A discursively oriented conceptualization of mathematical problem solving and its implications for practice
Boris Koichu, Weizmann Institute, Israel
The talk is based on results of three intervention studies with middle and high school students. In the first study, a practice of developing and using heuristic vocabulary in collaborative problem solving was facilitated in two 8th grade classes during a five-month period. This practice mainly affected problem-solving competencies of those students who were identified as “weak” at the beginning of the intervention. In the second study, a practice of verbalizing connections between solved and to-be-solved problems was systematically facilitated in 10th and 11th grade classes, for eight months. The students began using this practice voluntarily towards the end of the intervention and progressed as problem solvers. In the third study, effort was made to incorporate aesthetic discourse in problem-solving discussions in three middle-school classes, during eight-month period. Diverse patterns of gradual change in social and sociomathemtical norms related to mathematical problem solving were identified in the participating classes. The talk is concluded by an offer for an overarching discursively oriented conceptualization of mathematical problem solving and a discussion of its implications for practice.
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