Teachers\u2019 conceptual understanding of fraction operations: results from a national sample of elementary school teachers

Yasemin Copur-Gencturk

doi:10.1007/s10649-021-10033-4

Yasemin Copur-Gencturk

Open Access

https://doi.org/10.1007/s10649-021-10033-4

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Abstract

Teachers’ understanding of the concepts they teach affects the quality of instruction and students’ learning. This study used a sample of 303 teachers from across the USA to examine elementary school mathematics teachers’ knowledge of key concepts underlying fraction arithmetic. Teachers’ explanations were coded based on the accuracy of their explanations and the kinds of concepts and representations they used in their responses. The results showed that teachers’ understanding of fraction arithmetic was limited, especially for fraction division, yet a moderate relationship was found between teachers’ understanding of fraction addition and division. Furthermore, more experienced teachers seemed to have a deeper understanding of fraction arithmetic, whereas special education teachers had a substantially limited understanding.

Highlights

Teachers’ understanding of the concepts they teach affects the quality of instruction and students’ learning
Teachers are aware of such challenges, evidenced by a national sample of secondary mathematics teachers in public schools who reported that rational numbers and operations involving rational numbers was the second poorest area of preparation among incoming students, after solving word problems (Hoffer, Venkataraman, Hedberg, & Shagle, 2007)
About half (55.6%) of the teachers explained the need for a common denominator mathematically and included correct explanations for adding fractions with unlike denominators, whereas only 26.1% of the teachers provided a conceptual explanation for the division procedure

Summary

Introduction

Teachers’ understanding of the concepts they teach affects the quality of instruction and students’ learning. Research suggests that students struggle with understanding fractions, but so do prospective and in-service elementary school teachers (e.g., Ma, 2010; Newton, 2008; Olanoff, Lo, & Tobias, 2014) This understanding of current and prospective math teachers’ knowledge is critical, given that teachers’ knowledge of the mathematics they are expected to teach has an impact on the quality of their instruction (e.g., Borko et al, 1992; CopurGencturk, 2015; Hill et al, 2008). The lack of a deep and flexible knowledge base has critical implications and needs to be further understood

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