The role of manipulatives in enhancing pupils’ understanding on fraction concepts

Abstract

Zoltan Dienes and Josef Perner's work (24) convinced many researchers that the use of various representations of a concept, or 'multiple embodiments,' were needed to support pupils' understanding. Piaget (4) suggested that young children do not have the mental maturity to grasp abstract mathematical concepts presented in words or symbols alone and they need many experiences with concrete materials and drawings for learning to occur. Bruner (1,2) suggested that children demonstrate their understandings in three stages of representation: enactive (the role of physical objects), iconic and symbolic. Skemp's theories (22) supported the belief that pupils' early experiences and interactions with physical objects formed the basis for later learning at the abstract level. Based on theories of cognition and the social construction of knowledge (23), more recent research by Cobb (3) discusses cultural tools like hundreds boards, showing the complicated relationship between manipulatives and sociocultural perspectives. Current research in mathematics education views pupils as active participants who construct knowledge by reorganizing their current ways of knowing and extracting coherence and meaning from their experiences (8), (9), (17), (19). The impact of theories and research connecting pupils' actions on physical objects with mathematical learning has had an important influence on the emergence and use of manipulative in primary school classrooms. This paper reports on a study which examined how much manipulatives have been used in the teaching of fractions for Year 5 pupils in Brunei Darussalam. The purpose was to determine whether using manipulatives to teach fractions could promote active learning and enhance the achievement among those pupils. This small scale study used both qualitative and quantitative data obtained from the pre and post tests, interviews and classroom observation to determine the effectiveness of using manipulatives as implemented in the teacher- designed intervention lessons. The paper concludes with some recomendations on how different types of manipulatives can be used in their effective ways to promote pupils' understanding of fraction concepts.