• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.189-206
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• 2015

There has been a recurring call for using visual representations in textbooks to improve the teaching and learning of proportional reasoning. However, the quantity as well as quality of visual representations used in textbooks is still very limited. In this article, we analyzed visual representations presented in a Grade 6 textbook from two perspectives of proportional reasoning, multiple-batches perspective and variable-parts perspective, and discussed the potential of the double number line and the double tape diagram to help develop the idea 'things covary while something stays the same', which is critical to reason proportionally. We also classified situations that require proportional reasoning into five categories and provided ways of using the double number line and the double tape diagram for each category.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.791-810
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• 2017

This study explored the possibility of using visual models in teaching proportional reasoning based on the review of previous studies. Many studies on proportional reasoning emphasize that students tend to simply apply formal procedures without understanding the meaning behind them and that using visual models may be an alternative to help students develop informal strategies and proportional reasoning. Given these, we re-constructed and implemented the unit of a textbook to teach sixth graders proportional reasoning with ratio table, double number line, and double tape diagram. The results of this study showed that such visual models helped students understand the meaning of proportion, explore the properties of proportion, and solve proportional problems. However, several difficulties that students experienced in using the visual models led us to suggest cautionary notes when to teach proportional reasoning with visual models. As such, this study is expected to provide empirical information for textbook developers and teachers who teach proportional reasoning with visual models.