An Analysis of Sixth Graders’ Representational Thinking on Fraction Division: Focusing on the Contexts of Measurement Division and Determination of a Unit Rate

In the second semester of the sixth grade, the unit on fraction division covers the division of fractions where the divisor is a fraction. To support understanding, contexts such as measurement division and determination of a unit rate are introduced, which are connected to common denominators algorithm and the invert-and-multiply algorithm respectively. This study designed and implemented lessons that emphasized students’ representational thinking, enabling students to connect representations with fraction division situations, calculation principles, and problem-solving. As results, students were able to construct representations reflecting different situations of fraction division, however, some students exhibited misconceptions and errors, such as constructing representations that did not consider the relationship between the dividend and divisor or different levels of units. Based on the findings, this study provides pedagogical implications for enhancing students’ conceptual understanding through representational thinking in fraction division instruction.