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

摘要

As part of individual interviews incorporating whole number and rational numbertasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of twofractions for eight pairs, giving reasons for their choice. All tasks were expected to beundertaken 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, whichproved surprisingly difficult. Students who demonstrated the greatest success were likely to usebenchmark (transitive) and residual thinking. It is hypothesised that the methods of thesesuccessful students could form the basis of instructional approaches which may yield the kindof connected understanding promoted in various curriculum documents and required for thedevelopment of proportional reasoning in later years.