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How non-symbolic numerosity is visually extracted remains a matter of intense debate. Most evidence suggests that numerosity is directly extracted on individual objects following Weber’s law, at least for a moderate numerical range. Alternative accounts propose that, whatever the range, numerosity is indirectly derived from summary texture-statistics of the raw image such as spatial frequency (SF). Here, to disentangle these accounts, we tested whether the well-known behavioural signature of numerosity encoding (ratio effect) is preserved despite the equalisation of the SF content. In Experiment 1, participants had to select the numerically larger of two briefly presented moderate-range numerical sets (i.e., 8–18 dots) carefully matched for SF; the ratio between numerosities was manipulated by levels of increasing difficulty (e.g., 0.66, 0.75, 0.8). In Experiment 2, participants performed the same task, but they were presented with both the original and SF equalised stimuli. In both experiments, the results clearly showed a ratio-dependence of the performance: numerosity discrimination became harder and slower as the ratio between numerosities increased. Moreover, this effect was found to be independent of the stimulus type, although the overall performance was better with the original rather than the SF equalised stimuli (Experiment 2). Taken together, these findings indicate that the power spectrum per se cannot explain the main behavioural signature of Weber-like encoding of numerosities (the ratio effect), at least over the tested numerical range, partially challenging alternative indirect accounts of numerosity processing.

Current theories of intelligence maintain that intellectual development is the expression of a strict interplay among different cognitive abilities and the environment. Yet, the environment in which the individual develops has often been reduced to a single measure in empirical research, which thus loses sight of its inherent multifaceted structure. This work stems from the need to grasp such multifaceted complexity, by differentiating the associations of cultural and socioeconomic factors with crystallized and fluid intelligence in adolescence. An updated and digitalized version of the Verbal task from the Primary Mental Abilities battery (PMA Verbal) was administered to a large group of Italian adolescents as a measure of crystallized intelligence. Item Response Theory confirmed the good psychometric properties of the test. The relationship among cognitive abilities and the environment was explored through a Network Analysis on measures of crystallized intelligence (PMA Verbal), fluid intelligence (Raven SPM) and various environmental dimensions (socioeconomic status, home possessions, books at home, reading habits). Network Analysis is particularly suited for highlighting the individual role of each variable within such a complex system. Our results illustrated a key role of books at home, which was positively connected to verbal abilities on the one hand and to reading habits on the other, whereas no relationship to fluid intelligence was found. Crucially, these findings were independent of socioeconomic status. This study indicates that a more detailed conceptualization of the environment provides a better understanding of how cognitive abilities develop.

Many children fail in geometric learning, but factors underlying these failures have not been explored in detail. The present study addresses this issue by comparing fifth and sixth-grade children who had good or poor geometric learning, and were otherwise comparable on verbal intelligence, gender and age. Results showed that children with poor geometric learning have deficits in both arithmetic and geometric problem solving but they are more impaired in the latter. Results also showed that poor geometric learners have weaknesses in working memory, calculation, and visuospatial mental imagery. The results from logistic regressions pointed out that mental imagery skills and arithmetic problem solving ability had the highest discriminatory power in distinguishing between the two groups. Theoretical and practical implications of this research for designing interventions to help poor geometric learners are discussed. © 2018 Elsevier Inc.

It has long been thought that the primary cognitive and neural systems responsible for processing numerosities are not predisposed to encode empty sets (i.e., numerosity zero). A new study challenges this view by demonstrating that zero is translated into an abstract quantity along the numerical continuum by the primate parietofrontal magnitude system.

Although the existence of an association between numbers and space has been largely documented in educated adults, the origin of this association still remains debated. Recent evidence suggests that associations between numbers and space might originate during the preschool years from the repeated action of counting in peripersonal space. However, it is also possible that preschoolers may additionally acquire directional preferences by counting on their own body, specifically on their fingers. To address this hypothesis, the present study explores the presence of early directional indexes in processing numerical information in both peripersonal and personal space in a sample of 90 preschoolers. We identified children who consistently exhibited a counting directional bias and generalized it to their processing of numbers in space. Moreover, given the tight connection between counting routine and numerical knowledge, we investigated the relation between these indexes and numerical achievement, evaluated by means of various tasks. Results indicate that distinct spatial-numerical associations, in both peripersonal and personal space, coexist from an early age and can be used flexibly. However, regardless of its directionality, the presence of a consistent spatial-numerical association appears to be related to numerical comprehension.