The Set Model: A Flexible Approach for Dividing Fractions

ABSTRACT The set model for fractions is a way of representing fractions using sets of objects where the whole is represented by a set of items, and the fraction indicates how many of those items are being considered. It is a flexible model because the whole can be redefined, addressing limitations often faced using standard linear or area models. Two‐sided chips are an adaptable tool often used with the set model; the whole can be easily redefined. Preservice teachers explored the concept of dividing fractions using the set model, moving beyond the traditional algorithm and the more common models used in the elementary and middle school classrooms. The set model for fractional division can be used in conjunction with linear and area models to support rich learning experiences that encourage sense making while exploring what the division of fractions conceptually represents. The research question was: How does integrating the set model into teacher education affect preservice teachers' ability to explain and justify the process of dividing fractions? Even though there were some initial challenges, preservice teachers were able to justify their observations and connect mathematical concepts. Ready‐to‐use activities for elementary and middle school classrooms or university classes are provided.