Prospective teachers' knowledge: Concept of division

The purpose of this study was to determine prospective teachers' knowledge about the concept of division. One focus of interest was whether the prospective teachers were able to represent division of fractions. The participants were introduced to an alternative model for representation of fractions based on a rate or ratio model of division involving whole numbers. A second focus of interest was whether the prospective teachers would be able to apply this model to problems of division of fractions. The findings revealed that the prospective teachers' successfully represented division of whole numbers using models of fair sharing and, to a lesser extent, repeated subtraction. However, they had difficulty in successfully representing division of fractions. Some improvement was observed in participants' performance in attempts to represent division of fractions after introduction of the rate/ratio model. However the prospective teachers often used the rate or ratio model mistakenly where the situations were not appropriate for the model, which appeared to be associated with difficulty in multiplicative thinking.