Middle School Students’ Proportional Reasoning at Different Stages of Units Coordination

The goal of the present study is to illuminate students’ proportional reasoning using the theory of units coordination as an explanatory tool. We chose two seventh-grade students, Hyun and Junwoo, who demonstrated distinct levels of units coordination and analyzed their units-coordinating activities under proportion problem situations with respect to the two constituent properties of proportional reasoning: the invariance of internal ratios and constancy of external ratios of proportionality. The result of our study indicates that the ability to use the two properties of proportionality as given resources for their problem-solving is closely related to assimilating quantities with three levels of units and further transforming a three-levels-of-units structure to another. We finalize our study by proposing for further research what remains to be done to integrate the results of this study into a coherent explanatory model for students’ construction of proportional reasoning.