**Strategy solutions in mental arithmetic: are flexible strategists better than stable ones?**

Lucidi A.,
Lefevre J., Rossi-arnaud C., Cestari V.

First author's affiliation: L.U.M.S.A, Roma, Italy

Mental arithmetic has been investigated for some time but only recently have researchers explored the solution procedures that adults use to mentally solve arithmetic problems. Solution procedures vary considerably across individuals and across cultural backgrounds. In the present study individual differences in mental arithmetic were investigated by examining the solution strategies used by adults to mentally solve 2- plus 2-digit addition problems (e.g., 35 + 47) across four levels of complexity (no carry; carry in ones; carry in tens and carry in both). Operands were presented sequentially over 3 s in two conditions: visually (i.e., one addend of the addition problem at a time appeared at the centre of a computer screen) and aurally (the addition problems were presented through the headphones). Participants reported two broad categories of strategies: Digit strategies are versions of a standard algorithm, based on written addition and involve operating on a series of single digits, and Holistic strategies are based on more representations of the numbers that preserve overall magnitude and involve decomposing and recombining the operands in various ways. Participants could be grouped according to whether they were “flexible” (i.e. employed a variety of strategies, such as decomposition, transformation, standard algorithm) or “stable” in that they used one of these strategies throughout the experiment. Results suggest that the type of strategy solution has a greater effect on solution latency than on accuracy. Although response times were longer with auditory presentation, in this modality, flexible strategists solved problems more quickly than stable strategists. Results are discussed in terms of a contribution from working memory to the encoding and maintenance of operands and intermediate products during mental arithmetic.