Accounting for individual variability in inversion shortcut use

This study investigated whether children's inversion shortcut use (i.e., reasoning that no calculations are required for the problem 4 × 8 ÷ 8, as the answer is the first number) is related to their analogical reasoning ability, short-term memory capacity, and working memory capacity. Children from Grades 6 and 8 solved multiplication and division inversion problems and classical analogy word problems and completed memory tasks. Analogical reasoning ability and working memory functioning both accounted for individual variance in inversion shortcut use. These findings suggest that the ability to understand relationships and executive functioning may enable children to internally represent and manipulate mathematical problems, facilitating the application of conceptual mathematical knowledge to generate the inversion shortcut.

Research Highlights
► Grade 6 and 8 children solved three-term multiplication and division inversion problems and analogy problems as well as completed memory tasks.
► Analogical reasoning ability accounted for the most independent variance in inversion shortcut use.
► Working memory capacity also predicted independent variance in inversion shortcut use.
► Children's inversion shortcut use is mediated by their ability to understand relationships as well as their ability to manipulate problem information in working memory.