Investigating the effects of procedural variation on multiplicative reasoning

Procedural variation uses varied sequences of questions to draw children's attention to the invariant critical features of a mathematical concept. This pre- and post-test intervention study investigates the effects of teaching using procedural variation on 7-8-year-old children's distributive and scalar multiplicative reasoning. The first research question examines whether Year 3 children are capable of recognising the distributive and scalar relationships between sequences of multiplication questions. The second research question considers whether teaching using procedural variation can improve Year 3 children's distributive and scalar reasoning. 184 children were recruited from six Year 3 classes and were randomly allocated to three interventions: distributive reasoning, scalar reasoning or the active control. Each intervention comprised three 30-minute sessions; the distributive and scalar reasoning groups received procedural variation teaching, while the active control focused on times tables. The pre- and post-test comprised distributive and scalar reasoning tasks and was administered immediately before and after the interventions. Many of the children were capable of using procedural variation to recognise the distributive relationships between multiplications but could not identify the scalar relationships. There were significant post-test differences between groups, with the experimental groups outperforming the control group. There was also a significant interaction between the distributive and scaling groups and their respective tasks, meaning that procedural variation teaching had a specific effect on distributive or scalar reasoning. This is the first intervention study to empirically evaluate the effects of teaching using procedural variation and it therefore makes a small yet valuable contribution to primary mathematics research