Volume 13 · Number 1 · Pages 173–175
Co-evolution of Problem Posing and Problem‑Solving after Finding a Way In

Volkan Sevim

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Open peer commentary on the article “From Problem Solving to Problem Posing, and from Strategies to Laying Down a Path in Solving: Taking Varela’s Ideas to Mathematics Education Research” by Jérôme Proulx & Jean-François Maheux. Upshot: The significance of Proulx and Maheux’s target article lies in their thorough grounding of some of the ideas of the mathematical problem-posing and problem-solving literature in a strong theoretical framework. They direct our attention to two distinct epistemological assumptions that underlie explanations of problem-solving: the so-called “selection-then-execution hypothesis” and Varela’s problem-posing perspective. In this commentary, I will offer two ways their line of research could be extended.


Sevim V. (2017) Co-evolution of problem posing and problem‑solving after finding a way in. Constructivist Foundations 13(1): 173–175. http://constructivist.info/13/1/173

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Cifarelli V. & Sevim V. (2014) Examining the role of re-presentation in mathematical problem solving: An application of Ernst von Glasersfeld’s conceptual analysis. Constructivist Foundations 9(3): 360–369. http://constructivist.info/9/3/360
Cifarelli V. & Sevim V. (2015) Problem posing as re-formulation and sense-making within problem solving. In: Singer F. M. & Ellerton N. & Cai J. (eds.) Mathematical problem posing: From research to effective practice. Springer, New York: 177–194. ▸︎ 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: 45–67. http://cepa.info/1418
Maheux J. F. & Proulx J. (2015) Doing|mathematics: Analyzing data with/in an enactivist-inspired approach. ZDM Mathematics Education 47(2): 211–221. ▸︎ Google︎ Scholar
Proulx J. (2013) Mental mathematics, emergence of strategies, and the enactivist theory of cognition. Educational Studies in Mathematics 84(3): 309–328. ▸︎ Google︎ Scholar
Sevim V. & Cifarelli V. (2013) The co-evolution of problem posing and problem solving in the course of Sarah’s on-going solution activity. In: Lindmeier A. M. & Heinze A. (eds.) Proceedings of the annual meeting of the international group for the psychology of mathematics education. Volume 5. PME, Kiel: 165. ▸︎ Google︎ Scholar
Towers J. & Proulx J. (2013) An enactivist perspective on teaching mathematics: Reconceptualising and expanding teaching actions. Mathematics Teacher Education and Development 15(1): 5–28. http://cepa.info/4320

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