Exploring students’ understanding of multiplication with eye tracking: A study on the use of strategies in array representations

Abstract

A central concern of mathematics education is to develop students’ understanding of multiplication. To this end, it is necessary to investigate students’ strategies in multiplication tasks. Common representations for multiplication are array representations (AR) (i.e., rectangular arrangement of elements). Previous research has identified strategies in multiplication tasks with AR. However, little is known about students’ use of these strategies—which would allow inferences about students’ understanding of multiplication. This paper presents an eye-tracking study on strategies of 163 fifth-graders in multiplication tasks with AR, and their use of these strategies. Three strategies were found: In two of them, the students made use of multiplicative structures, while in one they did not (e.g., counting all dots). We found that the fifth graders used a counting strategy in almost one-fifth of the tasks, which suggests difficulties in the understanding of multiplication.

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