The influence of sharing on children's initial concept of division

We report three studies that investigate young children's ability to solve partitive division problems when presented with a concrete model of a problem. In the studies, 5- to 8-year-olds were given problems about sharing "sweets" between dolls, and the sweets were grouped in one of two different ways. When the sweets were grouped by the divisor, the number of groups coincided with the number of dolls (divisor) and the number in each group was the answer (quotient). When the sweets were grouped by the quotient, the reverse was true. In all three experiments, children found it much easier to solve the problems in the Grouping-by-Divisor condition than in the Grouping-by-Quotient condition (although there was some evidence of a developmental improvement in the tasks). It is suggested that the Grouping-by-Divisor condition is easier because it coincides with the end point of sharing. The findings are discussed with reference to schemas of action in children's mathematical understanding.