Year four pupils’ understanding of division of whole numbers

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 ...