Among mathematics educators there is an emerging consensus that the quality of prior knowledge developed by young children has a strong influence on transfer of that knowledge during the performance of other tasks such as problem solving. This concern is also reflected in the call for changes in classroom practices that are suggested by the National Council of Teachers of Mathematics.
A major recommendation concerns 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. This has been the case with the teaching and learning of fractions. While the emphasis on the development of multiple representations for fractions has considerable support, there is also a need to ensure that children can relate parts of one representation with that of the others. Children who are able to connect different representations of fractions can be assumed to have developed a deeper understanding of fractions as numbers. This is also a characteristic of knowledge of fractions that is better organized.
In this study I examine the quality of understanding shown by a group of ten-year old children (Year 5 in Australia) by analyzing the type of links they are able to construct between symbolic and diagrammatic representations of fractions. The diagrammatic representations provided in this study were constructed and modified within a dynamic learning environment provided by JavaBars, a software that was designed to explore fractions.
Results of the study showed that there was disparity in the quality and quantity of links identified by the children. The low-achievers were unable to explain the relationship between the numerator and denominator of a fraction, let alone indicate how this can be shown in JavaBars. On the other hand some of high-achieving children could go beyond the interpretation of basic fraction numbers and use JavaBars to discuss about percentages. I discuss these results in terms of schema theory. Tentative suggestions about ways to integrate JavaBars in teaching fractions are also provided.