Three experiments involving a Stroop-like paradigm were conducted. In Experiment 1, adults received a number comparison task in which large sets of dots, orthogonally varying along a discrete dimension (number of dots) and a continuous dimension (cumulative area), were presented. Incongruent trials were processed more slowly and with less accuracy than congruent trials, suggesting that continuous dimensions such as cumulative area are automatically processed and integrated during a discrete quantity judgement task. Experiment 2, in which adults were asked to perform area comparison on the same stimuli, revealed the reciprocal interference from number on the continuous quantity judgements. Experiment 3, in which participants received both the number and area comparison tasks, confirmed the results of Experiments 1 and 2. Contrasting with earlier statements, the results support the view that number acts as a more salient cue than continuous dimensions in adults. Furthermore, the individual predisposition to automatically access approximate number representations was found to correlate significantly with adults' exact arithmetical skills.

Fractions are well known to be difficult to learn. Various hypotheses have been proposed in order to explain those difficulties: fractions can denote different concepts; their understanding requires a conceptual reorganization with regard to natural numbers; and using fractions involves the articulation of conceptual knowledge with complex manipulation of procedures. In order to encompass the major aspects of knowledge about fractions, we propose to distinguish between conceptual and procedural knowledge. We designed a test aimed at assessing the main components of fraction knowledge. The test was carried out by fourth-, fifth- and sixth-graders from the French Community of Belgium. The results showed large differences between categories. Pupils seemed to master the part-whole concept, whereas numbers and operations posed problems. Moreover, pupils seemed to apply procedures they do not fully understand. Our results offer further directions to explain why fractions are amongst the most difficult mathematical topics in primary education. This study offers a number of recommendations on how to teach fractions.

The ability to handle approximate quantities, or number sense, has been recurrently linked to mathematical skills, although the nature of the mechanism allowing to extract numerical information (i.e., numerosity) from environmental stimuli is still debated. A set of objects is indeed not only characterized by its numerosity but also by other features, such as the summed area occupied by the elements, which often covary with numerosity. These intrinsic relations between numerosity and nonnumerical magnitudes led some authors to argue that numerosity is not independently processed but extracted through a weighting of continuous magnitudes. This view cannot be properly tested through classic behavioral and neuroimaging approaches due to these intrinsic correlations. The current study used a frequency-tagging EEG approach to separately measure responses to numerosity as well as to continuous magnitudes. We recorded occipital responses to numerosity, total area, and convex hull changes but not to density and dot size. We additionally applied a model predicting primary visual cortex responses to the set of stimuli. The model output was closely aligned with our electrophysiological data, since it predicted discrimination only for numerosity, total area, and convex hull. Our findings thus demonstrate that numerosity can be independently processed at an early stage in the visual cortex, even when completely isolated from other magnitude changes. The similar implicit discrimination for numerosity as for some continuous magnitudes, which correspond to basic visual percepts, shows that both can be extracted independently, hence substantiating the nature of numerosity as a primary feature of the visual scene. numerical cognition | numerosity extraction | fast periodic visual stimulation | quantities | nonsymbolic mathematical abilities

Summary. In two experiments the naming task was used to investigate the effect of spelling-to-sound regularity on performance for French words varying in frequency of usage. In both experiments the results showed a significant effect of regularity on naming latencies. Contrary to what has been found in previous experiments using English stimuli, the regularity effect did not vary as a function of word frequency. However, in both experiments significantly more errors, and specifically regularisation errors, were observed with low-frequency irregular words. Several possine interpretations of this atypical pattern of results are discussed. An additional observation was that the regularity effect, both on naming latencies and on error rates, and independently of frequency of use, was limited to the irregular words in which the idiosyncratic orthographic segment was either in initial or in medial position in the word.

Written symbols such as letters have been used extensively in cognitive psychology, whether to understand their contributions to written word recognition or to examine the processes involved in other mental functions. Sometimes, however, researchers want to manipulate letters while removing their associated characteristics. A powerful solution to do so is to use new characters, devised to be highly similar to letters, but without the associated sound or name. Given the growing use of artificial characters in experimental paradigms, the aim of the present study was to make available the Brussels Artificial Character Sets (BACS): two full, strictly controlled, and portable sets of artificial characters for a broad range of experimental situations.