Teaching practices for unfolding information and connecting multiple representations: the case of conditional probability information

Abstract

Multiple representations can enhance students’ understanding of mathematical concepts and complex information but can also pose well-documented challenges for students. Whereas instructional designs have been optimized to support students’ learning with multiple representations, little is known about supportive teaching practices for dealing with multiple representations in whole-class discussions. In this article, we qualitatively investigate two cases of teacher-student interaction in whole-class discussions in grades 10–12 (about the mathematical topic of complex conditional probability information). The analysis aims at decomposing the teaching practices into those actions that can support or hinder students’ understanding. The comparison of cases reveals that teaching practices can vary greatly: simply translating compacted concepts of a given text into other representations (visual area model, symbolic representation of fractions, and three language varieties) seems to be sufficient for students with advanced understanding. Other students need teachers’ supportive actions for unfolding the highly compacted concepts (such as part-of-part) into several concept elements (part, whole, and part-whole relationship) and explicitly connecting (rather than only translating) the concept elements in multiple representations for the different concept elements. The findings can inform both theory building on teaching practices with multiple representations and professional development.

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