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Title: Knowing mathematical representations: Pedagogical principles for cultural development
Authors: Hwang, Sungwon
Roth, Wolff-Michael
Kim, Mijung
Issue Date: 2010
Citation: Paper presented at the American Educational Research Association (AERA) Annual Meeting, Denver, Colorado, 30 April to 4 May 2010
Abstract: Mathematical representations constitute prevalent resources that mediate the understanding of science concepts. For example, in science lessons different types of mathematical representations (e.g., force diagram, chemical reaction equations, DNA models) assist science teachers in explaining science concepts. The inherently materials bodies (e.g., visual representations) are connected to other sense-making resources (e.g., science talk), and thereby come to stand for something (i.e., mathematical idea). Yet, students have difficulty reading mathematical representations that they encounter in science lessons and associated science talks. More so, this difficulty tends to be attributed to the matter of either students’ individual capacities or the qualities of mathematical representations, which exists independent of the concrete practice of communication. In this study, we take a holistic approach to students’ understanding of mathematical representations, which does not dichotomize sense-making from the sensuous experience of the world (objects) and therefore provides implications for the pedagogical problem of “representation.” We thematize the dynamic experience of mathematical representations in communication, which we summarize into three claims. First, the body reproduces and transforms cultural resources for translating mathematical representations. Second, the increase of heterogeneous sense-making resources in communication increases possibilities for realizing a new way of talking. Third, knowing mathematical representations emerges from the different, irreducible modes of communication as an integrated whole. We support the three claims by analyzing a case example in which children talk about a (randomly generated) geometrical representation in a mathematics lesson. We conclude that knowing mathematical representations is equivalent to (bodily and embodied) reading between different sense-making resources that constitute a series of references to bring about scientific conceptions in its totality.
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