Using context to enhance students' understanding of decimal fractions

Abstract

A total of 84 students from a lower economic area, aged 8 to 14, were interviewed about their understanding of decimal fractions. Results showed that most students could give a context in which they saw decimal fractions outside of school. The vast majority could draw a diagram of how a cake or field could be divided equally among 10 or 100 people. However, few students under 14 could give either decimal fraction symbols or common fraction symbols to represent these divisions. Less than half of the students at ages 10, 11 and 12 could visualize what might come between 0 and 1. About half of the students aged 11 and 12 could indicate what 0.1 or 0.01 meant. It was inferred that difficulty in relating these symbols to referents might be an important source of difficulty in understanding decimal fractions. Therefore, these interviews were followed by an intervention study that examined if working with contextualized decimal fractions aided understanding of these numbers when they were presented without context. Half of a group of 16 similar students, aged 11 and 12, were asked to solve problems in which numbers that incorporated decimal fractions were contextualized, and the other half were asked to solve similar problems given in purely numerical form. Students worked in pairs, on problems which incorporated common misconceptions. The group who worked on contextualized problems gained significantly more understanding than did the group that worked on purely numerical problems, as measured by the difference between pretest and posttest scores. Transcripts of the students' discussions were analysed for the effect of prior learning, aspects of peer collaboration that appeared to be beneficial to learning, and the effect of cognitive conflict. The students who gained most from collaboration were not too distant in initial expertise, showed a degree of social equity, and worked on contextualized problems. Much of students' learning appeared to result from needing to reconsider their views following a conflict between their expectations and the results of operating on a calculator or in writing, or hearing an alternative view.