Preschoolers' Precision of the Approximate Number System Predicts Later School Mathematics Performance

The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities

A New Approach for Assessment of Mental Architecture: Repeated Tagging

A new approach to the study of a relatively neglected property of mental architecture—whether and when the already-processed elements are separated from the to-be-processed elements—is proposed. The process of numerical proportion discrimination between two sets of elements defined either by color or by orientation can be described as sampling with or without replacement (characterized by binomial or hypergeometric probability distributions respectively) depending on the possibility to tag an element once or repeatedly. All empirical psychometric functions were approximated by a theoretical model showing that the ability to keep track of the already tagged elements is not an inflexible part of the mental architecture but rather an individually variable strategy which also depends on conspicuity of perceptual attributes. Strong evidence is provided that in a considerable number of trials, observers tagged the same element repeatedly which can only be done serially at two separate time moments

Dot Display Affects Approximate Number System Acuity and Relationships with Mathematical Achievement and Inhibitory Control

Much research has investigated the relationship between the Approximate Number System (ANS) and mathematical achievement, with continued debate surrounding the existence of such a link. The use of different stimulus displays may account for discrepancies in the findings. Indeed, closer scrutiny of the literature suggests that studies supporting a link between ANS acuity and mathematical achievement in adults have mostly measured the ANS using spatially intermixed displays (e.g. of blue and yellow dots), whereas those failing to replicate a link have primarily used spatially separated dot displays. The current study directly compared ANS acuity when using intermixed or separate dots, investigating how such methodological variation mediated the relationship between ANS acuity and mathematical achievement. ANS acuity was poorer and less reliable when measured with intermixed displays, with performance during both conditions related to inhibitory control. Crucially, mathematical achievement was significantly related to ANS accuracy difference (accuracy on congruent trials minus accuracy on incongruent trials) when measured with intermixed displays, but not with separate displays. The findings indicate that methodological variation affects ANS acuity outcomes, as well as the apparent relationship between the ANS and mathematical achievement. Moreover, the current study highlights the problem of low reliabilities of ANS measures. Further research is required to construct ANS measures with improved reliability, and to understand which processes may be responsible for the increased likelihood of finding a correlation between the ANS and mathematical achievement when using intermixed displays

Metacognitive developments in word learning:mutual exclusivity and theory of mind

This study examines the flexibility with which children can use pragmatic information to determine word reference. Extensive previous research shows that children choose an unfamiliar object as referent of a novel name: the disambiguation effect. We added a pragmatic cue indirectly indicating a familiar object as intended referent. In three experiments, preschool children’s ability to take this cue into account was specifically associated with false belief understanding and the ability to produce familiar alternative names (e.g., rabbit, animal) for a given referent. The association was predicted by the hypothesis that all three tasks require an understanding of perspective (linguistic or mental). The findings indicate that perspectival understanding is required to take into account indirect pragmatic information to suspend the disambiguation effect. Implications for lexical principles and socio-pragmatic theories of word learning are discussed

The Role of Visual Information in Numerosity Estimation

Mainstream theory suggests that the approximate number system supports our non-symbolic number abilities (e.g. estimating or comparing different sets of items). It is argued that this system can extract number independently of the visual cues present in the stimulus (diameter, aggregate surface, etc.). However, in a recent report we argue that this might not be the case. We showed that participants combined information from different visual cues to derive their answers. While numerosity comparison requires a rough comparison of two sets of items (smaller versus larger), numerosity estimation requires a more precise mechanism. It could therefore be that numerosity estimation, in contrast to numerosity comparison, might rely on the approximate number system. To test this hypothesis, we conducted a numerosity estimation experiment. We controlled for the visual cues according to current standards: each single visual property was not informative about numerosity. Nevertheless, the results reveal that participants were influenced by the visual properties of the dot arrays. They gave a larger estimate when the dot arrays consisted of dots with, on average, a smaller diameter, aggregate surface or density but a larger convex hull. The reliance on visual cues to estimate numerosity suggests that the existence of an approximate number system that can extract numerosity independently of the visual cues is unlikely. Instead, we propose that humans estimate numerosity by weighing the different visual cues present in the stimuli

Altered Ratio of D1 and D2 Dopamine Receptors in Mouse Striatum Is Associated with Behavioral Sensitization to Cocaine

BACKGROUND: Drugs of abuse elevate brain dopamine levels, and, in vivo, chronic drug use is accompanied by a selective decrease in dopamine D2 receptor (D2R) availability in the brain. Such a decrease consequently alters the ratio of D1R:D2R signaling towards the D1R. Despite a plethora of behavioral studies dedicated to the understanding of the role of dopamine in addiction, a molecular mechanism responsible for the downregulation of the D2R, in vivo, in response to chronic drug use has yet to be identified. METHODS AND FINDINGS: ETHICS STATEMENT: All animal work was approved by the Gallo Center IACUC committee and was performed in our AAALAC approved facility. In this study, we used wild type (WT) and G protein coupled receptor associated sorting protein-1 (GASP-1) knock out (KO) mice to assess molecular changes that accompany cocaine sensitization. Here, we show that downregulation of D2Rs or upregulation of D1Rs is associated with a sensitized locomotor response to an acute injection of cocaine. Furthermore, we demonstrate that disruption of GASP-1, that targets D2Rs for degradation after endocytosis, prevents cocaine-induced downregulation of D2Rs. As a consequence, mice with a GASP-1 disruption show a reduction in the sensitized locomotor response to cocaine. CONCLUSIONS: Together, our data suggests that changes in the ratio of the D1:D2R could contribute to cocaine-induced behavioral plasticity and demonstrates a role of GASP-1 in regulating both the levels of the D2R and cocaine sensitization

Impact of High Mathematics Education on the Number Sense

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS

Why do we differ in number sense? Evidence from a genetically sensitive investigation

Basic intellectual abilities of quantity and numerosity estimation have been detected across animal species. Such abilities are referred to as ‘number sense’. For human species, individual differences in number sense are detectable early in life, persist in later development, and relate to general intelligence. The origins of these individual differences are unknown. To address this question, we conducted the first large-scale genetically sensitive investigation of number sense, assessing numerosity discrimination abilities in 837 pairs of monozygotic and 1422 pairs of dizygotic 16-year-old twin pairs. Univariate genetic analysis of the twin data revealed that number sense is modestly heritable (32%), with individual differences being largely explained by non-shared environmental influences (68%) and no contribution from shared environmental factors. Sex-Limitation model fitting revealed no differences between males and females in the etiology of individual differences in number sense abilities. We also carried out Genome-wide Complex Trait Analysis (GCTA) that estimates the population variance explained by additive effects of DNA differences among unrelated individuals. For 1118 unrelated individuals in our sample with genotyping information on 1.7 million DNA markers, GCTA estimated zero heritability for number sense, unlike other cognitive abilities in the same twin study where the GCTA heritability estimates were about 25%. The low heritability of number sense, observed in this study, is consistent with the directional selection explanation whereby additive genetic variance for evolutionary important traits is reduced

Monolingual Biases in Simulations of Cultural Transmission

Recent research suggests that the evolution of language is affected by the inductive biases of its learners. I suggest that there is an implicit assumption that one of these biases is to expect a single linguistic system in the input. Given the prevalence of bilingual cultures, this may not be a valid abstraction. This is illustrated by demonstrating that the ‘minimal naming game’ model, in which a shared lexicon evolves in a population of agents, includes an implicit mutual exclusivity bias. Since recent research suggests that children raised in bilingual cultures do not exhibit mutual exclusivity, the individual learning algorithm of the agents is not as abstract as it appears to be. A modification of this model demonstrates that communicative success can be achieved without mutual exclusivity. It is concluded that complex cultural phenomena, such as bilingualism, do not necessarily result from complex individual learning mechanisms. Rather, the cultural process itself can bring about this complexity

Evidence against global attention filters selective for absolute bar-orientation in human vision

The finding that an item of type A pops out from an array of distractors of type B typically is taken to support the inference that human vision contains a neural mechanism that is activated by items of type A but not by items of type B. Such a mechanism might be expected to yield a neural image in which items of type A produce high activation and items of type B low (or zero) activation. Access to such a neural image might further be expected to enable accurate estimation of the centroid of an ensemble of items of type A intermixed with to-be-ignored items of type B. Here, it is shown that as the number of items in stimulus displays is increased, performance in estimating the centroids of horizontal (vertical) items amid vertical (horizontal) distractors degrades much more quickly and dramatically than does performance in estimating the centroids of white (black) items among black (white) distractors. Together with previous findings, these results suggest that, although human vision does possess bottom-up neural mechanisms sensitive to abrupt local changes in bar-orientation, and although human vision does possess and utilize top-down global attention filters capable of selecting multiple items of one brightness or of one color from among others, it cannot use a top-down global attention filter capable of selecting multiple bars of a given absolute orientation and filtering bars of the opposite orientation in a centroid task