Efficient Assessment of Students’ Proportional Reasoning

Abstract

ABSTRACT Teachers need ways to efficiently assess students’ cognitive understanding. One promising approach involves easily adapted and administered item types that yield quantitative scores that can be interpreted in terms of whether or not students likely possess key understandings. This study illustrates an approach to analyzing response process validity evidence from item types for assessing two important aspects of proportional reasoning. Data include results from an interview protocol used with 33 middle school students to compare their responses to prototypical item types to their conceptions of composed unit and multiplicative comparison. The findings provide validity evidence in support of the score interpretations for the item types but also detail important item specifications and caveats. Discussion includes recommendations for extending the research for examining response process validity evidence in support of claims related to cognitive interpretations of scores for other key mathematical conceptions.