Educational Studies in Mathematics

, Volume 72, Issue 1, pp 127–138 | Cite as

Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction

Article

Abstract

As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that predicted, with the exception of fractions with the same numerators and different denominators, which proved surprisingly difficult. Students who demonstrated the greatest success were likely to use benchmark (transitive) and residual thinking. It is hypothesised that the methods of these successful students could form the basis of instructional approaches which may yield the kind of connected understanding promoted in various curriculum documents and required for the development of proportional reasoning in later years.

Keywords

Fractions Strategies Assessment tasks One-to-one interviews Understanding Misconceptions 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Australian Catholic UniversityMelbourneAustralia

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