One of the important challenges in the philosophy of mathematics is to account for the semantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can (...) be addressed by accepting a Chomskyan conception of natural languages and a matching internalist, mentalist and nativist view of semantics. A helpful perspective on the epistemic aspect of the puzzle can be gained by translating Kurt G ̈odel’s neo-Kantian conception of the nature of mathematics and its objects into modern, cognitive terms. (shrink)

Mathematical cognition is one of the most important cognitive functions of human beings. The latest brain and cognitive research have shown that mathematical cognition is a system with multiple components and subsystems. It has phylogenetic root, also is related to ontogenetic development and learning, relying on a large-scale cerebral network including parietal, frontal and temporal regions. Especially, the parietal cortex plays an important role during mathematical cognitive processes. This indicates that language and visuospatial functions are both key to mathematical cognition. (...) All of those advances have important implications for basic mathematical education. (shrink)

Math and reading are related, and math problems are often accompanied by problems in reading. In the present study, we used a dimensional approach and we aimed to assess the relationship of reading and math with the cognitive skills assumed to underlie the development of math. The sample included 97 children from 4th and 5th grades of a primary school. Children were administered measures of reading and math, non-verbal IQ, and various underlying cognitive abilities of math. We also included measures (...) of phonological awareness and working memory. Two approaches were undertaken to elucidate the relations of the cognitive skills with math and reading. In the first approach, we examined the unique contributions of math and reading ability, as well as their interaction, to each cognitive ability. In the second approach, the cognitive abilities were taken to predict math and reading. Results from the first set of analyses showed specific effects of math on number sense and number system knowledge, whereas counting was affected by both math and reading. No math-by-reading interactions were observed. In contrast, for phonological awareness, an interaction of math and reading was found. Lower performing children on both math and reading performed disproportionately lower. Results with respect to the second approach confirmed the specific relation of counting, number sense, and number system knowledge to math and the relation of counting to reading but added that each math-related marker contributed independently to math. Following this approach, no unique effects of phonological awareness on math and reading were found. In all, the results show that math is specifically related to counting, number sense, and number system knowledge. The results also highlight what each approach can contribute to an understanding of the relations of the various cognitive correlates with reading and math. (shrink)

Leibovich et al. challenge the prevailing view that non-symbolic number sense is innate, that detection of numerosity is distinct from detection of continuous magnitude. In the present commentary, the authors' viewpoint is discussed in light of the integrative theory of numerical development along with implications for understanding mathematics disabilities.

The pivotal problem of comorbidity research lies in the psychometric foundation it rests on, that is, latent variable theory, in which a mental disorder is viewed as a latent variable that causes a constellation of symptoms. From this perspective, comorbidity is a (bi)directional relationship between multiple latent variables. We argue that such a latent variable perspective encounters serious problems in the study of comorbidity, and offer a radically different conceptualization in terms of a network approach, where comorbidity is hypothesized to (...) arise from direct relations between symptoms of multiple disorders. We propose a method to visualize comorbidity networks and, based on an empirical network for major depression and generalized anxiety, we argue that this approach generates realistic hypotheses about pathways to comorbidity, overlapping symptoms, and diagnostic boundaries, that are not naturally accommodated by latent variable models: Some pathways to comorbidity through the symptom space are more likely than others; those pathways generally have the same direction (i.e., from symptoms of one disorder to symptoms of the other); overlapping symptoms play an important role in comorbidity; and boundaries between diagnostic categories are necessarily fuzzy. (shrink)

Math difficulties manifest across various domain-specific and domain-general abilities. However, the existing cognitive profile of MD is incomplete and thus not applicable in typical settings such as schools or clinics. So far, no review has applied inclusion criteria according to DSM or ICD, summarized domain-specific abilities or examined the validity of response time scores for MD identification. Based upon stringent clinical criteria, the current meta-analysis included 34 studies which compared cognitive performances of a group with MD and a group without (...) MD. Criteria according to DSM and ICD were applied to identify MD. Effect sizes for 22 abilities were estimated and separated by their level and type of scoring. A cognitive profile of MD was identified, characterized by distinct weaknesses in: computation, number sense, and visual-spatial short-term storage [AC]. No particular strength was found. Severity of MD, group differences in reading performance and IQ did not significantly moderate the results. Further analyses revealed that effects are larger when dealing with numbers or number words than with quantities, MD is not accompanied by any weakness in abilities typically assigned to reading, and weaknesses in visual-spatial short-term storage emphasize the notion that number and space are interlinked. The need for high-quality studies investigating domain-general abilities is discussed. (shrink)

The majority of commentators agree on one thing: Our network approach might be the prime candidate for offering a new perspective on the origins of mental disorders. In our response, we elaborate on refinements (e.g., cognitive and genetic levels) and extensions (e.g., to Axis II disorders) of the network model, as well as discuss ways to test its validity.

In a previous study we examined reading, spelling, and maths skills in an unselected group of 129 Italian children attending fifth grade by testing various cognitive predictors; results showed a high degree of predictors’ selectivity for each of these three behaviors. In the present study, we focused on the specificity of the predictors by performing cross-analyses on the same dataset; i.e., we predicted spelling and maths skills based on reading predictors, reading based on maths predictors and so on. Results indicated (...) that some predictors, such as the Orthographic Decision and the Arithmetic Facts tests, predicted reading, spelling and maths skills in similar ways, while others predicted different behaviors but only for a specific parameter, such as fluency but not accuracy, and still others were specific for a single behavior. To interpret these results, we propose a novel model of learning skills separately considering factors in terms of competence, performance and acquisition. Reading, spelling and calculation skills would depend on the development of discrete and different abstract competences. By contrast, overlap among behaviors would be accounted for by defective acquisition in automatized responses to individual “instances”; this latter skill is item specific but domain independent. Finally, performance factors implied in task’s characteristics may contribute to the partial association among learning skills. It is proposed that this new model may provide a useful base for interpreting the diffuse presence of comorbidities among learning disorders. (shrink)

Developmental dyscalculia (DD) is a pervasive difficulty affecting number processing and arithmetic. It is encountered in around 6% of school-aged children. While previous studies have mainly focused on general cognitive functions, the present paper aims to further investigate the hypothesis of a specific numerical deficit in dyscalculia. The performance of 10- and 11-year-old children with DD characterised by a weakness in arithmetic facts retrieval and age-matched control children was compared on various number comparison tasks. Participants were asked to compare a (...) quantity presented in either a symbolic (Arabic numerals, number words, canonical dots patterns) or a nonsymbolic format (noncanonical dots patterns, and random sticks patterns) to the reference quantity 5. DD children showed a greater numerical distance effect than control children, irrespective of the number format. This favours a deficit in the specialised cognitive system underlying the processing of number magnitude in children with DD. Results are discussed in terms of access and representation deficit hypotheses. (shrink)

Early mathematical abilities matter for later formal arithmetical performances, school and professional success. Accordingly, it seems central to accurately assess numerical school readiness at school entrance. This is a prerequisite for identifying school-starters who are at risk to encounter difficulties in mathematics and stimulate their acquisition of mathematical fundamentals as soon as possible. In the present study, we present a new test which allows professionals working with children (e.g., teachers, school psychologists, speech therapists, school doctors) to assess children’s numerical school (...) readiness when they enter formal schooling in a simple, rapid and efficient manner. 346 children were assessed at the entrance of 1st grade (6-to-7-year-olds) with the novel numerical school readiness test (T1). In addition, children’s numerical skill levels were evaluated with classical arithmetical tests at T1 and a year later in 2nd grade (T2, 7-to-8-year-olds). Performance in these classical tests in 1st and 2nd grade systematically related to their early mathematical abilities assessed with the numerical school readiness test. By using the present test to evaluate numerical school readiness it is possible to identify pupils at risk for developing poor mathematical skills right from the start of formal schooling. Such a tool is needed, as a child’s scholastic level in mathematic at school entrance (or school readiness) is known to be critical for his or her future school and professional carrier (Currie & Thomas, 1999; Duncan et al., 2007; Pagani, Fitzpatrick, Archambault, & Janosz, 2010; Rivera-Batiz, 1992; Romano, Babchishin, Pagani, & Kohen, 2010). (shrink)

The present study examines the comorbidity between specific learning disorders and attention deficit and hyperactivity disorder by comparing the neuropsychological profiles of children with and without this comorbidity. Ninety-seven schoolchildren from 8 to 14 years old were tested: a clinical sample of 49 children with ADHD, SLD or SLD in comorbidity with ADHD, and 48 typically-developing children matched for age and intelligence. Participants were administered tasks and questionnaires to confirm their initial diagnosis, and a battery of executive function tasks testing (...) inhibition, shifting, and verbal and visuospatial updating. Using one-way ANOVAs, our results showed that all children in the clinical samples exhibited impairments on EF measures when compared with TD children. A more specific pattern only emerged for the updating tasks. Only children with SLD had significant impairment in verbal updating, whereas children with ADHD, and those with SLD in comorbidity with ADHD, had the worst performance in visuospatial updating. The clinical and educational implications of these findings are discussed. (shrink)

Abstract In the present article, we provide a critical overview of the emerging field of ‘neuroeducation’ also frequently referred to as ‘mind, brain and education’ or ‘educational neuroscience’. We describe the growing energy behind linking education and neuroscience in an effort to improve learning and instruction. We explore reasons behind such drives for interdisciplinary research. Reviewing some of the key advances in neuroscientific studies that have come to bear on neuroeducation, we discuss recent evidence on the brain circuits underlying reading, (...) mathematical abilities as well as the potential to use neuroscience to design training programs of neurocognitive functions, such as working memory, that are expected to have effects on overall brain function. Throughout this review we describe how such research can enrich our understanding of the acquisition of academic skills. Furthermore, we discuss the potential for modern brain imaging methods to serve as diagnostic tools as well as measures of the effects of educational interventions. Throughout this discussion, we draw attention to limitations of the available evidence and propose future avenues for research. We also discuss the challenges that face this growing discipline. Specifically, we draw attention to unrealistic expectations for the immediate impact of neuroscience on education, methodological difficulties, and lack of interdisciplinary training, which results in poor communication between educators and neuroscientists. We point out that there should be bi-directional and reciprocal interactions between both disciplines of neuroscience and education, in which research originating from each of these traditions is considered to be compelling in its own right. While there are many obstacles that lie in the way of a productive field of neuroeducation, we contend that there is much reason to be optimistic and that the groundwork has been laid to advance this field in earnest. Content Type Journal Article Category Original Paper Pages 1-13 DOI 10.1007/s12152-011-9119-3 Authors Daniel Ansari, Numerical Cognition Laboratory, Department of Psychology, The University of Western Ontario, Westminster Hall, London, ON N6A 3K7, Canada Bert De Smedt, Parenting and Special Education Research Group, Katholieke Universiteit Leuven, Leuven, Belgium Roland H. Grabner, Institute for Behavioral Sciences, Swiss Federal Institute of Technology (ETH) Zurich, Zurich, Switzerland Journal Neuroethics Online ISSN 1874-5504 Print ISSN 1874-5490. (shrink)