Affect and Meta-Affect in Mathematical Problem Solving: a Representational Perspective |
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Authors: | Valerie A DeBellis Gerald A Goldin |
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Institution: | (1) The Shodor Education Foundation, Inc., 214 Pineview Drive, Greenville, NC, 27834, U.S.A.;(2) Professor of Mathematics, Physics, and Education, Rutgers University, SERC Bldg. Rm. 239 Busch Campus 118 Frelinghuysen Road, Piscataway, NJ, 08854, U.S.A. |
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Abstract: | We discuss a research-based theoretical framework based on affect as an internal representational system. Key ideas include the concepts of meta-affect and affective structures, and the constructs of mathematical intimacy and mathematical integrity. We understand these as fundamental to powerful mathematical problem solving, and deserving of closer attention by educators. In a study of elementary school children we characterize some features of emotional states inferred from individual problem solving behavior, including interactions between affect and cognition. We describe our methodology, illustrating theoretical ideas with brief qualitative examples from a longitudinal series of task-based interviews. |
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Keywords: | affect and cognition affective structures attitudes beliefs emotions mathematical integrity mathematical intimacy mathematical problem solving meta-affect representational systems values |
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