Analysis and Applications, 64, 114-134.

Dreyfus, T., & Dym, H. (1978). Product formulas for the eigenvalues of a class of boundary value problems. Duke Mathematical Journal, 45 (1), 15-37.

Dreyfus, T., & Eisenberg, T. (1986). On the aesthetics of mathematical thought. For the Learning of Mathematics, 6, 2-10.

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

Vinner, S., & Dreyfus, T. (1989). Images and definitions for the notion of function. Journal for Research in Mathematics Education, 20, 356-366.

Dreyfus, T. (1991). Advanced mathematical thinking processes. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 25-41). Dordrecht, Holland: Kluwer, Mathematics Education Library.

Eisenberg, T., & Dreyfus, T. (1991). On the reluctance to visualize in mathematics. In W. Zimmermann and S. Cunningham (Eds.), Visualization in Teaching and Learning Mathematics (pp. 25-37). Notes Series, Vol. 19. Washington, DC: Mathematical Association of America.

Dreyfus, T. (1993). Didactic design of computerized learning environments. In C. Keitel & K. Ruthven (Eds.), Learning from computers: mathematics education and technology (pp. 101-130). Berlin, Germany: Springer, NATO ASI Series F: Computer and System Sciences, Vol. 121.

Shama, G., & Dreyfus, T. (1994). Visual, algebraic and mixed strategies in visually presented linear programming problems. Educational Studies in Mathematics, 26, 45-70.

Dreyfus, T. (1994). Imagery and reasoning in mathematics and mathematics education. In D. Robitaille, D. Wheeler & C. Kieran  (Eds.), Selected Lectures from the 7th International Congress on Mathematical Education (pp. 107-122). Sainte-Foy, Québec, Canada: Les presses de l'université Laval.

Dreyfus, T., & Hadas, N. (1996). Proof as answer to the question why. Zentralblatt für Didaktik der Mathematik, 28 (1), 1-5.

Dreyfus, T. (1999). Why Johnny can’t prove. Educational Studies in Mathematics, 38 (1), 85-109.

Hershkowitz, R., Schwarz, B., & Dreyfus T.  (2001). Abstraction in context: epistemic actions. Journal for Research in Mathematics Education, 32, 195-222.

Dreyfus, T. & Tsamir, P. (2004). Ben's consolidation of knowledge structures about infinite sets. Journal of Mathematical Behavior, 23, 271-300.

Dreyfus, T. & Kidron, I. (2006). Interacting parallel constructions. A solitary learner and the bifurcation diagram. Recherches en didactique des mathématiques 26, 295-336.

Dreyfus, T., & Monaghan, J. (2009). Abstraction beyond a delicate shift of attention. In S. Lerman and B. Davis (Eds.), Mathematical action and structures of noticing: Studies on John Mason’s contribution to mathematics education (pp. 101-110). Rotterdam, The Netherlands: Sense Publishers.

Kidron, I., & Dreyfus, T. (2010). Justification enlightenment and combining constructions of knowledge. Educational Studies in Mathematics, 74, 75-93.

Ron, G., Dreyfus, T., & Hershkowitz, R. (2010). Partially correct constructs illuminate students’ inconsistent answers. Educational Studies in Mathematics, 75, 65-87.

Yoon, C., Thomas, M. O. J., & Dreyfus, T. (2011). Grounded blends and mathematical gesture spaces: Developing mathematical understandings via gestures. Educational Studies in Mathematics, 78, 371-393.

Dreyfus, T., Nardi, E., & Leikin, R. (2012). Forms of proof and proving in the classroom. In G. Hanna & M. de Villiers (Eds.), Proof and proving in mathematics education – the 19^th ICMI study (pp. 191-213). Dordrecht: Springer, New ICMI Study series, Vol. 15.

Dreyfus, T. (2014). Mutual expectations between mathematicians and mathematics educators (with contributions by U. Onn, I. Mamona-Downs & S. Lerman). In M. Fried & T. Dreyfus (Eds.), Mathematics and mathematics education: searching for common ground (pp. 57 -71). Springer: Advances in Mathematics Education series.

Kouropatov, A., & Dreyfus, T. (2014). Learning the integral concept by constructing knowledge about accumulation. ZDM - The International Journal on Mathematics Education, 46, 533-548.

Hershkowitz, R., Tabach, M., Rasmussen, C., & Dreyfus, T. (2014). Knowledge shifts in a probability classroom – a case Study coordinating two methodologies. ZDM - The International Journal on Mathematics Education, 46, 363-387.

Dreyfus, T., Sabena, C., Kidron, I., & Arzarello, F. (2014). The epistemic role of gestures. In A. Bikner-Ahsbahs & S. Prediger (Eds.), Networking of theories as a research practice (pp. 127-151). Switzerland: Springer, Advances in Mathematics Education series.

Dreyfus, T., Hershkowitz, R., & Schwarz, B. (2015). The nested epistemic actions model for abstraction in context - theory as methodological tool and methodological tool as theory. In A. Bikner-Ahsbahs, C. Knipping & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 185-217). Dordrecht: Springer, Advances in Mathematics Education series.

Ron, G., Dreyfus, T., & Hershkowitz R. (2017). Partially correct constructs for the area-square model in probability. Journal of Mathematical Behavior, 45, 15-34.

Gabel, M., & Dreyfus, T. (2017). Affecting the flow of a proof by creating presence - a case study in Number Theory. Educational Studies in Mathematics, 96, 187-205.

Apkarian, N., Tabach, M., Dreyfus, T., & Rasmussen, C. (2019). The Sierpinski smoothie: Blending area and perimeter. Educational Studies in Mathematics, 101(1), 19-34.

Rasmussen, C., Apkarian, N., Tabach, M., & Dreyfus, T. (2020) Ways in which engaging in someone else’s reasoning is productive for one’s own reasoning. Journal of Mathematical Behavior, 58. doi.org/10.1016/j.jmathb.2019.100742

Tabach, M., Rasmussen, C., Dreyfus, T., & Apkarian, N. (2020). Towards an argumentative grammar for networking: A case of coordinating two approaches. Educational Studies in Mathematics, 103(2), 139-155.

Dreyfus, T., Kouropatov, A., & Ron, G. (2021). Research as a resource in a high school calculus curriculum. ZDM Mathematics Education 53(3).

Edited books

Schwarz, B. B., Dreyfus, T. and Hershkowitz, R. (Eds.) (2009), Transformation of Knowledge through Classroom Interaction. London, UK: Routledge.

Fried, M., & Dreyfus, T. (Eds.) (2013). Mathematics and Mathematics Education: Searching for Common Ground. Springer: Advances in Mathematics Education series.

Dreyfus, T., Artigue, M., Potari, D., Prediger, S., & Ruthven, K. (Eds.) (2018). Developing research in mathematics education - twenty years of communication, cooperation and collaboration in Europe. London: Routledge. (ERME series inaugural volume)