Year four pupils’ understanding of division of whole numbers

Abstract

Abstract. Based on the theory of radical constructivism, this study investigated Year Four pupils' understandings of division by identifying their schemes of the division of whole numbers and how they used them in solving related problematic situations. Data incorporating both verbal and non-verbal behaviors were gathered from seven pupils based on the five clinical interview sessions involving imagining division, representing division, describing process and product of division, interpreting division statement, and solving division problem tasks. Four schemes that were identified are partitioning scheme, measuring scheme, repeated subtraction scheme, and inverse of multiplication scheme. Findings revealed that the measuring scheme was the dominant scheme for the division of whole numbers and the pupils only used the repeated and the inverse of multiplication schemes when they were asked to relate the subtraction or multiplication process with the division process. Further, the pupils were observed to use the long division algorithm in some situations, but there were indications that they used them with little understandings. It is suggested that more remains to be learnt about the nature of pupils' understanding of the division of whole numbers and how schemes of the division of whole numbers are formed and modified. Also, in order to provide appropriate guidance, mathematics teachers need to have some knowledge about pupils' available schemes of the division of whole numbers, no matter how primitive they might seem to the teachers.