Characterizing persistent Developmental Dyscalculia: A cognitive neuroscience approach

Developmental dyscalculia (DD) is a specific learning disorder of calculation abilities. In the present thesis I report a series behavioural and functional neuroimaging studies to further elucidate the core numerical deficits underlying DD. I recruited a sample of children with DD who demonstrated persistent impairments in arithmetic. In Chapter 2, to validate the selection criteria, I compared the performance of children with and without persistent DD on a test of numerical magnitude processing. The data showed that only children with persistent DD presented with deficits in numerical magnitude processing, while those with inconsistent DD perform at the level of age-matched typically developing (TD) controls. In Chapter 3, I compared the performance of children with persistent DD on tasks assessing symbolic (e.g. Arabic digits) and non-symbolic (e.g. dot arrays) processing skills. Children with DD performed significantly worse on symbolic but not non-symbolic numerical magnitude processing tasks. These findings suggest that DD arises not from a format-independent magnitude processing deficit, but rather from difficulties in processing symbolic number representations. In Chapter 4, I investigated the influence of non-numerical variables (e.g. size) on non-symbolic numerical magnitude processing in children with and without DD. Children with DD were found to exhibit deficits in non-symbolic processing only when the visual perceptual cues were anticorrelated with numerical magnitude. When numerical magnitude and area were congruent no group differences in performance emerged. Therefore, rather than presenting with a core deficit in non-symbolic processing, children with DD have difficulties in disentangling numerical and non-numerical cues. In Chapter 5, I used functional neuroimaging to investigate whether children with DD exhibit atypical brain activation during numerical magnitude processing (symbolic, non-symbolic and mixed comparison). The data from this study revealed atypical cortical activity in the Intraparietal Sulcus (IPS) during symbolic and mixed format (comparing symbolic with non-symbolic) tasks. In contrast, children with DD did not exhibit differences in the IPS during non-symbolic numerical magnitude processing. These neuroimaging findings complement the behavioral data in Chapter 3 and 4 by suggesting that children with DD have a deficit in semantic representation of symbolic numerical magnitudes rather than a core deficit in representing both symbolic and non-symbolic numerical magnitudes. The findings from these studies provide converging evidence to support a core deficit in processing the semantic meaning of symbolic numerals in children with persistent DD

The role of the left intraparietal sulcus in the relationship between symbolic number processing and children\u27s arithmetic competence

The neural foundations of arithmetic learning are not well understood. While behavioral studies have revealed relationships between symbolic number processing and individual differences in children\u27s arithmetic performance, the neurocognitive mechanisms that bind symbolic number processing and arithmetic are unknown. The current fMRI study investigated the relationship between children\u27s brain activation during symbolic number comparison (Arabic digits) and individual differences in arithmetic fluency. A significant correlation was found between the numerical ratio effect on reaction times and accuracy and children\u27s arithmetic scores. Furthermore, children with a stronger neural ratio effect in the left intraparietal sulcus (IPS) during symbolic number processing exhibited higher arithmetic scores. Previous research has demonstrated that activation of the IPS during numerical magnitude processing increases over the course of development, and that the left IPS plays an important role in symbolic number processing. The present findings extend this knowledge to show that children with more mature response modulation of the IPS during symbolic number processing exhibit higher arithmetic competence. These results suggest that the left IPS is a key neural substrate for the relationship between the relative of precision of the representation of numerical magnitude and school-level arithmetic competence. © 2012 Elsevier Ltd

A Two-Minute Paper-and-Pencil Test of Symbolic and Nonsymbolic Numerical Magnitude Processing Explains Variability in Primary School Children\u27s Arithmetic Competence

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\u27s 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\u27s 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\u27s 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. © 2013 Nosworthy et al

The role of the left intraparietal sulcus in the relationship between symbolic number processing and children\u27s arithmetic competence

The neural foundations of arithmetic learning are not well understood. While behavioral studies have revealed relationships between symbolic number processing and individual differences in children\u27s arithmetic performance, the neurocognitive mechanisms that bind symbolic number processing and arithmetic are unknown. The current fMRI study investigated the relationship between children\u27s brain activation during symbolic number comparison (Arabic digits) and individual differences in arithmetic fluency. A significant correlation was found between the numerical ratio effect on reaction times and accuracy and children\u27s arithmetic scores. Furthermore, children with a stronger neural ratio effect in the left intraparietal sulcus (IPS) during symbolic number processing exhibited higher arithmetic scores. Previous research has demonstrated that activation of the IPS during numerical magnitude processing increases over the course of development, and that the left IPS plays an important role in symbolic number processing. The present findings extend this knowledge to show that children with more mature response modulation of the IPS during symbolic number processing exhibit higher arithmetic competence. These results suggest that the left IPS is a key neural substrate for the relationship between the relative of precision of the representation of numerical magnitude and school-level arithmetic competence. © 2012 Elsevier Ltd

A two-minute paper and pencil test of symbolic and nonsymbolic numerical magnitude processing explains variability in primary school children’s arithmetic competence

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

Rules of Order: Evidence for a novel influence on ordinal processing of numbers

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

A Two-Minute Paper-and-Pencil Test of Symbolic and Nonsymbolic Numerical Magnitude Processing Explains Variability in Primary School Children\u27s Arithmetic Competence

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\u27s 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\u27s 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\u27s 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. © 2013 Nosworthy et al

Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners

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\u27s 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. (PsycINFO Database Recor