Abstract
This chapter examines a type of problem posing that has received little attention in the mathematics education literature. Silver (For the Learning of Mathematics 14:19–28, 1994) defined within-solution problem posing as “problem formulation or reformulation [that] occurs within the process of problem solving” (p. 19). Our analysis documents and explains the role that within-solution problem posing plays during problem solving, focusing on episodes of students from two grade levels: (a) Two fourth-grade students solving a multiplication task, and (b) A mathematics education graduate student solving a number array task. Our research examines: (a) How problem posing evolves from the students’ ongoing interpretations of problematic situations, and (b) How these posed problems contribute to the students’ problem solving. The results provide an explanation of how problem posing and problem solving coevolve in the course of solution activity and thus indicate the beneficial role that problem posing can play in the solution of mathematics problems.
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Notes
- 1.
Italicized comments are used to indicate the actions performed by the students as observed by the researchers.
- 2.
We use a bracket notation that lists the top-to-bottom rows of the block being considered. For example, the 2 × 2 block is indicated by [1, 2: 2, 4], the 3 × 3 block is indicated by [1, 2, 3: 2, 4, 6: 3, 6, 9].
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Cifarelli, V.V., Sevim, V. (2015). Problem Posing as Reformulation and Sense-Making Within Problem Solving. In: Singer, F., F. Ellerton, N., Cai, J. (eds) Mathematical Problem Posing. Research in Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6258-3_8
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