Recently, there has been a growing emphasis on basic number processing competencies (such as the ability to judge which of two numbers is larger) and their role in predicting individual differences ...in school-relevant math achievement. Children's ability to compare both symbolic (e.g. Arabic numerals) and nonsymbolic (e.g. dot arrays) magnitudes has been found to correlate with their math achievement. The available evidence, however, has focused on computerized paradigms, which may not always be suitable for universal, quick application in the classroom. Furthermore, it is currently unclear whether both symbolic and nonsymbolic magnitude comparison are related to children's performance on tests of arithmetic competence and whether either of these factors relate to arithmetic achievement over and above other factors such as working memory and reading ability. In order to address these outstanding issues, we designed a quick (2 minute) paper-and-pencil tool to assess children's ability to compare symbolic and nonsymbolic numerical magnitudes and assessed the degree to which performance on this measure explains individual differences in achievement. Children were required to cross out the larger of two, single-digit numerical magnitudes under time constraints. Results from a group of 160 children from grades 1-3 revealed that both symbolic and nonsymbolic number comparison accuracy were related to individual differences in arithmetic achievement. However, only symbolic number comparison performance accounted for unique variance in arithmetic achievement. The theoretical and practical implications of these findings are discussed which include the use of this measure as a possible tool for identifying students at risk for future difficulties in mathematics.
In the present study we examined whether children with Developmental Dyscalculia (DD) exhibit a deficit in the so‐called ‘Approximate Number System’ (ANS). To do so, we examined a group of elementary ...school children who demonstrated persistent low math achievement over 4 years and compared them to typically developing (TD), aged‐matched controls. The integrity of the ANS was measured using the Panamath (www.panamath.org) non‐symbolic numerical discrimination test. Children with DD demonstrated imprecise ANS acuity indexed by larger Weber fraction (w) compared to TD controls. Given recent findings showing that non‐symbolic numerical discrimination is affected by visual parameters, we went further and investigated whether children performed differently on trials on which number of dots and their overall area were either congruent or incongruent with each other. This analysis revealed that differences in w were only found between DD and TD children on the incongruent trials. In addition, visuo‐spatial working memory strongly predicts individual differences in ANS acuity (w) during the incongruent trials. Thus the purported ANS deficit in DD can be explained by a difficulty in extracting number from an array of dots when area is anti‐correlated with number. These data highlight the role of visuo‐spatial working memory during the extraction process, and demonstrate that close attention needs to be paid to perceptual processes invoked by tasks thought to represent measures of the ANS.
In this study, children with persistent dyscalculia (DD) exhibited (a) larger Weber fraction and (b) greater error rates when the size of the individual dot stimuli were incongruent with the more numerous dot array during a non‐symbolic numerical discrimination task compared to typically developing children. These findings reveal that indices commonly used to assess internal numerical representations are affected by visual perceptual variables and affects children with DD to a greater extent than their typically developing peers. Multiple explanations for the present set of findings are discussed herein.
Neuroimaging has undergone enormous progress during the last two and a half decades. The combination of neuroscientific methods and educational practice has become a focus of interdisciplinary ...research in order to answer more applied questions. In this realm, conditions that hamper learning success and have deleterious effects in the population - such as learning disorders (LD) - could especially profit from neuroimaging findings. At the moment, however, there is an ongoing debate about how far neuroscientific research can go to inform the practical work in educational settings. Here, we put forward a theoretical translational framework as a method of conducting neuroimaging and bridging it to education, with a main focus on dyscalculia and dyslexia. Our work seeks to represent a theoretical but mainly empirical guide on the benefits of neuroimaging, which can help people working with different aspects of LD, who need to act collaboratively to reach the full potential of neuroimaging. We provide possible ideas regarding how neuroimaging can inform LD at different levels within our multidirectional framework, i.e., mechanisms, diagnosis/prognosis, training/intervention, and community/education. In addition, we discuss methodological, conceptual, and structural limitations that need to be addressed by future research.
In recent years, there has been an increasing focus on the role played by basic numerical magnitude processing in the typical and atypical development of mathematical skills. In this context, tasks ...measuring both the intentional and automatic processing of numerical magnitude have been employed to characterize how children’s representation and processing of numerical magnitude changes over developmental time. To date, however, there has been little effort to differentiate between different measures of ‘number sense’. The aim of the present study was to examine the relationship between automatic and intentional measures of magnitude processing as well as their relationships to individual differences in children’s mathematical achievement. A group of 119 children in 1st and 2nd grade were tested on the physical size congruity paradigm (automatic processing) as well as the number comparison paradigm to measure the ratio effect (intentional processing). The results reveal that measures of intentional and automatic processing are uncorrelated with one another, suggesting that these tasks tap into different levels of numerical magnitude processing in children. Furthermore, while children’s performance on the number comparison paradigm was found to correlate with their mathematical achievement scores, no such correlations could be obtained for any of the measures typically derived from the physical size congruity task. These findings therefore suggest that different tasks measuring ‘number sense’ tap into different levels of numerical magnitude representation that may be unrelated to one another and have differential predictive power for individual differences in mathematical achievement.
Education is indispensable for the flourishing of people from all backgrounds and stages of life. However, given the accelerating demographic, environmental, economical, socio-political, and ...technological changes—and their associated risks and opportunities—there is increasing consensus that our current educational systems are falling short and that we need to repurpose education and rethink the organization of learning to meet the challenges of the 21st century. The United Nations Educational Scientific and Cultural Organization (UNESCO) “Futures of Education” initiative was formally launched at the United Nations General Assembly in 2019 to provide such a vision of education for the future. The International Scientific and Evidence-based Education (ISEE) Assessment synthesizes knowledge streams generated by different communities and stakeholders at all levels and scales and will thereby essentially contribute to re-envisioning this future of education. The overall aim of the ISEE Assessment is to pool the expertise from a broad range of knowledge holders and stakeholders to undertake a scientifically robust and evidence-based assessment in an open and inclusive manner of our current educational systems and its necessary reforms. In this commentary, we discuss the aims and goals of the ISEE Assessment. We describe how the ISEE Assessment will address key questions on the purpose of education and what, how, where and when we learn, and evaluate the alignment of today’s education and theory of learning with the current and forthcoming needs and challenges and to inform policymaking for future education.
There is currently considerable discussion about the relative influences of evolutionary and cultural factors in the development of early numerical skills. In particular, there has been substantial ...debate and study of the relationship between approximate, nonverbal (approximate magnitude system AMS) and exact, symbolic (symbolic number system SNS) representations of number. Here we examined several hypotheses concerning whether, in the earliest stages of formal education, AMS abilities predict growth in SNS abilities, or the other way around. In addition to tasks involving symbolic (Arabic numerals) and nonsymbolic (dot arrays) number comparisons, we also tested children's ability to translate between the 2 systems (i.e., mixed-format comparison). Our data included a sample of 539 kindergarten children (M = 5.17 years, SD = .29), with AMS, SNS, and mixed-comparison skills assessed at the beginning and end of the academic year. In this way, we provide, to the best of our knowledge, the most comprehensive test to date of the direction of influence between the AMS and SNS in early formal schooling. Results were more consistent with the view that SNS abilities at the beginning of kindergarten lay the foundation for improvement in both AMS abilities and the ability to translate between the 2 systems. It is important to note that we found no evidence to support the reverse. We conclude that, once one acquires a basic grasp of exact number symbols, it is this understanding of exact number (and perhaps repeated practice therewith) that facilitates growth in the AMS. Though the precise mechanism remains to be understood, these data challenge the widely held view that the AMS scaffolds the acquisition of the SNS.
Research on how people process numerical order carries implications for our theoretical understanding of what a number means and our practical understanding of the foundation upon which more ...sophisticated mathematics is built. Current thinking posits that ordinal processing of numbers is linked to repeated practice with the integer count list, but the mechanisms underlying this link remain unclear. For instance, in standard ordinal verification paradigms, participants more rapidly and accurately verify that count-list sequences (e.g., 3-4-5) are "in-order" than non-count-list sequences (e.g., 2-4-6), although it remains unclear whether this is due to strong count-list processing or poor non-count-list processing. If the count list primarily facilitates ordinal processing of count-list sequences, then forcing participants to classify sequences like 3-4-5 as "not-in-order" should adversely affect ordinal verification performance. We found that it does, but only moderately in single-digit sequences (d = −.26), and not at all in the case of double-digit sequences (d = −.02). Alternatively, the count list may influence ordinal processing in an exclusionary manner, creating a tendency to view anything that does not match the count-list as not-in-order. If so, then allowing participants to classify ordered (but non-count-list) sequences like 2-4-6 as not-in-order should improve ordinal verification performance. It did, with strong effects for both single-digit (d = .74) and double-digit sequences (d = 1.04). Furthermore, we demonstrated that the reverse distance effect found in standard ordinal verification paradigms is driven primarily by poor non-count-list processing. Taken together, our results advance our understanding of the mechanisms by which the count list shapes ordinal processing, even in highly numerate adults.
Cover Image Bugden, Stephanie; Woldorff, Marty G.; Brannon, Elizabeth M.
Human brain mapping,
02/2019, Letnik:
40, Številka:
4
Journal Article
Recenzirano
COVER ILLUSTRATION
The cover is a hand carved linocut prints of the sagittal and coronal slices of the brain showing the intraparietal sulcus colored in green (top left) and purple in the (bottom ...right). In Bugden et al., we found that the bilateral intraparietal sulcus was similarly activated when adults performed double digit addition irrespective of the numerical format (e.g. dots or numbers) relative to color matching control tasks.
Symbolic arithmetic is a complex, uniquely human ability that is acquired through direct instruction. In contrast, the capacity to mentally add and subtract nonsymbolic quantities such as dot arrays ...emerges without instruction and can be seen in human infants and nonhuman animals. One possibility is that the mental manipulation of nonsymbolic arrays provides a critical scaffold for developing symbolic arithmetic abilities. To explore this hypothesis, we examined whether there is a shared neural basis for nonsymbolic and symbolic double‐digit addition. In parallel, we asked whether there are brain regions that are associated with nonsymbolic and symbolic addition independently. First, relative to visually matched control tasks, we found that both nonsymbolic and symbolic addition elicited greater neural signal in the bilateral intraparietal sulcus (IPS), bilateral inferior temporal gyrus, and the right superior parietal lobule. Subsequent representational similarity analyses revealed that the neural similarity between nonsymbolic and symbolic addition was stronger relative to the similarity between each addition condition and its visually matched control task, but only in the bilateral IPS. These findings suggest that the IPS is involved in arithmetic calculation independent of stimulus format.
PDF
