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

Ontogeny of Numerical Abilities in Fish

Background: It has been hypothesised that human adults, infants, and non-human primates share two non-verbal systems for enumerating objects, one for representing precisely small quantities (up to 3–4 items) and one for representing approximately larger quantities. Recent studies exploiting fish’s spontaneous tendency to join the larger group showed that their ability in numerical discrimination closely resembles that of primates but little is known as to whether these capacities are innate or acquired. Methodology/Principal Findings: We used the spontaneous tendency to join the larger shoal to study the limits of the quantity discrimination of newborn and juvenile guppies. One-day old fish chose the larger shoal when the choice was between numbers in the small quantity range, 2 vs. 3 fish, but not when they had to choose between large numbers, 4 vs. 8 or 4 vs. 12, although the numerical ratio was larger in the latter case. To investigate the relative role of maturation and experience in large number discrimination, fish were raised in pairs (with no numerical experience) or in large social groups and tested at three ages. Forty-day old guppies from both treatments were able to discriminate 4 vs. 8 fish while at 20 days this was only observed in fish grown in groups. Control experiments showed that these capacities were maintained after guppies were prevented from using non numerical perceptual variables that co-vary with numerosity. Conclusions/Significance: Overall, our results suggest the ability of guppies to discriminate small numbers is innate and i

Children Base Their Investment on Calculated Pay-Off

To investigate the rise of economic abilities during development we studied children aged between 3 and 10 in an exchange situation requiring them to calculate their investment based on different offers. One experimenter gave back a reward twice the amount given by the children, and a second always gave back the same quantity regardless of the amount received. To maximize pay-offs children had to invest a maximal amount with the first, and a minimal amount with the second. About one third of the 5-year-olds and most 7- and 10-year-olds were able to adjust their investment according to the partner, while all 3-year-olds failed. Such performances should be related to the rise of cognitive and social skills after 4 years

Symbolic arithmetic knowledge without instruction

This article was published in the journal, Nature [© The Nature Publishing Group]. The definitive version is available at: http://dx.doi.org/10.1038/nature05850Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill. When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations and their performance suffers if this nonsymbolic system is impaired. Nonsymbolic number representations also allow adults, children, and even infants to add or subtract pairs of dot arrays and to compare the resulting sum or difference to a third array, provided that only approximate accuracy is required. Here we report that young children, who have mastered verbal counting and are on the threshold of arithmetic instruction, can build on their nonsymbolic number system to perform symbolic addition and subtraction. Children across a broad socio-economic spectrum solved symbolic problems involving approximate addition or subtraction of large numbers, both in a laboratory test and in a school setting. Aspects of symbolic arithmetic therefore lie within the reach of children who have learned no algorithms for manipulating numerical symbols. Our findings help to delimit the sources of children’s difficulties learning symbolic arithmetic, and they suggest ways to enhance children’s engagement with formal mathematics

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

The legal framework for financial advertising:curbing behavioural exploitation

Policy makers and behavioural finance scholars express growing concern that marketing practices by financial institutions exploit retail investors’ behavioural biases. Investor protection regulation should thus address these marketing practices and include mechanisms curbing behavioural exploitation. That raises the question whether the marketing communications regime of the new Markets in Financial Instruments Directive can live up to this demand. This article develops a regulatory model that integrates behavioural finance insights into the new marketing communications regime. It then determines how regulatory authorities can apply this model when they interpret and apply specific regulatory requirements. It demonstrates how a regulatory authority or a court can translate empirical behavioural finance research findings into legal arguments when assessing whether marketing practices can significantly distort a model investor’s decision-making process. The article further establishes that the detailed requirements imposed on investment firms by the new Markets in Financial Instruments Directive are necessary in order to protect investors from behavioural exploitation. Finally, the article submits policy proposals that aim to protect investors more effectively from behavioural exploitation

The NEWMEDS rodent touchscreen test battery for cognition relevant to schizophrenia.

RATIONALE: The NEWMEDS initiative (Novel Methods leading to New Medications in Depression and Schizophrenia, http://www.newmeds-europe.com ) is a large industrial-academic collaborative project aimed at developing new methods for drug discovery for schizophrenia. As part of this project, Work package 2 (WP02) has developed and validated a comprehensive battery of novel touchscreen tasks for rats and mice for assessing cognitive domains relevant to schizophrenia. OBJECTIVES: This article provides a review of the touchscreen battery of tasks for rats and mice for assessing cognitive domains relevant to schizophrenia and highlights validation data presented in several primary articles in this issue and elsewhere. METHODS: The battery consists of the five-choice serial reaction time task and a novel rodent continuous performance task for measuring attention, a three-stimulus visual reversal and the serial visual reversal task for measuring cognitive flexibility, novel non-matching to sample-based tasks for measuring spatial working memory and paired-associates learning for measuring long-term memory. RESULTS: The rodent (i.e. both rats and mice) touchscreen operant chamber and battery has high translational value across species due to its emphasis on construct as well as face validity. In addition, it offers cognitive profiling of models of diseases with cognitive symptoms (not limited to schizophrenia) through a battery approach, whereby multiple cognitive constructs can be measured using the same apparatus, enabling comparisons of performance across tasks. CONCLUSION: This battery of tests constitutes an extensive tool package for both model characterisation and pre-clinical drug discovery.This work was supported by the Innovative Medicine Initiative Joint Undertaking under grant agreement no. 115008 of which resources are composed of EFPIA in-kind contribution and financial contribution from the European Union’s Seventh Framework Programme (FP7/2007-2013). The authors thank Charlotte Oomen for valuable comments on the manuscript.This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s00213-015-4007-

The disability oriented rehabilitation unit--a major factor influencing stroke outcome.

Many investigators have analyzed the effectiveness of the cardiac care unit (as a model of a disability oriented, specially staffed, geographically isolated unit) in altering outcome following acute myocardial infarction. Little data are available, however, on the efficacy of caring for patients with stroke on specially staffed disability oriented units. Of 667 patients with stroke recently discharged from the Burke Rehabilitation Center, 589 were admitted to the stroke unit (SU group) and 78 were admitted to other units (NSU group). Statistical analysis showed that the SU patients were significantly weaker, had longer onset-admission intervals, and exhibited more concurrent medical problems and neurologic deficits. There were no statistically significant intergroup differences in age, sex, and distribution of weakness. Both groups had similar treatment programs provided by staff who had rotated through the stroke unit. Ability to perform activities of daily living (dressing, feeding, hygiene, bowel and bladder routines) and length of hospitalization were similar for both groups. SU patients walked better and went home more frequently than NSU patients. These data indicate than even in a rehabilitation center specializing in treating functional disabilities, patients with stroke are more likely to improve if placed on a disability oriented unit than if they are admitted to mixed disability units which are scattered throughout the hospital