From sharing to dividing: young children’s understanding of division

Abstract

Children have particular difficulty with division problems, as compared to sharing problems. An inability to discriminate between the dividend, divisor and quotient might contribute to their difficulty with division. This study investigates whether young children (5–9 years) were able to discriminate between the divisor and quotient in simple division problems that were modeled for them. Children were presented with partitive and quotitive division problems in which the dividend was grouped either by the divisor or by the quotient. The children showed a very different pattern of results in the partitive and quotitive problems; they found it easier to identify the answer (quotient) when the dividend was grouped by the divisor in partitive problems and by the quotient in quotitive problems. It is argued that children rely on a schema of action of creating ‘portions’ when they first learn about division, and that the ‘portions’ produced by sharing are different in partitive and quotitive problems. We discuss this finding in terms of the importance of problem representation, children’s schemas of action and mental models.