Proportional reasoning is key to students’ acquisition and application of complex mathematics and science topics. Research is needed regarding how students’ progress towards and come to demonstrate key developmental understandings within proportional reasoning. To this end we created and administered assessment items to 297 middle grades students. We categorized student solution processes qualitatively, followed by Rasch analysis to examine item difficulty and strategy use in relation to an anticipated trajectory. Our findings indicate that different strategies manifest themselves in a hierarchical manner, providing initial confirmation of categories based on strategy efficiency and emphasizing the importance of teacher (and researcher) analysis of classroom assessments from a student cognition perspective.
This document was originally published in PMENA-37: Proceedings Thirty-Seventh Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education by Psychology of Mathematics Education - North American Chapter (PME-NA). Copyright restrictions may apply.
Carney, Michele; Smith, Ev; Hughes, Gwyneth; Brendefur, Jonathan; Crawford, Angela; and Totorica, Tatia. (2015). "Analysis of Students’ Proportional Reasoning Strategies". PMENA-37: Proceedings of the Thirty-Seventh Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Critical Responses to Enduring Challenges in Mathematics Education, 141-148.