A Slide Rule for the Evaluation of Geochemical and Mineral Survey Data. EUR 4608.

<p>FB = false belief, TB/MC = true belief/memory control, *Control trials include TB/MC + filler trials, ** Such deficit could be combined with difficulties in processing the input information if the performance on the control trials is below the cut-off albeit better than the performance on the FB trials.</p

Efficient belief tracking in adults:The role of task instruction, low-level associative processes and dispositional social functioning

A growing body of evidence suggests that adults can monitor other people’s beliefs in an efficient way. However, the nature and the limits of efficient belief tracking are still being debated. The present study addressed these issues by testing (a) whether adults spontaneously process other people’s beliefs when overt task instructions assign priority to participants’ own belief, (b) whether this processing relies on low-level associative processes and (c) whether the propensity to track other people’s beliefs is linked to empathic disposition. Adult participants were asked to alternately judge an agent’s belief and their own belief. These beliefs were either consistent or inconsistent with each other. Furthermore, visual association between the agent and the object at which he was looking was either possible or impeded. Results showed interference from the agent’s belief when participants judged their own belief, even when low-level associations were impeded. This indicates that adults still process other people’s beliefs when priority is given to their own belief at the time of computation, and that this processing does not depend on low-level associative processes. Finally, performance on the belief task was associated with the Empathy Quotient and the Perspective Taking scale of the Interpersonal Reactivity Index, indicating that efficient belief processing is linked to a dispositional dimension of social functioning

Quand le rapport de deux nombres naturels ouvre sur le continu : étude comportementale du traitement de la magnitude des fractions chez l'enfant et l'adulte

In the field of numerical cognition, researches have mainly investigated the processing of the magnitude of natural numbers, letting the issue of the processing of the magnitude of fractions open. In order to identify the processes and the representations involved in this processing, we carried out four behavioural studies in adults and children. The first three studies investigated the ability of fifth-graders, seventh-graders and adults to represent the holistic value of fractions mentally. Their performance on the numerical comparison of fractions was analyzed according to the numerical distance between the fractions (e.g., 0.27 for 2/5 and 2/3) and between the components (e.g., 2 for 2/5 and 2/3). Results showed that fifth-graders, seventh-graders and adults are able to activate an approximate representation of the holistic value of fractions. Moreover, the effect of the congruence of the components with the magnitude of the fractions suggests a hybrid processing: the magnitudes of the components would be compared while the magnitude of the holistic values was being processed (e.g., comparing 3 and 5 when comparing 0.67 and 0.40 for 2/3 and 2/5). Eventually, these studies showed the strategic aspects of the processing of fractions. Even if adults are able to represent the magnitude of fractions mentally, they compare the components, without accessing the mental representation of the holistic values, in some experimental tasks (e.g., comparing the numerators for 3/7 and 5/7). This componential strategy could be less consuming in time and in resources than the processing of the holistic values. The fourth study tested the specificity of the processing of the magnitude of fractions and investigated the mechanism by which the mental representation of a magnitude is activated from a fraction. Adults performed a numerical estimation task on fractions and non-symbolic ratios (ratios between two collections of dots or between two surface areas). The ratios varied in magnitude and in the size of their components (e.g., 2/5, 3/8, 11/28 for 0.40). The effect of the format showed that, in adults, the mental representation is more precise for fractions than for non-symbolic ratios. The effect of the size of the components suggested that the indirect access might be one of the mechanisms that allow the mental representation of the magnitude of fractions to be activated. The mental representations of the components would be first activated and their numerical relation would be then estimated. We will close the manuscript by a general discussion that summarizes the results of our studies, links them to the recent literature on the processing of the fraction magnitude, and underlines the theoretical implications.Les recherches en cognition numérique se sont principalement penchées sur le traitement de la magnitude des nombres naturels, laissant ouverte la question du traitement de la magnitude des fractions. Afin d’identifier les processus et les représentations impliqués dans ce traitement, nous avons mené quatre études comportementales chez l’enfant et l’adulte. Nos trois premières études ont testé la capacité des élèves de 5ème primaire, des élèves de 1ère secondaire et des adultes à représenter mentalement la valeur holistique des fractions. Leurs performances dans des tâches de comparaison numérique de fractions ont été analysées en fonction de la distance numérique entre les fractions (p.ex., 0,27 pour 2/5 et 2/3) et entre les composants (p.ex., 2 pour 2/5 et 2/3). Les résultats montrent que les adultes et les élèves des deux années scolaires sont capables d’activer une représentation approximative de la valeur holistique des fractions. Par ailleurs, l’effet de la congruence des composants avec la magnitude de la fraction suggère un traitement hybride : la magnitude relative des composants serait également traitée lors du traitement de la valeur holistique des fractions (p.ex., comparaison de 3 et 5 lors de la comparaison de la valeur holistique de 2/3 et 2/5). Enfin, ces études mettent en évidence les aspects stratégiques du traitement des fractions. En effet, même si l’adulte a la capacité de représenter mentalement la valeur holistique des fractions, il compare les composants, sans traiter la valeur holistique des fractions, dans certains contextes expérimentaux (p.ex., comparer les numérateurs pour 3/7 et 5/7). Cette stratégie componentielle pourrait être moins coûteuse que le traitement de la valeur holistique des fractions. La quatrième étude a testé la spécificité du traitement de la magnitude des fractions et a exploré l’accès à la représentation mentale de la valeur holistique d’une fraction. Des adultes ont réalisé une tâche d’estimation de la magnitude de fractions et de rapports non symboliques (rapports entre deux collections de points et rapports entre deux surfaces) qui variaient en taille de rapports et en taille des composants (p.ex., 2/5, 3/8, 11/28 pour 0,40). L’effet du format indique que les adultes ont une représentation numérique mentale plus précise des fractions que des rapports non symboliques. L’effet de la taille des composants suggère qu’un des mécanismes permettant d’activer la représentation mentale de la valeur holistique d’une fraction est l’accès indirect. Cette représentation serait activée à partir de la représentation mentale de la magnitude des composants et l’approximation de leur relation numérique. Nous terminerons notre exposé par une discussion générale qui synthétise les résultats de nos études en les intégrant à la récente littérature sur le traitement cognitif des fractions et en soulignant leurs implications théoriques.(PSY 3) -- UCL, 201

L'apprentissage des nombres rationnels et ses obstacles.

La grande majorité des recherches sur la cognition numérique s’est concentrée sur les nombres naturels. Peu de travaux ont été consacrés à l’apprentissage et aux traitements cognitifs d’autres catégories de nombres. C’est le cas des fractions et des nombres décimaux qui font l’objet du présent chapitre. Dans le cadre de la théorie contemporaine des nombres, les fractions et les décimaux font partie de l’ensemble des nombres rationnels. Cet ensemble comprend des nombres positifs et négatifs. Ces derniers ne sont toutefois pas enseignés, ni utilisés régulièrement avant l’enseignement secondaire. Comme notre propos ne concerne que les apprentissages numériques réalisés à l’école primaire, nous ferons l’impasse sur les rationnels négatifs et nous nous focaliserons sur les seuls positifs. Dans une première section, nous commencerons par définir le concept de nombre rationnel du point de vue mathématique et nous en retracerons brièvement l’histoire. La section suivante sera consacrée à l’apprentissage des nombres rationnels positifs à l’école primaire et à ses vicissitudes. La dernière section abordera, quant à elle, la question des modèles cognitifs de l’apprentissage et du traitement des rationnels positifs

Moral judgments depend on information presentation: Evidence for recency and transfer effects

Moral judgements are crucial for social life and rely on the analysis of the agent’s intention and the outcome of the agent’s action. The current study examines to the influence of how the information is presented on moral judgement. The first experiment investigated the effects of the order in which intention and outcome information was presented. The results showed that participants relied more on the last presented information, suggesting a recency effect. The second experiment required participants to make two types of judgments (wrongness vs. punishment) and manipulated the order of the requested two types of judgments. Results showed an asymmetrical transfer effect whereby punishment judgements, but not wrongness judgements were affected by the order of presentation. This asymmetrical transfer effect was likely linked to the ambiguity of the punishment judgement. Altogether, the study showed that the order in which information was presented and the order in which one was asked to think about the wrongness of an action or the punishment that the action deserves were two factors that should be irrelevant, but actually influenced moral judgements. The influence of these factors was mostly observed during the most difficult judgements, precisely in situations where human decision is called upon, such as in court trials

Thinking ratios in symbolic and analogical format: Sensitivity to the interference of natural numbers/counting knowledge

This study investigates the reason of the interference of natural numbers with the processing of fractions in adults. Mix et al. (1999) hypothesized that the Arabic digits making up a fraction can activate the natural number knowledge in children, as they are frequently used to express natural numbers. If this hypothesis is right in adults, natural number knowledge should interfere with the processing of probabilities with the same number of favourable cases (for a given number of favourable cases, higher is the number of possible cases lower is the probability to have a favourable case), only when they are expressed by a fraction. Adults had to compare two probabilities, either with the same number of possible cases either with the same number of favourable cases. Probabilities were presented symbolically (fraction) and analogically (subset of a set of items). In our sample, comparing probabilities with the same number of favourable cases is more complex than comparing probabilities with the same number of possible cases, but whatever the way of representation. However, the difference between the two types of comparison is higher in the symbolic way than in the analogical ways. These results suggest that natural number/counting knowledge interferes with the processing of probabilities expressed symbolically and analogically. Consequently, the interference of natural numbers with the processing of fractions cannot only be explained by the presence of Arabic digits in the fraction symbol

Représentation mentale de la magnitude des fractions chez des enfants de 10 et 12 ans

Cette étude teste la représentation mentale de la magnitude des fractions qui est activée lors de la comparaison de fractions avec composants communs (e.g., 2/3 _ 2/5 ; 3/7 _ 5/7) chez des enfants de 10 et 12 ans. Plus spécifiquement, nous avons testé si les enfants qui comparent correctement ces fractions accèdent à la magnitude de la fraction ou s’ils comparent uniquement les composants (e.g., 3 et 5 pour 2/3 _ 2/5). Les temps de réponse sont prédits par la distance entre les fractions, ce qui suggère un accès à leur magnitude. Les enfants comparent plus lentement les fractions de numérateur commun (e.g., 2/3 _ 2/5) que les fractions de dénominateur commun (3/7 _ 5/7). Cet effet indique une interférence des dénominateurs. En effet, la magnitude relative des dénominateurs est incongruente avec la magnitude relative des fractions puisque la plus grande fraction est composée du plus petit dénominateur. Enfin, un paradigme de priming a été utilisé afin de tester si le traitement des dénominateurs est inhibé lors de la comparaison des fractions. La comparaison de nombres naturels était amorcée par la comparaison de fractions. Un effet d’amorçage négatif a été observé pour les nombres naturels précédés de fractions de numérateur commun, confirmant une inhibition de la comparaison des dénominateurs lors du traitement des fractions. En conclusion, les enfants qui comparent correctement les fractions de composants communs accèdent à la magnitude de la fraction entière, mais restent sensibles à l’interférence des dénominateurs. Cette étude souligne qu’au-delà de l’interférence conceptuelle des nombres naturels avec l’apprentissage des fractions (appelée le biais des nombres naturels par Ni & Zhou, 2005), les enfants doivent aussi gérer l’interférence des dénominateurs lors du traitement des fractions (effet de type Stroop)

Comparing the magnitude of two fractions with common components : which representations are used by 10- and 12-year-olds?

This study tested whether 10- and 12-year-olds who can correctly compare the magnitudes of fractions with common components access the magnitudes of the whole fractions rather than only compare the magnitudes of their components. Time for comparing two fractions was predicted by the numerical distance between the whole fractions, suggesting an access to their magnitude. In addition, we tested whether the relative magnitude of the denominator interferes with the processing of the fraction magnitude and, thus, needs to be inhibited. Response times were slower for fractions with common numerators than for fractions with common denominators, indicating an interference of the magnitude of the denominators with the selection of the larger fraction. A negative priming effect was shown for the comparison of natural numbers primed by fractions with common numerators, suggesting an inhibition of the selection of the larger denominator during the comparison of fractions. In conclusion, children who can correctly compare fractions with common components can access the magnitude of the whole fractions but remain sensitive to the interference of the relative magnitude of the denominators. This study highlights the fact that beyond the interference of natural number knowledge at the conceptual level (called the "whole number bias" by Ni & Zhou, 2005), children need to manage the interference of the magnitude of the denominators (Stroop-like effect)

Processing the magnitude of fractions

This study explored the cognitive processes and representations involved in the numerical comparison of fractions. The fractions magnitude could be processed in an analytic way (based on the magnitude of their components) or in a holistic way. In this study, fractions had either a common denominator or a common numerator. To identify the representations involved in the comparison of each category of fractions, we analyzed: (1) the effect of the numerical distance between fractions and between their components and (2) the effect of comparing fractions on subsequent comparison of natural numbers

Rational numbers : componential versus holistic representation of fractions in a magnitude comparison task

This study investigated whether the mental representation of the fraction magnitude was componential and/or holistic in a numerical comparison task performed by adults. In Experiment 1, the comparison of fractions with common numerators (x/a_x/b) and of fractions with common denominators (a/x_b/x) primed the comparison of natural numbers. In Experiment 2, fillers (i.e., fractions without common components) were added to reduce the regularity of the stimuli. In both experiments, distance effects indicated that participants compared the numerators for a/x_b/x fractions, but that the magnitudes of the whole fractions were accessed and compared for x/a_x/b fractions. The priming effect of x/a_x/b fractions on natural numbers suggested that the interference of the denominator magnitude was controlled during the comparison of these fractions. These results suggested a hybrid representation of their magnitude (i.e., componential and holistic). In conclusion, the magnitude of the whole fraction can be accessed, probably by estimating the ratio between the magnitude of the denominator and the magnitude of the numerator. However, adults might prefer to rely on the magnitudes of the components and compare the magnitudes of the whole fractions only when the use of a componential strategy is made difficult