Monitoring and Prompting Emergent Algebraic Reasoning in the Middle Years: Using Reverse Fraction Tasks

To succeed in mathematics middle-years' students must move from additive to multiplicative thinking and from arithmetic calculations to generalised algebraic strategies. If we ask the right questions this progression can be monitored and prompted through fraction tasks. Students' solution strategies for fraction tasks vary from a dependence on diagrams, to methods that demonstrate algebraic reasoning. Based on testing and interviews two frameworks have been developed. The first is used to classify strategies students use to find an unknown whole, when given a known fractional part of the whole, and its equivalent quantity. The second framework monitors the extent to which algebraic reasoning is apparent when opportunities for generalised responses are prompted.