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An Analysis of Lessons to Teach Proportional Reasoning with Visual Models: Focused on Ratio table, Double Number Line, and Double Tape Diagram  

Seo, Eunmi (Graduate School, Korea National University of Education)
Pang, JeongSuk (Korea National University of Education)
Lee, Jiyoung (Paldal Elementary School)
Publication Information
Journal of Educational Research in Mathematics / v.27, no.4, 2017 , pp. 791-810 More about this Journal
Abstract
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.
Keywords
proportional reasoning; visual model; ratio table; double number line; double tape diagram;
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