Characterizing the Proportional Reasoning of Middle School Students

The purpose of this study was to identify characteristics of middle school students’ proportional reasoning. The participants were 70 7th grade, 68 8th grade, and 69 9th grade students in Seoul. This study was conducted using written test to analyze students’ proportional reasoning strategies and interview to investigate their thoughts. In the results, there was no statistically significant difference between the grades. Also the students often chose solving strategies depending on the context of the problems, and they showed a lack of multiplicative understanding. In conclusion, we identified a pseudo-formal stage, which jumps from the additive strategy to the formal strategy with procedural understanding and not conceptual understanding. Therefore the multiplicative strategy could serve the role of a bridge from an additive strategy to a formal strategy on proportional reasoning.