Mental Arithmetic and Interactivity: the Effect of Manipulating External Number Representations on Older Children’s Mental Arithmetic Success

Manipulative artefacts are considered useful scaffolds of arithmetic during early years education, but their use is considered less important as children get older. Yet adult arithmetic performance often recruits artefacts to improve accuracy and efficiency, and so the same benefits should accrue to children beyond early years. We propose that interacting with manipulatives supports working memory by extending the mental workspace. This is a hitherto poorly explored aspect of the pedagogical benefits of manipulatives. Forty-three children aged between 7 and 9 years old were invited to assess whether interacting with artefacts supported arithmetic when under a working memory load. Interactivity and load were manipulated in a 2 × 2 repeated measures design. Children calculated the total of seven digits either with hands down—low interactivity—or moving numbered tokens—high interactivity. Additionally, in half the conditions, the children performed a second task designed to tax working memory. The children were also assessed across a battery of measures examining individual differences. As expected, performance was considerably worse under load. More sums were answered correctly in high-interactivity conditions regardless of working memory load. In the high-interactivity condition with a load, there were significant correlations between performance and both numeracy and fluid intelligence suggesting that even for more numerate children manipulatives confer benefits. The expression of arithmetic skills depends on the nature of the external resources offered by the environment. This dynamic agent–environment transaction highlights the pedagogical importance of external resources when assessing children’s arithmetic abilities