Educational Studies in Mathematics
, Volume 72, Issue 1, pp 127138
First online:
Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction
 Doug M. ClarkeAffiliated withAustralian Catholic University
 , Anne RocheAffiliated withAustralian Catholic University Email author
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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 Onetoone interviews Understanding Misconceptions Title
 Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction
 Journal

Educational Studies in Mathematics
Volume 72, Issue 1 , pp 127138
 Cover Date
 200909
 DOI
 10.1007/s1064900991989
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Fractions
 Strategies
 Assessment tasks
 Onetoone interviews
 Understanding
 Misconceptions
 Authors

 Doug M. Clarke ^{(1)}
 Anne Roche ^{(1)}
 Author Affiliations

 1. Australian Catholic University, Melbourne, Australia