Number Processing and Heterogeneity of Developmental Dyscalculia: Subtypes With Different Cognitive Profiles and Deficits

This study investigated if developmental dyscalculia (DD) in children with different profiles of mathematical deficits has the same or different cognitive origins. The defective approximate number system hypothesis and the access deficit hypothesis were tested using two different groups of children with DD (11-13 years old): a group with arithmetic fact dyscalculia (AFD) and a group with general dyscalculia (GD). Several different aspects of number magnitude processing were assessed in these two groups and compared with age-matched typically achieving children. The GD group displayed weaknesses with both symbolic and nonsymbolic number processing, whereas the AFD group displayed problems only with symbolic number processing. These findings provide evidence that the origins of DD in children with different profiles of mathematical problems diverge. Children with GD have impairment in the innate approximate number system, whereas children with AFD suffer from an access deficit. These findings have implications for researchers selection procedures when studying dyscalculia, and also for practitioners in the educational setting.Funding Agencies|Swedish Research Council [421-2007-1881]</p

Development of Cognitive Functions and Academic Skills in 9-to 10-year-old Children with Borderline Intellectual Functioning

This longitudinal study examined whether the cognitive and academic development of children (M-age = 10.52 years) with Borderline Intellectual Functioning (BIF), is characterized by developmental delay or atypical development. Cognitive tasks, arithmetic tasks, and reading tasks were administrated during three succeeding years to the BIF group and a Chronological Age-Matched Comparison (CAMC) group. The BIF children displayed weaknesses in relation to all tasks, and slower developmental rates on four arithmetic tasks and word reading. The results provide evidence in support of the developmental delay model as the BIF children overall displayed similar developmental growth and trends as the CAMC group.Funding Agencies|Swedish Council for Working Life and Social ResearchSwedish Research CouncilSwedish Research Council for Health Working Life &amp; Welfare (Forte) [2010-0078]</p

Neurodevelopmental differences in child and adult number processing : An fMRI-based validation of the triple code model

The triple code model of numerical cognition (TCM) details the neurocognitive mechanisms associated with perceiving and manipulating numerical information in exact symbolic (Arabic digits and number words) and approximate nonsymbolic numerical magnitude (e.g., dot arrays) representation codes. The current study provides a first empirical fMRI-based investigation into neurodevelopmental differences in 30 healthy children?s and 44 healthy adults? recruitment of neural correlates associated with the Arabic digit, number word, and nonsymbolic magnitude codes. Differences between the two groups were found in cingulate regions commonly associated with domain-general aspects of cognitive control, as opposed to neural correlates of number processing per se. A primary developmental difference was identified in verbal number discrimination, where only adults recruited left-lateralized perisylvian language areas in accordance with the TCM. We therefore call for a revision of the verbal code and a formulation of separate child and adult-specific neurocognitive mechanisms associated with the discrimination of number words. Although further research is necessary, results indicate that numerical discrimination abilities in middle-school-aged children operate close to adult-level maturity. Neurodevelopmental differences may be more apparent in younger children, or on the level of functional network dynamics as opposed to a shift in recruited neural substrates.Funding Agencies|Linkoping University [LiU-2009-01356]; Swedish Brain Foundation [PS-2019-0041]; Department of Behavioral Sciences and Learning, Linkoping University</p

Neurodevelopmental differences in task-evoked number network connectivity : Comparing symbolic and nonsymbolic number discrimination in children and adults

Numerical cognition can take place in multiple representational formats, such as Arabic digits (e.g., 1), verbal number words (e.g., “two”), and nonsymbolic (e.g., •••) numerical magnitude. Basic numerical discrimination abilities are key factors underlying the development of arithmetic abilities, acting as an important developmental precursor of adult-level numeracy. While prior research has begun to detail the neural correlates associated with basic numerical discrimination skills in different representational formats, the interactions between functional neural circuits are less understood. A growing body of evidence suggests that the functional networks recruited by number discrimination tasks differ between children and adults, which may provide valuable insights into the development of numerical cognition. To this end, we posed two questions: how do the interactions between functional circuits associated with number processing differ in children and adults? Are differences in functional network connectivity modulated by numerical representational codes? A theoretically motivated 22 ROI analysis indicated significant functional connectivity differences between children and adults across all three codes. Adults demonstrated sparser and more consistent connectivity patterns across codes, indicative of developmental domain-specialization for number processing. Although neural activity in children and adults is similar, the functional connectivity supporting number processing appears subject to substantial developmental maturation effects

Contrasting two models of academic self-efficacy – domain-specific versus cross-domain– in children receiving and not receiving special instruction in Mathematics

In social cognitive theory, self‐efficacy is domain‐specific. An alternative model, the cross‐domain influence model, would predict that self‐efficacy beliefs in one domain might influence performance in other domains. Research has also found that children who receive special instruction are not good at estimating their performance. The aim was to test two models of how self‐efficacy beliefs influence achievement, and to contrast children receiving special instruction in mathematics with normally‐achieving children. The participants were 73 fifth‐grade children who receive special instruction and 70 children who do not receive any special instruction. In year four and five, the children's skills in mathematics and reading were assessed by national curriculum tests, and in their fifth year, self‐efficacy in mathematics and reading were measured. Structural equation modeling showed that in domains where children do not receive special instruction in mathematics, self‐efficacy is a mediating variable between earlier and later achievement in the same domain. Achievement in mathematics was not mediated by self‐efficacy in mathematics for children who receive special instruction. For normal achieving children, earlier achievement in the language domain had an influence on later self‐efficacy in the mathematics domain, and self‐efficacy beliefs in different domains were correlated. Self‐efficacy is mostly domain specific, but may play a different role in academic performance depending on whether children receive special instruction. The results of the present study provided some support of the Cross‐Domain Influence Model for normal achieving children

Magnitude processing in the brain : an fMRI study of time, space, and numerosity as a shared cortical system

Continuous dimensions, such as time, space, and numerosity, have been suggested to be subserved by common neurocognitive mechanisms. Neuroimaging studies that have investigated either one or two dimensions simultaneously have consistently identified neural correlates in the parietal cortex of the brain. However, the degree of neural overlap across several dimensions has yet to be established, and it remains an open question whether a potential overlap can be conceptualized as a neurocognitive magnitude processing system. The current functional resonance imaging (fMRI) study investigated the potential neurocognitive overlap across three dimensions. A sample of adults (N = 24) performed three different magnitude processing tasks: a temporal discrimination task, a number discrimination task, and a line length discrimination task. A conjunction analysis revealed several overlapping neural substrates across multiple magnitude dimensions, and we argue that these cortical nodes comprise a distributed magnitude processing system. Key components of this predominantly right-lateralized system include the intraparietal sulcus, insula, premotor cortex, inferior frontal gyrus and frontal eye-fields. Together with previous research highlighting IPS, our results suggest that the insula also is a core component of the magnitude processing system. We discuss the functional role of each of these components in the magnitude processing system and suggest that further research of this system may provide insight into the etiology of neurodevelopmental disorders where cognitive deficits in magnitude processing are manifest.Funding Agencies|Swedish Council for Working Life and Social Research [2010-0078]</p

Development of early domain-specific and domain-general cognitive precursors of high and low math achievers in grade 6

This study investigated from a longitudinal retrospective perspective what characterizes and predicts 6th graders (M-age = 12.95, SD = 0.27) with low (LMA) or high (HMA) math achievement concerning the development of early domain-specific and domain-general cognitive abilities. They were examined and compared to average achievers (n = 88) at four-time points from kindergarten (M-age = 6.58, SD = 0.36) to third grade (M-age = 9.53, SD = 0.33). The LMA (n = 27) or HMA (n = 41) children exhibited persistent multi-weakness and multi-strength profiles, respectively, present already prior to formal schooling. The cognitive profiles of the two groups, and their development, were mostly qualitatively similar, but there were also important qualitative differences. Logistic regression analyzes showed that superior verbal arithmetic, logical reasoning, and executive functions are vital for developing superior mathematical skills while inferior verbal arithmetic, logical reasoning, and spatial processing ability constitute unique potential risk factors for low mathematical skills.Funding Agencies|Swedish Council for Working Life and Social ResearchSwedish Research CouncilSwedish Research Council for Health Working Life &amp; Welfare (Forte) [2008-0238]</p

Current Parole Admission and Release Trends at the Massachusetts Department of Correction: Overview of Parole Admissions and Releases from July 2011 to June 2012

The Triple Code Model (TCM) of numerical cognition argues for the existence of three representational codes for number: Arabic digits, verbal number words, and analog nonsymbolic magnitude representations, each subserved by functionally dissociated neural substrates. Despite the popularity of the TCM, no study to date has explored all three numerical codes within one fMRI paradigm. We administered three tasks, associated with each of the aforementioned numerical codes, in order to explore the neural correlates of numerosity processing in a sample of adults (N=46). Independent task-control contrast analyses revealed task-dependent activity in partial support of the model, but also highlight the inherent complexity of a distributed and overlapping fronto-parietal network involved in all numerical codes. The results indicate that the TCM correctly predicts the existence of some functionally dissociated neural substrates, but requires an update that accounts for interactions with attentional processes. Parametric contrasts corresponding to differences in task difficulty revealed specific neural correlates of the distance effect, where closely spaced numbers become more difficult to discriminate than numbers spaced further apart. A conjunction analysis illustrated overlapping neural correlates across all tasks, in line with recent proposals for a fronto-parietal network of number processing. We additionally provide tentative results suggesting the involvement of format-independent numerosity-sensitive retinotopic maps in the early visual stream, extending previous findings of nonsymbolic stimulus selectivity. We discuss the functional roles of the components associated with the model, as well as the purported fronto-parietal network, and offer arguments in favor of revising the TCM.Funding Agencies|Linkoping University [LiU-2009-01356]; Marianne and Marcus Wallenberg Foundation [2014-0173]</p