# U.S. and Chinese Teachers' Conceptions and Constructions of Representations: A Case of Teaching Ratio Concept

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## Abstract

This study examines U.S. and Chinese teachers' constructing, knowing, and evaluating representations to teach the concept of ratio. All Chinese lesson plans are very similar with details in teaching contents and procedure. The U.S lesson plans are extremely varied although they all adopted the ‘outline and worksheet’ format. Both the Chinese and the U.S. teachers relied on concrete representations in introducing the concept of ratio, but they have very different thinking in selecting and presenting the concrete representations, as well as in the functions of the representations. The U.S. teachers are much more likely than Chinese teachers to predict drawing and guess-and-check strategies. Chinese teachers are much more likely than U.S. teachers to predict algebraic approaches. For the responses using conventional strategies, both the U.S. and Chinese teachers gave them high and almost identical scores. If a response involved a drawing or an estimate of an answer, the Chinese teachers usually gave a relatively lower score than U.S. teachers. This study contributes to our understanding about U.S. and Chinese teachers' beliefs about mathematics teaching and learning.

## Key Words

classroom instruction cross-national perspective mathematical problem solving pedagogical representation ratio concept solution representation## Preview

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