Children's Constructions of Knowledge for Fraction Division After Solving Realistic Problems

Abstract

The authors examined the thinking of children who had the opportunity to construct personal knowledge about division of fractions. The authors based this study on a teaching experiment design and used relevant contexts/situations to foster students' development of knowledge. Participants were a group of mixed-ability, 5th-grade mathematics students. They used pictures, symbols, and words to resolve situations and communicate their solutions. The authors analyzed the solutions to describe the students' constructions of division-of-fractions concepts and procedures. All strategies that the students used represented some manifestation of conceptual knowledge about addition and subtraction of fractions and a definition of division. Some students developed formal symbolic procedures, and others developed pictorial procedures; none invented an invert-and-multiply procedure. Through the window of constructivism, this study allowed the authors to glimpse children's constructions of knowledge and provided alternatives to the traditional view of the expected procedure (invert and multiply) that children should learn for division of fractions.