Dynamic Connections between Problem Posing and Problem‑Solving: On the Usefulness of Multiple Perspectives

Victor V. Cifarelli

Download the full text in

PDF (79 kB)

> Citation
> Similar
> References
**> Add Comment**

## Abstract

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: Drawing from the ideas of Varela, Proulx and Maheux, I propose a theoretical framework to examine problem-posing and problem-solving and provide evidence for their ideas with examples of student work from their research studies. I will draw comparisons between the approach taken by the researchers to the constructivist approach I have taken in my studies of problem-solving and those conducted with collaborators. My intent with these comments is not to argue the merits of one perspective over the other; rather, I look to point out and elaborate on these differences and make some specific suggestions to the researchers.

## Citation

Cifarelli V. V. (2017) Dynamic connections between problem posing and problem‑solving: On the usefulness of multiple perspectives. Constructivist Foundations 13(1): 172–173. http://constructivist.info/13/1/172

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

## References

Borasi R. (1986) On the nature of problems. Educational Studies in Mathematics 17(2): 125–141.

▸︎ Google︎ Scholar
Brown S. I. & Walter M. I. (1993) The art of problem posing. Second edition. Franklin Institute Press, Philadelphia PA.

▸︎ Google︎ Scholar
Cai J. & Cifarelli V. V. (2005) Exploring mathematical exploration: How two college students formulated and solved their own mathematical problems. FOCUS on Learning Problems in Mathematics 27(3): 43–72.

▸︎ Google︎ Scholar
Cifarelli V. V. & Cai J. (2005) The evolution of mathematical explorations in open ended problem solving situations. Journal of Mathematical Behavior 24(3–4): 302–324.

▸︎ Google︎ Scholar
Cifarelli V. V. & Sevim V. (2015) Problem posing as reformulation and sense-making within problem solving. In: Singer F. H., Ellerton N. F. & Cai J. (eds.) Mathematical problem posing: From research to effective practice. Springer, New York: 177–194.

▸︎ Google︎ Scholar
Cifarelli V. V. (2010) Mathematical problem solving and problem centered learning: Old promises and new challenges. In: Reynolds A. (ed.) Problem centered learning in mathematics: Reaching all students. Lambert Academic, Saarbrücken: 149–168.

▸︎ Google︎ Scholar
Cifarelli V. V. (2015) The importance of abductive reasoning in mathematical problem solving. In: Saenz-Ludlow A. & Kadunz G. (eds.) Semiotics as a tool for learning mathematics: How to describe the construction, visualization, and communication of mathematical concepts. Sense Publications, Rotterdam: 209–225.

▸︎ Google︎ Scholar
Glasersfeld E. von (1987) Learning as a constructive activity. In: Janvier C. (ed.) Problems of representation in the teaching and learning of mathematics. Lawrence Erlbaum, Mahwah NJ: 1–18.

▸︎ Google︎ Scholar
Hiebert J., Carpenter T. P., Fennema E., Fuson K., Human P., Murray H., Olivier A. & Wearne D. (1996) Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher 25(4): 12–21.

▸︎ Google︎ Scholar
Lave J. (1988) Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge University Press, New York.

▸︎ Google︎ Scholar
Lave J. (1992) Word problems: A microcosm of theories of learning. In: Light P. & Butterworth G. (eds.) Context and cognition: Ways of learning and knowing. Lawrence Erlbaum, Mahwah NJ: 74–92.

▸︎ Google︎ Scholar
Sevim V. & Cifarelli V. 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 37th Meeting of the International Group for the Psychology of Mathematics Education. Volume 5. PME, Kiel: 165.

▸︎ Google︎ Scholar
Silver E. A. (1994) On mathematical problem posing. For the Learning of Mathematics 14(1): 19–28.

▸︎ Google︎ Scholar
Sowder L. (1985) Cognitive psychology and mathematical problem solving: A discussion of Mayer’s paper. In: Silver E. (ed.) Teaching and learning mathematical problem solving: Multiple research perspectives. Lawrence Erlbaum, Mahwah NJ: 139–145.

▸︎ Google︎ Scholar
Steffe L. P. (1988) Cognitive conflict in learning mathematics. In: Wilson P. S. (ed.) The role of inconsistent ideas in learning mathematics. Symposium for the Special Interest Group for Research in Mathematics Education of the Annual Conference of the American Educational Research Association. University of Georgia, Georgia: 47–50.

▸︎ Google︎ Scholar
## Comments: 0

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