Engaging Whole-Number Knowledge for Rational-Number Learning Using a Computer-Based Tool

Abstract

We present data from a two-year teaching experiment involving 8- and 9-year-old children. The purpose of the teaching experiment was to investigate children's fraction learning and the role their whole-number knowledge might play in it. A major source for the children's experiences and experiments was an operator-like computer program called Copycat. In particular, we focus on the accomplishments of Elliot and Shannon as they solved fraction comparison problems. We identify and discuss three cognitive schemes that Elliot and Shannon used. These were an Equal Outputs scheme, limited in effectiveness to unit fraction comparisons; an Equal Inputs scheme that activated strategies for determining a common multiple; and a Scaling scheme in which fractions were scaled up or down using ratios. The major focus of the discussion is the role whole-number knowledge played in the application of these schemes. This study demonstrates an interdependence between development of rational-number knowledge and whole-number knowledge. Rational-number tasks in operator settings can help stimulate and extend children's whole-number knowledge. Facility with whole-number relationships enables students to solve fraction comparison problems.