Volume 16 · Number 3 · Pages 278–280
Generalization of Students’ Enactive Metaphorizing: The Handshake Problem and Beyond

Victor V. Cifarelli

Log in to download the full text for free

> Citation > Similar > References > Add Comment


Open peer commentary on the article “Enactive Metaphorizing in the Mathematical Experience” by Daniela Díaz-Rojas, Jorge Soto-Andrade & Ronnie Videla-Reyes. Abstract: Díaz-Rojas, Soto-Andrade and Videla-Reyes advocate an approach to the teaching and learning of mathematics that emphasizes enaction, embodiment and metaphorization. I comment on their analysis of one of the illustrative examples, the handshake problem. First, I provide some historical context and rationale from mathematics education for how tasks such as the handshake problem have been used in studies of problem solving and why they also can be effective examples of rich problem-solving tasks that can be used in instructional settings. Then I comment on the robustness of the researchers’ analysis of the handshake problem by examining an extension problem, finding the number of diagonals in an n-sided polygon.


Cifarelli V. V. (2021) Generalization of students’ enactive metaphorizing: The handshake problem and beyond. Constructivist Foundations 16(3): 278–280. https://constructivist.info/16/3/278

Export article citation data: Plain Text · BibTex · EndNote · Reference Manager (RIS)


Cai J. (2000) Mathematical thinking involved in U. S. & Chinese students’ solving of process-constrained and process-open problems. Mathematical Thinking and Learning 2(4): 309–340. ▸︎ Google︎ Scholar
Cifarelli V. V. & Pugalee (2018) The role of informal algorithms in students’ conceptual understanding in problem solving situations. In: Thomas J. N. & Mohr-Schroeder M. J. (eds.) Proceedings of the 117th annual convention of the School Science and Mathematics Association. Volume 5. SSMA, Little Rock AR: 14–22. ▸︎ Google︎ Scholar
Glasersfeld E. von (1991) Abstraction, re-presentation, and reflection: An interpretation of experience and Piaget’s approach. In: Steffe L. P. (ed.) Epistemological foundations of mathematical experience. Springer, New York NY. https://cepa.info/1418
Heid M. K., Choate J., Sheets C. & Rose Mary Zbiek (1995) Algebra in a technological world. Curriculum and Evaluation Standards for School Mathematics Addenda Series, Grades 9–12. SNCTM, Reston VA: 66–68. ▸︎ Google︎ Scholar
Irvine J. (2018) A new lens on a familiar problem: The handshake problem. Gazette – Ontario Association for Mathematics 57(1): 12–13. ▸︎ Google︎ Scholar
National Council of Teachers of Mathematics (1989) Curriculum and evaluation standards for school mathematics. NCTM, Reston VA. ▸︎ Google︎ Scholar
Polya G. (1962) Mathematical discovery: On understanding, learning, and teaching problem solving. John Wiley, New York NY. ▸︎ Google︎ Scholar
Sáenz-Ludlow A. (2004) Metaphors and numerical diagrams in the arithmetical activity of a fourth-grade class. Journal for Research in Mathematics Education 1(35): 34–56. ▸︎ Google︎ Scholar
Yackel E. B. S. (1984) Characteristics of problem representation indicative of understanding in mathematics problem solving. Doctoral dissertation, Purdue University. ▸︎ Google︎ Scholar

Comments: 0

To stay informed about comments to this publication and post comments yourself, please log in first.