Spatial Intuition in Elementary Arithmetic: A Neurocomputational Account

Elementary arithmetic (e.g., addition, subtraction) in humans has been shown to exhibit spatial properties. Its exact nature has remained elusive, however. To address this issue, we combine two earlier models for parietal cortex: A model we recently proposed on number-space interactions and a modeling framework of parietal cortex that implements radial basis functions for performing spatial transformations. Together, they provide us with a framework in which elementary arithmetic is based on evolutionarily more basic spatial transformations, thus providing the first implemented instance of Dehaene and Cohen's recycling hypothesis

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

Understanding the Interplay Among Regulatory Self-Efficacy, Moral Disengagement, and Academic Cheating Behaviour During Vocational Education: A Three-Wave Study

The literature has suggested that to understand the diffusion of unethical conduct in the workplace, it is important to investigate the underlying processes sustaining engagement in misbehaviour and to study what occurs during vocational education. Drawing on social-cognitive theory, in this study, we longitudinally examined the role of two opposite dimensions of the self-regulatory moral system, regulatory self-efficacy and moral disengagement, in influencing academic cheating behaviour. In addition, in line with the theories highlighting the bidirectional relationship between cognitive processes and behaviour, we aimed to also examine the reciprocal influence of behaviour on these dimensions over time. Overall, no previous studies have examined the longitudinal interplay between these variables. The sample included 866 (62.8% female) nursing students who were assessed three times annually from the beginning of their vocational education. The findings from a cross-lagged model confirmed that regulatory self-efficacy and moral disengagement have opposite influences on cheating behaviour, that regulatory self-efficacy negatively influences not only the engagement in misconduct but also the justification mechanisms that allow the divorce between moral standards and action, and that moral disengagement and cheating behaviour reciprocally support each other over time. Specifically, not only did moral disengagement influence cheating behaviour even when controlling for its prior levels, but also cheating behaviour affected moral disengagement one year later, controlling for its prior levels. These findings suggest that recourse to wrongdoing could gradually lead to further normalising this kind of behaviour and morally desensitising individuals to misconduct

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

Learning to represent exact numbers

This article focuses on how young children acquire concepts for exact, cardinal numbers (e.g., three, seven, two hundred, etc.). I believe that exact numbers are a conceptual structure that was invented by people, and that most children acquire gradually, over a period of months or years during early childhood. This article reviews studies that explore children’s number knowledge at various points during this acquisition process. Most of these studies were done in my own lab, and assume the theoretical framework proposed by Carey (2009). In this framework, the counting list (‘one,’ ‘two,’ ‘three,’ etc.) and the counting routine (i.e., reciting the list and pointing to objects, one at a time) form a placeholder structure. Over time, the placeholder structure is gradually filled in with meaning to become a conceptual structure that allows the child to represent exact numbers (e.g., There are 24 children in my class, so I need to bring 24 cupcakes for the party.) A number system is a socially shared, structured set of symbols that pose a learning challenge for children. But once children have acquired a number system, it allows them to represent information (i.e., large, exact cardinal values) that they had no way of representing before