The use of automated procedures by older adults with high arithmetic skills during addition problem solving.

International audienceIn contrast to other cognitive abilities, arithmetic skills are known to be preserved in healthy elderly adults. In fact, they would even outperform young adults because they more often retrieve arithmetic facts from long-term memory. Nevertheless, we suggest here that the superiority of older over younger adults could also stem from the use of more efficient automated and unconscious counting procedures. We tested 35 older participants using the sign priming paradigm and selected the 18 most efficient ones, aged from 60 to 77. Sign priming are interpreted as the indicator of the pre-activation of an abstract procedure as soon as the arithmetic sign is presented. We showed that expert elderly arithmeticians behaved exactly as 26 young participants presenting the same level of arithmetic proficiency. More precisely, we showed that presenting the “+” sign 150 ms before the operands speeds up the solving process compared to a situation wherein the problem is classically presented in itswhole on the screen. Only tie problems and problems involving 0 were not subjected to these priming effects and we concluded that only these problems were solved by retrieval, either of the answer for tie problems or of a rule for + 0 problems. These results could provide new insights for the conception of training programs aiming at preserving older individuals’ arithmetical skills and, in a longer-term perspective, at maintaining their financial autonomy, which is decisive for keeping them in charge of their daily life

Spatial-Numerical Associations Enhance the Short-Term Memorization of Digit Locations

Little is known about how spatial-numerical associations (SNAs) affect the way individuals process their environment, especially in terms of learning and memory. In this study, we investigated the potential effects of SNAs in a digit memory task in order to determine whether spatially organized mental representations of numbers can influence the short-term encoding of digits positioned on an external display. To this aim, we designed a memory game in which participants had to match pairs of identical digits in a 9 × 2 matrix of cards. The nine cards of the first row had to be turned face up and then face down, one by one, to reveal a digit from 1 to 9. When a card was turned face up in the second row, the position of the matching digit in the first row had to be recalled. Our results showed that performance was better when small numbers were placed on the left side of the row and large numbers on the right side (i.e., congruent) as compared to the inverse (i.e., incongruent) or a random configuration. Our findings suggests that SNAs can enhance the memorization of digit positions and therefore that spatial mental representations of numbers can play an important role on the way humans process and encode the information around them. To our knowledge, this study is the first that reaches this conclusion in a context where digits did not have to be processed as numerical values

SCRUTINIZING PROBLEM-SIZE EFFECTS IN ARITHMETIC THROUGHOUT DEVELOPMENT TO BETTER UNDERSTAND COGNITIVE LEARNING

Several theories attempt to explain how individuals learn a new cognitive and procedural skill. Within the adaptive control of thought of Anderson, expertise is translated by an acceleration of procedures. In contrast, within the instance theory of Logan, gain of expertise is viewed as a gradual shift from procedural strategies to retrieval of knowledge from long-term memory. In this thesis and to examine the relevance of these theories, we focused on a skill that has been widely studied and is relatively easy to model, that is mental addition solving. More specifically, we focused our attention on the problem-size effect, which corresponds to the increase of solution times with the size of the operands involved in a problem. We scrutinized the shape and evolution of this effect for tie problems, constructed with repeated operands (e.g., 3 + 3), for non-tie problems (e.g., 4 + 3), and for 1-problems, in which one of the operands is 1. This thesis is organised around four articles. In the first one, the evolution of the problem-size effect has been precisely observed for the three problem types in children aged from 6 to 11 years old as well as in adults. In the second article, we observed changes of problem-size effect when Grade 1 children stop. using their fingers for tie and non-tie problems. In the third article, variations of event-related potentials between the different problem types have been -studied in adults in an EEG experiment. Finally, in the last article, the evolution of the size effect has been analysed again in adults but in an alphabet arithmetic task, which allows us to mimic the addition learning process while controlling for some determinant factors. Results of these articles combined with the current literature seem to indicate that retrieval is not always or rarely used to salve non-tie problems even in experts, which is in opposition with the dominant theory on addition solving and the instance theory of Logan. However, tie additions are almost exclusively solved by retrieval very early on, contrary to what was expected within the adaptive control of thought of Anderson. None of these theories on learning thus seem to be able to account for the entirety of the learning process, which would depend on the characteristic of the acquired skill. -- Plusieurs théories essaient d'expliquer comment des individus apprennent une nouvelle compétence cognitive et procédurale. Dans la théorie du contrôle adaptatif des pensées d'Anderson, l'expertise se traduit par une accélération des procédures. Au contraire, dans la théorie des instances de Logan, l'acquisition d'expertise est vue comme un changement graduel des stratégies procédurales à la récupération des connaissances en mémoire à long-terme. Dans cette thèse, pour étudier la pertinence de ces théories, nous nous sommes concentrés sur une compétence largement étudiée et relativement facile à modéliser qui est la résolution des additions. Plus particulièrement, nous nous sommes intéressés à l'effet de taille qui correspond à I’augmentation des temps de réponse avec la taille des opérandes d'un problème. Nous avons examiné la structure et l'évolution de cet effet pour les problèmes doubles construits avec deux fois le même opérande (e.g., 3 + 3), non-doubles (e.g. 4 + 3) et les problèmes dont l’une des opérandes est 1. Cette thèse est organisée autour de quatre articles. Dans le premier 1'évolution de l'effet de taille a été observée pour les trois types de problèmes chez les enfants âgés de 6 à 11 ans ainsi que chez les adultes. Dans la deuxième étude, nous avons observé les changements de l'effet de taille quand les enfants de 3H arrêtent d'utiliser leurs doigts pour les problèmes doubles et non-doubles. Dans le troisième article, les variations des potentiels évoqués entre les différents types de problèmes ont été étudiées chez les adultes dans une expérience EEG. Finalement, dans le dernier article, l'évolution de l'effet de taille a été analysée chez les adultes dans une tâche d'alphabet arithmétique qui nous permet de simuler le processus d'apprentissage des additions en contrôlant certains facteurs déterminants. Les résultats de ces articles combinés avec la littérature actuelle indiquent que la récupération n'est pas toujours, voire rarement, utilisée pour résoudre les problèmes non-doubles même chez les experts ce qui contredit la théorie dominante sur la résolution d'addition et la théorie des instances. Cependant, les additions doubles sont presque toujours résolues par récupération contrairement aux prédictions de la théorie du contrôle adaptatif des pensées. Aucune de ces théories ne semble donc pouvoir rendre compte de l'entièreté du processus_d' apprentissage qui dépendrait des caractéristiques de la compétence acquise

Arithmetic word problems describing discrete quantities: E.E.G evidence for the construction of a situation model

In this research, university students were asked to solve arithmetic word problems constructed either with discrete quantities, such as apples or marbles, or continuous quantities such as meters of rope or grams of sand. An analysis of their brain activity showed different alpha levels between the two types of problems with, in particular, a lower alpha power in the parieto-occipital area for problems describing discrete quantities. This suggests that processing discrete quantities during problem solving prompts more mental imagery than processing continuous quantities. These results are difficult to reconcile with the schema theory, according to which arithmetic problem solving depends on the activation of ready-made mental frames stored in long-term memory and triggered by the mathematical expression used in the texts. Within the schema framework, the nature of the objects described in the text should be quickly abstracted during problem solving because it cannot impact the semantic structure of the problem. On the contrary, our results support the situation model theory, which places greater emphasis on the problem context in order to account for individuals' behaviour. On a more methodological point of view, this study constitutes the first attempt to infer the characteristics of individual's mental representations of arithmetic text problems from EEG recordings. This opens the door for the application of brain activity measures in the field of arithmetic word problem