Characterizing the proportional reasoning of middle school students

Abstract

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.