On fractions and non-standard representations: Pre-service teachers' concepts

Abstract

The present study examined the reasoning strategies and arguments given by pre-service school teachers as they solved two problems regarding fractions in different symbolic representations. In the first problem, the pre-service school teachers were asked to compare between two different fractions having the same numerical representation, and in the second problem, they were asked to compare between different notational representations of the same fraction. Numeration systems in bases other than ten were used to generate various representations of fractions. All students were asked to provide justifications to their responses. Strategies and arguments relative to pre-service teachers' concepts of fractions and place value were identified and analyzed based on results of 38 individual clinical interviews, and written responses of 124 students. It was found that the majority of students believe that fractions change their numerical value under different symbolic representations.