The effects of situations on children's understanding of fractions

• Main Author: Mamede, Ema Paula Botelho da Costa
• Published: Oxford Brookes University 2007
• Subjects: 371.3
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.490511

The hypothesis examined in this thesis is that the situation in which the concept of fractions is used affects children's understanding of fractions. Children's performance in logical and labelling tasks in Quotient, Part-whole' and Operator situations is compared using two surveys and a brief intervention. The first and second studies were a survey of children's performance in problems where they judged the equivalence and order of magnitude of quantities in division situations, which would be represented by fractions. These are the logical questions examined throughout the thesis. The children were also taught how to represent the quantities using fractions. Six- and 7-year-olds were randomly assigned to work either in Quotient (N=40), or in Part-whole (N=40) or in Operator situations (N=40). They performed significantly better both in the logical and labelling items in Quotient than in Part-whole situations. They performed better in logical items in Operator than in Part-whole situations, but the reverse was true of fraction labelling items. The third study aimed to replicate these results using a within-participants design (same age children, N=37). Performance was again significantly better in Quotient than in the other situations; the difference between Part-whole and Operator situations was not replicated. The same children participated in a brief intervention, delivered to small groups randomly assigned to learn about fractions in one of the three situations or to a control group. Analyses of covariance showed that only the children taught in Quotient situations differed from the control group in both the logical and the naming items. Those in the other groups only differed in the naming items. There was no evidence of transfer from Quotient situations to the other situations but there was transfer in the labelling items between Part-whole and Operator situations. Thus an effect of situations on children's understanding of fractions is demonstrated. Educational implications are discussed.