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 main aim of this study was to analyze the patterns of changes in Approximate Number Sense precision from grade 1 to grade 9 in a sample of Russian schoolchildren. To fulfill this aim, the data from a longitudinal study of two cohorts of children were used. The first cohort was assessed at grades 1–5, and the second cohort was assessed at grades 5–9. ANS precision was assessed by accuracy and reaction time in a non-symbolic comparison test. The patterns of (...) change were estimated via mixed-effect growth models. The results revealed that in the first cohort, the average accuracy increased from grade 1 to grade 5 following a non-linear pattern and that the rate of growth slowed after grade 3. The non-linear pattern of changes in the second cohort indicated that accuracy started to increase from grade 7 to grade 9, while there were no changes from grade 5 to grade 7. However, the RT in the non-symbolic comparison test decreased evenly from grade 1 to grade 7, and the rate of processing non-symbolic information tended to stabilize from grade 7 to grade 9. Moreover, the changes in the rate of processing non-symbolic information were not explained by the changes in general processing speed. The results also demonstrated that accuracy and RT were positively correlated across all grades. These results indicate that accuracy and the rate of non-symbolic processing reflect two different processes, namely, the maturation and development of a non-symbolic representation system. (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 number of elements in a small set of items is appraised in a fast and exact manner, a phenomenon called subitizing. In contrast, humans provide imprecise responses when comparing larger numerosities, with decreasing precision as the number of elements increases. Estimation is thought to rely on a dedicated system for the approximate representation of numerosity. While previous behavioral and neuroimaging studies associate subitizing to a domain-general system related to object tracking and identification, the nature of small numerosity processing is (...) still debated. We investigated the neural processing of numerosity across subitizing and estimation ranges by examining electrophysiological activity during the memory retention period in a delayed numerical match-to-sample task. We also assessed potential differences in the neural signature of numerical magnitude in a fully non-symbolic or cross-format comparison. In line with behavioral performance, we observed modulation of parietal-occipital neural activity as a function of numerosity that differed in two ranges, with distinctive neural signatures of small numerosities showing clear similarities with those observed in visuospatial working memory tasks. We also found differences in neural activity related to numerical information in anticipation of single vs. cross-format comparison, suggesting a top-down modulation of numerical processing. Finally, behavioral results revealed enhanced performance in the mixed-format conditions and a significant correlation between task performance and symbolic mathematical skills. Overall, we provide evidence for distinct mechanisms related to small and large numerosity and differences in numerical encoding based on task demands. (shrink)

This paper summarizes a theory of cognitive development and elaborates on its educational implications. The theory postulates that development occurs in cycles along multiple fronts. Cognitive competence in each cycle comprises a different profile of executive, inferential, and awareness processes, reflecting changes in developmental priorities in each cycle. Changes reflect varying needs in representing, understanding, and interacting with the world. Interaction control dominates episodic representation in infancy; attention control and perceptual awareness dominate in realistic representations in preschool; inferential control and (...) awareness dominate rule-based representation in primary school; truth and validity control and precise self-evaluation dominate in principle-based thought in adolescence. We demonstrate that the best predictors of school learning in each cycle are the cycle’s cognitive priorities. Also learning in different domains, e.g., language and mathematics, depends on an interaction between the general cognitive processes dominating in each cycle and the state of the representational systems associated with each domain. When a representational system is deficient, specific learning difficulties may emerge, e.g., dyslexia and dyscalculia. We also discuss the educational implications for evaluation and learning at school. (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)

Humans and other animals have an evolved ability to detect discrete magnitudes in their environment. Does this observation support evolutionary debunking arguments against mathematical realism, as has been recently argued by Clarke-Doane, or does it bolster mathematical realism, as authors such as Joyce and Sinnott-Armstrong have assumed? To find out, we need to pay closer attention to the features of evolved numerical cognition. I provide a detailed examination of the functional properties of evolved numerical cognition, and propose that they prima (...) facie favor a realist account of numbers. (shrink)

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics education. (...) By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)