Relationship and transfer between mental and written arithmetic

Abstract

In a first experiment, adults practiced single- and two-digit mental addition over a 6-day period. There was a clear training effect for both types of problems, even if two-digit additions were different from one day to another. Moreover, participants were tested on their written calculation abilities before and after the training programme. We showed that participants who entered the mental arithmetic training programme did not progress more in written arithmetic than participants who did not receive any training between the pre- and the post-tests. Conversely, in a second experiment, participants were trained in multidigit written addition and we examined the effect of such training on single- and two-digit mental addition. Again and trivially, there was a clear effect of training on written addition, but, more importantly, a transfer on mental addition. The implications of these results on the nature of the relationship between mental and written arithmetic are discussed.

Keywords:

• Addition
• Arithmetic abilities
• Numerical cognition
• Practice

Acknowledgements

This work was supported by an FNRS Project Grant (ref. 100014-126919) and by the Ernst & Lucie Schmidheiny Foundation. We would like to thank Patrick Bruderlein, Sonja Doswald, Isabelle Gay-Dembinski, and Ombeline Goy for collecting and analysing the data. Finally, we would like to thank Patrick Lemaire, Mark Ashcraft, and an anonymous reviewer for their thoughtful suggestions on a first version of this manuscript.