How to make ‘more’ better? Principles for effective use of multiple representations to enhance students’ learning about fractions

Abstract

To make complex mathematics concepts accessible to students, teachers often rely on visual representations. Because no single representation can depict all aspects of a mathematics concept, instruction typically uses multiple representations. Much research shows that multiple representations can have immense benefits for students’ learning. However, some re-search also cautions that multiple representations may fail to enhance students’ learning if they are not used in the “right” way. For example, unless students can (1) properly interpret each individual representation and (2) make connections among multiple representations and the information they intend to convey, the use of multiple representations may actually confuse students rather than aid their learning. In this article, we review research-based principles for how to use multiple representations effectively so that they enhance student learning. Using fractions as an illustrative domain, we discuss how the choice of visual representation may affect student learning based on the conceptual aspects of the to-be-learned content emphasized by the representation. Next, we describe ways to help students interpret individual representations and to make connections among them. We illustrate these arguments with our own empirical research on fractions learning. We conclude by laying out open questions that future research should address.