Catherine Thevenot

Studies about strategies used by adults to solve multi-digit written additions are very scarce. However, as advocated here, the specificity and characteristics of written calculations are of undeniable interest. The originality of our approach lies in part in the presentation of two-digit addition problems on a graphics tablet, which allowed us to precisely follow and analyse individuals’ solving process. Not only classic solution times and accuracy measures were recorded but also initiation times and starting positions of the calculations. Our results show that adults largely prefer the fixed columnar strategy taught at school rather than more flexible mental strategies. Moreover, the columnar strategy is executed faster and as accurately as other strategies, which suggests that individuals’ choice is usually well adapted. This result contradicts past educational intuitions that the use of rigid algorithms might be detrimental to performance. We also demonstrate that a minority of adults can modulate their strategy choice as a function of the characteristics of the problems. Tie problems and additions without carry were indeed solved less frequently through the columnar strategy than non-tie problems and additions with a carry. We conclude that the working memory demand of the arithmetic operation influences strategy selection in written problem-solving.

In this study, we assessed basic and more complex non-symbolic and symbolic numerical task abilities in children with hemiplegia and obtained a detailed picture of their strengths and weaknesses in the numerical domain. Those children, who experience difficulties in finger gnosia and spontaneous use of fingers in counting, exhibit difficulties in finger pattern recognition and symbolic numerical tasks. However, their non-symbolic numerical abilities and arithmetic skills are preserved. These original results are discussed in light of the “manumerical cognition” hypothesis, which postulates that the use of fingers in numerical activities during childhood shapes our comprehension of numbers.

The directionality of finger counting (i.e., from left to right or right to left) is supposed to compete with the orientation of the mental number line in determining number mental representations. Indeed, Western individuals who count on their fingers from right to left present a weaker SNARC effect than do individuals for whom the directionality of counting is the same as the mental number line. Observations of natural behavior should be the preferred methodology for classifying individuals according to their counting habits. Yet, to perform such classification, researchers usually rely on questionnaires or reports of imagined behaviors. However, we show in a series of three experiments that, on average, 26 % of a sample of adults reported the opposite behavior from the one they actually implemented spontaneously when tested with an original ecological task. In a fourth experiment, this new task proved reliable, using a test–retest method. These results suggest that future studies about counting habits could benefit from the use of more ecological and functional tasks, rather than depending on noncontextualized questionnaires.

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.

Determining how individuals solve arithmetic problems is crucial for our understanding of human cognitive architecture. Elderly adults are supposed to use memory retrieval more often than younger ones. However, they might backup their retrieval by reconstructive strategies. In order to investigate this issue, we used the operand-recognition paradigm, which capitalizes on the fact that algorithmic procedures degrade the memory traces of the operands. Twenty-three older adults (M = 70.4) and 23 younger adults (M = 20.0) solved easy, difficult, and medium-difficulty addition and comparison problems and were then presented with a recognition task of the operands. When one-digit numbers with sums larger than 10 were involved (medium-difficulty problem), it was more difficult for younger adults to recognize the operands after addition than comparison. In contrast, in older adults, recognition times of the operands were the same after addition and comparison. Older adults, in contrast with younger adults, are able to retrieve the results of addition problems of medium difficulty. Contrary to what was suggested, older participants do not seem to resort to backup strategies for such problems. Finally, older adults’ reliance on the more efficient retrieval strategy allowed them to catch up to younger adults in terms of solution times.

This paper addresses the relationship between basic numerical processes and higher level numerical abilities in normal achieving adults. In the first experiment we inferred the elementary numerical abilities of university students from the time they needed to encode numerical information involved in complex additions and subtractions. We interpreted the shorter encoding times in good arithmetic problem solvers as revealing clearer or more accessible representations of numbers. The second experiment shows that these results cannot be due to the fact that lower skilled individuals experience more maths anxiety or put more cognitive efforts into calculations than do higher skilled individuals. Moreover, the third experiment involving non-numerical information supports the hypothesis that these interindividual differences are specific to number processing. The possible causal relationships between basic and higher level numerical abilities are discussed.