Preservice Elementary Teachers' Understanding of Operations for Fraction Multiplication and Division

Abstract

This study examined preservice elementary teachers' change in their understanding of fraction operations while taking a mathematics methods course focused on grades 3-5. The preservice teachers (n = 48) completed an assessment before and after the course's unit on the teaching and learning of fractions. Specifically, the preservice teachers were asked to explain why the traditional algorithms for multiplication and division of fractions work. Additionally, they were asked to identify errors in students' work and provide rationales for why the strategies were faulty. All responses on the pre- and post-assessments were coded using an existing framework for the assessment of understanding. Paired t-tests indicated a statistically significant improvement on most items on the assessment and on the total test score. However, an in-depth analysis of how the scores changed gave insights into the proportion of preservice teachers who demonstrated no change, improvement, or regression on each question. The percent of teachers improving on each question ranged from 33% to 46%. Implications for mathematics teacher education programs and future research are discussed.