An exploratory framework for handling the complexity of mathematical problem posing in small groups |
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Authors: | Igor Kontorovich Boris Koichu |
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Institution: | a Department of Education in Technology and Science, Technion - Israel Institute of Technology, Haifa 32000, Israel b Faculty of Education, University of Haifa, Mount Carmel, Haifa 31905, Israel |
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Abstract: | The paper introduces an exploratory framework for handling the complexity of students’ mathematical problem posing in small groups. The framework integrates four facets known from past research: task organization, students’ knowledge base, problem-posing heuristics and schemes, and group dynamics and interactions. In addition, it contains a new facet, individual considerations of aptness, which accounts for the posers’ comprehensions of implicit requirements of a problem-posing task and reflects their assumptions about the relative importance of these requirements. The framework is first argued theoretically. The framework at work is illustrated by its application to a situation, in which two groups of high-school students with similar background were given the same problem-posing task, but acted very differently. The novelty and usefulness of the framework is attributed to its three main features: it supports fine-grained analysis of directly observed problem-posing processes, it has a confluence nature, it attempts to account for hidden mechanisms involved in students’ decision making while posing problems. |
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Keywords: | Mathematical problem posing Problem posing strategies Considerations of aptness Group dynamics Small group interactions Task organization |
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