Ten-year old children's understanding of fractions

Abstract

This study was conducted within the of the constructivist theory knowledge. The aims the study were identify children's fractional schemes and to investigate how these schemes were recognise units, to establish improper or equivalent fractions to fractions. Nine children, aged ten, were presented with tasks involving continuous regions, marked regions and collections. The one-to-one clinical interviews were video recorded, thus enabling analysis of the children's responses to be carried out afterwards. children who had developed the more sophisticated schemes were generally more successful in the tasks than the other children who interpreted fractional situations using more primitive schemes. Hence, a hierarchy of schemes was established as follows: intuitive whole number, ratio, splitting regions, splitting split regions, splitting composite units, denominator-based, regions, iterating, partitioning composite multiple-pa1titioning coordinating, It was times a child used a primitive or inappropriate scheme even though a more sophisticated or appropriate scheme was available that child. Thus, the context-dependent nature of schemes was observed. In general, the children appeared to more familiar with indicating fractions regions rather than of collections. Although all the children could a given them were 1/x of a collection of nx items.