Analysis of Fractional Knowledge in a Computer Environment by Pre-service Primary Teachers

Abstract

Among mathematics educators there is an emerging consensus that learning and transfer of what is learnt is better accomplished if teaching is directed at drawing on students' prior knowledge and understandings. This concern is reflected in calls for changes in the way children are introduced to primary mathematics (National Council of Teachers of Mathematics, 1991). A major recommendation of such reform documents is the need to provide young children with multiple representations of concepts in the primary curriculum. Traditionally teachers tended to use concrete material in providing alternate perspectives about concepts and their applications. More recently, however, it is recognised that computer softwares can be used to provide a rich and dynamic learning environment for young children. The potential pedagogical value of computer softwares is based on the assumption that teachers will be competent in utilising them as teaching tools. While this enthusiasm for computer use by teachers is encouraging and indeed necessary, we have little information about the type of knowledge that teacher need in order to function effectively in the computer environment. In this research I examine this issue by describing the quality of pre-service teachers' knowledge base when they are required to teach fractions to year 5 and 6 students using JavaBars, a software that was designed to teach fractions (Olive, 2000).I describe pre-service primary teachers' knowledge of three dimensions of subject-matter knowledge of fractions: algorithmic, intuitive and formal, and explore two dimensions of their pedagogical knowledge (Shulman, 1986): knowledge of various forms of representations and student misconceptions (Feiman-Nemser,1990). The use of JavaBars is analysed in the context of representations that pre-service teachers' are able to generate with fractions. Six students who are enrolled in the first-year BEd program were individually interviewed about their knowledge of fractions and how they would use JavaBars in their teaching.

Results of the study showed that pre-service primary teachers have built reasonably robust formal knowledge of fractions. However, they experienced difficulty in using JavaBars to produce different representations to teach fractions to young children. The pre-service primary teachers' also exhibited a tendency to overlook young children's intuitive knowledge and misconceptions about fractions. This gap in their knowledge is particularly significant given that the software could have easily been utilised to address these shortcomings. It seems that pre-service primary teachers' subject-matter knowledge of fractions is not structured well enough to help them construct alternative representations for teaching the concept. Tentative suggestions about ways to integrate computer use are provided for pre-service teacher education methods courses.