Extending and refining models for thinking about division of fractions

Abstract

Many students experience great difficulty when studying topics related to fractions, especially division of fractions. One explanation for this may be that learning how to divide fractions is often taught devoid of meaning. The lack of sense making in carrying out algorithms without making connections to concrete or other types of representations contributes to the inability of students to use previously taught algorithms to solve new problems, especially after long periods of time have elapsed. In this paper we explore the flexibility and durability of knowledge that students acquire when they study this topic in a way that encourages understanding.