Validating a Written Instrument for Assessing Students' Fractions Schemes and Operations

Abstract

Previous research has documented schemes and operations that undergird students’ understanding of fractions. This prior research was based, in large part, on small-group teaching experiments. However, written assessments are needed in order for teachers and researchers to assess students’ ways of operating on a whole-class scale. In this study, scores from written instruments used to assess students’ fractions schemes and operations were examined for validity and reliability. Scores from the written assessments were correlated with scores from clinical interviews of 33 sixth graders. Results suggest that the written instruments provide reliable and valid measures for assessing the partitive unit fraction scheme and the splitting operation. However, there is no such evidence regarding the partitive fraction scheme. Implications for teachers and researchers are considered, and possible explanations for the scores from the written assessments related to the partitive fraction scheme are discussed.