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Hwang, S., Roth, W., & Kim, M. (2010, April). Knowing mathematical representations: Pedagogical principles for cultural development. Paper presented at the American Educational Research Association Annual Meeting (AERA), Denver, Colorado, USA.
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.
This paper was presented at the American Educational Research Association Annual Meeting (AERA), held in Denver, Colorado, USA from 30 Apr to 4 May 2010
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