A new look in representations for mathematics and science learning |
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| Authors: | David N Perkins Chris Unger |
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| Institution: | (1) Harvard Graduate School of Education, 02138 Cambridge, MA, USA |
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| Abstract: | Representations such as formal notations and diagrams routinely figure in students' learning of mathematics and science. However, in light of the extensive research on students' misunderstanding in these subject matters, it is reasonable to ask whether other kinds of representations might help students to reach better understandings. Indeed, a number of educators have developed innovative representations, typically on computers, that supposedly foster understanding through suggestive visual analogies and  microworlds to manipulate. Evaluative research on these new look representations as we call them suggests that they indeed can help students to understand.In this review, we focus on exactlyhow these representations aid understanding. We propose that they do so by facilitating the learner's construction of explanations, justifications, predictions, and the like. These constructions require search in problem spaces, in the sense of Newell and Simon (1972). The representations in question reduce the cognitive load of such searches, clarify the structure of the problem spaces that need to be searched, and make certain moves in the problem spaces more immediate. We invoke Gentner's (1983) theory of structure mapping to explain how these advantages are attained. We also examine several characteristic pitfalls of representations in this style. |
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