Using Multiple Representations to Foster Multiplicative Reasoning in Students With Mathematics Learning Disabilities

Developing and supporting understanding of the meaning of multiplication and multiplicative relationships in students with mathematics learning disabilities requires carefully designed instruction that emphasizes strategic representation use. This article discusses three ways in which teachers can incorporate multiple representations within multiplication instruction to develop a deep understanding of underlying mathematical structures. First, it is important to select concrete and semi-concrete representations (e.g., discrete objects and those that illustrate continuous quantities as length or area) that will help students most accurately model the multiplication or division concept or procedure. Next, provide students with multiple representations that are presented concurrently within the same lesson so that they can make connections among the different types of representations. Last, teachers can support students to use and connect representations through mathematical discourse that elicits student thinking by not only structuring tasks around three processes, reversibility, flexibility, and generalization, but also by posing questions to elicit different ways that students can communicate their ideas using accurate and precise vocabulary.