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
(2010)
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- Abstract
- (en) 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.
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Citations
Meert, G. (2010). 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. https://hdl.handle.net/2078.5/92343