Parental socioeconomic status and the neural basis of arithmetic: differential relations to verbal and visuo‐spatial representations

We examined the relation of parental socioeconomic status (SES) to the neural bases of subtraction in school‐age children (9‐ to 12‐year‐olds). We independently localized brain regions subserving verbal versus visuo‐spatial representations to determine whether the parental SES‐related differences in children's reliance on these neural representations vary as a function of math skill. At higher SES levels, higher skill was associated with greater recruitment of the left temporal cortex, identified by the verbal localizer. At lower SES levels, higher skill was associated with greater recruitment of right parietal cortex, identified by the visuo‐spatial localizer. This suggests that depending on parental SES, children engage different neural systems to solve subtraction problems. Furthermore, SES was related to the activation in the left temporal and frontal cortex during the independent verbal localizer task, but it was not related to activation during the independent visuo‐spatial localizer task. Differences in activation during the verbal localizer task in turn were related to differences in activation during the subtraction task in right parietal cortex. The relation was stronger at lower SES levels. This result suggests that SES‐related differences in the visuo‐spatial regions during subtraction might be based in SES‐related verbal differences.     

Probing the nature of deficits in the ‘Approximate Number System’ in children with persistent Developmental Dyscalculia

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.     

Patterns of problem‐solving in children's literacy and arithmetic

Patterns of problem‐solving among 5‐to‐7 year‐olds' were examined on a range of literacy (reading and spelling) and arithmetic‐based (addition and subtraction) problem‐solving tasks using verbal self‐reports to monitor strategy choice. The results showed higher levels of variability in the children's strategy choice across Years 1 and 2 on the arithmetic (addition and subtraction) than literacy‐based tasks (reading and spelling). However, across all four tasks, the children showed a tendency to move from less sophisticated procedural‐based strategies, which included phonological strategies for reading and spelling and counting‐all and finger modelling for addition and subtraction, to more efficient retrieval methods from Years 1 to 2. Distinct patterns in children's problem‐solving skill were identified on the literacy and arithmetic tasks using two separate cluster analyses. There was a strong association between these two profiles showing that those children with more advanced problem‐solving skills on the arithmetic tasks also showed more advanced profiles on the literacy tasks. The results highlight how different‐aged children show flexibility in their use of problem‐solving strategies across literacy and arithmetical contexts and reinforce the importance of studying variations in children's problem‐solving skill across different educational contexts.     

Cognitive correlates of mathematical achievement in children with cerebral palsy and typically developing children

Background . Remarkably few studies have investigated the nature and origin of learning difficulties in children with cerebral palsy (CP). Aims . To investigate math achievement in terms of word‐problem solving ability in children with CP and controls. Because of the potential importance of reading for word‐problem solving, we investigated reading as well. Sample . Children with CP attending either special (n= 41) or mainstream schools (n= 16) and a control group of typically developing children in mainstream schools (n= 16). Method . Group differences in third grade math and reading, controlled for IQ, were tested with analyses of co‐variance (ANCOVAs). Hierarchical regression was used to investigate cognitive correlates of third grade math and reading. Predictors included verbal and non‐verbal IQ measured in first grade, components of working memory (WM) and executive function (EF) measured in second grade, and arithmetic fact fluency and reading measured in third grade. Results . Children with CP in special schools performed significantly worse than their peers on word‐problem solving and reading. There was a trend towards worse performance in children with CP in mainstream schools compared to typically developing children. Conclusions . Impairments of non‐verbal IQ and WM updating predicted future difficulties in both word‐problem solving and reading. Impairments of visuospatial sketchpad and inhibition predicted future word‐problem, but not reading difficulty. Conversely, deficits of phonological loop predicted reading but not word‐problem difficulty. Concurrent arithmetic fact fluency and reading ability were both important for word‐problem solving ability. These results could potentially help to predict which children are likely to develop specific learning difficulties, facilitating early intervention.     

Neurocognitive development of relational reasoning

Relational reasoning is an essential component of fluid intelligence, and is known to have a protracted developmental trajectory. To date, little is known about the neural changes that underlie improvements in reasoning ability over development. In this event‐related functional magnetic resonance imaging (fMRI) study, children aged 8–12 and adults aged 18–25 performed a relational reasoning task adapted from Raven's Progressive Matrices. The task included three levels of relational reasoning demands: REL‐0, REL‐1, and REL‐2. Children exhibited disproportionately lower accuracy than adults on trials that required integration of two relations (REL‐2). Like adults, children engaged lateral prefrontal cortex (PFC) and parietal cortex during task performance; however, they exhibited different time courses and activation profiles, providing insight into their approach to the problems. As in prior studies, adults exhibited increased rostrolateral PFC (RLPFC) activation when relational integration was required (REL‐2 > REL‐1, REL‐0). Children also engaged RLPFC most strongly for REL‐2 problems at early stages of processing, but this differential activation relative to REL‐1 trials was not sustained throughout the trial. These results suggest that the children recruited RLPFC while processing relations, but failed to use it to integrate across two relations. Relational integration is critical for solving a variety of problems, and for appreciating analogies; the current findings suggest that developmental improvements in this function rely on changes in the profile of engagement of RLPFC, as well as dorsolateral PFC and parietal cortex.     

Functional connectivity differences in autism during face and car recognition: underconnectivity and atypical age‐related changes

Face recognition abilities improve between adolescence and adulthood over typical development (TD), but plateau in autism, leading to increasing face recognition deficits in autism later in life. Developmental differences between autism and TD may reflect changes between neural systems involved in the development of face encoding and recognition. Here, we focused on whole‐brain connectivity with the fusiform face area (FFA), a well‐established face‐preferential brain region. Older children, adolescents, and adults with and without autism completed the Cambridge Face Memory Test, and a matched car memory test, during fMRI scanning. We then examined task‐based functional connectivity between the FFA and the rest of the brain, comparing autism and TD groups during encoding and recognition of face and car stimuli. The autism group exhibited underconnectivity, relative to the TD group, between the FFA and frontal and primary visual cortices, independent of age. Underconnectivity with the medial and rostral lateral prefrontal cortex was face‐specific during encoding and recognition, respectively. Conversely, underconnectivity with the L orbitofrontal cortex was evident for both face and car encoding. Atypical age‐related changes in connectivity emerged between the FFA and the R temporoparietal junction, and R dorsal striatum for face stimuli only. Similar differences in age‐related changes in autism emerged for FFA connectivity with the amygdala across both face and car recognition. Thus, underconnectivity and atypical development of functional connectivity may lead to a less optimal face‐processing network in the context of increasing general and social cognitive deficits in autism.     

Developmental changes in neural letter‐selectivity: A 1‐year follow‐up of beginning readers

The developmental course of neural tuning to visual letter strings is unclear. Here we tested 39 children longitudinally, at the beginning of grade 1 (6.45 ± 0.33 years old) and 1 year after, with fast periodic visual stimulation in electroencephalography to assess the evolution of selective neural responses to letter strings and their relationship with emerging reading abilities. At both grades, frequency‐tagged letter strings were discriminated from pseudofont strings (i.e. letter‐selectivity) over the left occipito‐temporal cortex, with effects observed at the individual level in 62% of children. However, visual words were not discriminated from pseudowords (lexical access) at either grade. Following 1 year of schooling, letter‐selective responses showed a specific increase in amplitude, a more complex pattern of harmonics, and were located more anteriorly over the left occipito‐temporal cortex. Remarkably, at both grades, neural responses were highly significant at the individual level and correlated with individual reading scores. The amplitude increase in letter‐selective responses between grades was not found for discrimination responses of familiar keyboard symbols from pseudosymbols, and was not related to a general increase in visual stimulation responses. These findings demonstrate a rapid onset of left hemispheric letter selectivity, with 1 year of reading instruction resulting in increased emerging reading abilities and a clear quantitative and qualitative evolution within left hemispheric neural circuits for reading.     

Individual differences in children's understanding of inversion and arithmetical skill

Background and aims. In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between their conceptual understanding and arithmetical skills. Sample. A group of 127 children from primary schools took part in the study. The children were from 2 age groups (6–7 and 8–9 years). Methods. Children's accuracy on inverse and control problems in a variety of presentation formats and in canonical and non‐canonical forms was measured. Tests of general arithmetic ability were also administered. Results. Children consistently performed better on inverse than control problems, which indicates that they could make use of the inverse principle. Presentation format affected performance: picture presentation allowed children to apply their conceptual understanding flexibly regardless of the problem type, while word problems restricted their ability to use their conceptual knowledge. Cluster analyses revealed three subgroups with different profiles of conceptual understanding and arithmetical skill. Children in the ‘high ability’ and ‘low ability’ groups showed conceptual understanding that was in‐line with their arithmetical skill, whilst a 3rd group of children had more advanced conceptual understanding than arithmetical skill. Conclusions. The three subgroups may represent different points along a single developmental path or distinct developmental paths. The discovery of the existence of the three groups has important consequences for education. It demonstrates the importance of considering the pattern of individual children's conceptual understanding and problem‐solving skills.     

Numerical and non-numerical ordinality processing in children with and without developmental dyscalculia: Evidence from fMRI

Ordinality is – beyond numerical magnitude (i.e., quantity) – an important characteristic of the number system. There is converging empirical evidence that (intra)parietal brain regions mediate number magnitude processing. Furthermore, recent findings suggest that the human intraparietal sulcus (IPS) supports magnitude and ordinality in a domain-general way. However, the latter findings are derived from adult studies and with respect to children (i.e., developing brain systems) both the neural correlates of ordinality processing and the precise role of the IPS (domain-general vs. domain-specific) in ordinality processing are thus far unknown. The present study aims at filling this gap by employing functional magnetic resonance imaging (fMRI) to investigate numerical and non-numerical ordinality knowledge in children with and without developmental dyscalculia. In children (without DD) processing of numerical and non-numerical ordinality alike is supported by (intra)parietal cortex, thus extending the notion of a domain-general (intra)parietal cortex to developing brain systems. Moreover, activation extents in response to numerical ordinality processing differ significantly between children with and without dyscalculia in inferior parietal regions (supramarginal gyrus and IPS).     

Social problem‐solving skills following childhood traumatic brain injury and its association with self‐regulation and social and behavioural functioning

This study examines social problem‐solving skills following childhood traumatic brain injury (TBI) and its association with self‐regulation, and social and behavioural functioning. Participants included 65 children with moderate to severe TBI and 65 children without TBI, all between 6 and 11 years of age. Social problem‐solving, self‐regulation, and social and behavioural functioning were assessed 2–5 years following injury. Children were administered a newly developed semi‐structured task to assess their solutions to hypothetical situations involving social problems or dilemmas. When compared with uninjured children, those with TBI suggested avoidant and aggressive solutions more often and assertive solutions less often in response to the hypothetical situations. Children's self‐regulatory skills, as measured by the Matching Familiar Figures Test (MFFT), Test of Everyday Attention for Children (TEA‐Ch) and the Delay of Gratification Task (DGT), collectively accounted for significant variance in their solutions to social problems, such that better self‐regulation predicted more assertive solutions and fewer aggressive solutions. Assertive solutions were positively related to parent‐ and teacher‐rated social and behavioural outcomes, whereas aggressive solutions were negatively related to the outcomes. The difficulties in social problem‐solving skills demonstrated by children with TBI may help account for their poor social and behavioural functioning.     

The role of relational reasoning in children's addition concepts

The study addresses the relational reasoning of different‐aged children and how addition reasoning is related to problem‐solving skills within addition and to reasoning skills outside addition. Ninety‐two 5‐ to 8‐year‐olds were asked to solve a series of conceptually related and unrelated addition problems, and the speed and accuracy of all self‐reported strategies were used to monitor their addition performance. Children were also given a series of general relational reasoning tasks to assess their ability to solve problems based on thematic, causal and visual relations. The results revealed that, while children were able to reason about commutativity relations, recognition of relations based on additive composition was rare. Furthermore, children's ability to reason about addition concepts increased with age and problem‐solving proficiency. Reasoning about addition concepts was related to performance on the thematic, causal and visual reasoning tasks for older children but not for younger children. Overall, the findings suggest that while children's early knowledge of addition relations is domain specific, as children develop in their broader reasoning abilities these developments enhance their addition reasoning.     

小学生图形推理策略发展特点的研究

本研究用我们修订的瑞文推理为材料,对145名儿童图形推理策略进行研究。结果发现：小学生在解决图形推理问题时使用六种策略,它们分别是分析策略、不完全分析策略、知觉分析策略、知觉匹配策略、格式塔策略和自主想象策略;不同年龄儿童在解决不同类型题目时的策略使用表现出不同的特点,儿童在解决数量规则题中,知觉分析策略在整个小学儿童阶段占主导地位,而在解决加减规则题中,分析策略占主导地位,随年龄增长而呈上升趋势;小学二年级开始出现图形推理能力发展的飞跃,二年级儿童开始能够同时观察到两种规则,五六年级儿童更能够不受题目形式的影响．而是从本质上把握逻辑规则。     

Amygdala sub‐regional functional connectivity predicts anxiety in children with reading disorder

Pediatric reading disorder (RD) is associated with an increased risk of anxiety symptoms, yet understudied are the neurobiological factors that might underlie anxiety in children with RD. Given the role of the amygdala in anxiety, we assessed resting state functional connectivity of amygdalar subregions in children with RD to identify functional correlates of anxiety and reading impairment. We collected resting state functional MRI data from 22 children with RD and 21 typically developing (TD) children, ages 7 to 13 years. We assessed group differences in resting state functional connectivity (RSFC) from amygdalar subregions. Associations of amygdalar RSFC and volume with reading impairment, reading fluency scores, and anxiety symptoms were explored. Relative to TD children, those with RD showed increased RSFC from amygdalar nuclei to medial prefrontal cortex. Across all subjects, RSFC from right centromedial amygdala to left medial prefrontal cortex positively predicted both reading impairment and self‐reported anxiety, and anxiety mediated the relationship between RSFC and reading impairment. These findings are consistent with amygdalar functional abnormalities in pediatric anxiety disorders, suggesting a common neurobiological mechanism underlying anxiety and reading impairment in children. Thus, aberrant patterns of RSFC from amygdalar subregions may serve as potential targets for the treatment of anxiety symptoms that typically co‐occur with RD. Our dimensional approach to studying anxiety in RD revealed how amygdalar connectivity underlies anxiety and reading impairment across a continuum from normal to abnormal.     

小学一～三年级儿童加减法策略选择的发展特点研究

随机选取90名小学一～三年级的儿童为被试,采用实验法和访谈法对儿童解决加减法算术题的策略发展特点进行了探讨。结果发现:1儿童能运用多种策略解决加减法算术题,在解决两个数的算术题时用到了13种策略,在解决三个数的算术题时用到了8种策略。2儿童在解决同一道题时大多能同时运用两种或两种以上的策略。3随着年龄的增长,儿童使用策略的总目呈简约化发展的趋势。4在解决两个数的算术题时,不同年级的儿童在使用出声策略、拆十策略、手势策略、逆算策略、数数策略的次数上差异显著,随着年级的增长其使用频率逐渐降低。5儿童在解决三个数的算术题时,各年级儿童使用出声策略、手势策略、对位策略差异显著,随着年级的增长其使用频率逐渐增高。     

Working Memory Capacity and Self‐Explanation Strategy Use Provide Additive Problem‐Solving Benefits

The present study examined the impact of working memory capacity (WMC) on college students' ability to solve probability problems while using a self‐explanation strategy. Participants learned to solve probability problems in one of three conditions: a backward‐faded self‐explanation condition, an example problem pairs self‐explanation condition, or a control (no self‐explanation) condition. Even when accounting for the impact of WMC, learning to problem‐solve using self‐explanation led to superior problem‐solving performance. Conditions that prompted self‐explanation during problem‐solving resulted in significantly better problem‐solving performance than the control condition. These findings provide insight into the influence of individual differences on problem‐solving when strategies are provided, as well as information about the effectiveness of the self‐explanation strategy during mathematical problem‐solving. Copyright © 2016 John Wiley & Sons, Ltd.     

Unfamiliar face recognition in children with autistic spectrum disorders

We investigated unfamiliar face recognition in low‐functioning children with autistic spectrum disorders (ASD) using a ‘part‐of‐face’ method. This method has not previously been used for unfamiliar faces with this population. The ‘part‐of‐face’ procedure provides measures of both face recognition accuracy and of processing style. We compared the performance of the children with ASD with three control groups: children with developmental delay (DD), typically developing (TD) children matched for verbal cognitive ability and TD children matched for chronological age (CA). Compared to the DD group, the ASD group showed similar processing in recognition accuracy and processing style. Compared to the TD children, the ASD group did not show the same level of accuracy as controls of the same CA, instead showing similar performance to younger TD children. However, as both children with ASD and DD showed the same performance, no ASD‐specific deficit was found. Copyright © 2009 John Wiley & Sons, Ltd.     

How does a child solve 7 + 8? Decoding brain activity patterns associated with counting and retrieval strategies

Cognitive development and learning are characterized by diminished reliance on effortful procedures and increased use of memory-based problem solving. Here we identify the neural correlates of this strategy shift in 7-9-year-old children at an important developmental period for arithmetic skill acquisition. Univariate and multivariate approaches were used to contrast brain responses between two groups of children who relied primarily on either retrieval or procedural counting strategies. Children who used retrieval strategies showed greater responses in the left ventrolateral prefrontal cortex; notably, this was the only brain region which showed univariate differences in signal intensity between the two groups. In contrast, multivariate analysis revealed distinct multivoxel activity patterns in bilateral hippocampus, posterior parietal cortex and left ventrolateral prefrontal cortex regions between the two groups. These results demonstrate that retrieval and counting strategies during early learning are characterized by distinct patterns of activity in a distributed network of brain regions involved in arithmetic problem solving and controlled retrieval of arithmetic facts. Our findings suggest that the reorganization and refinement of neural activity patterns in multiple brain regions plays a dominant role in the transition to memory-based arithmetic problem solving. Our findings further demonstrate how multivariate approaches can provide novel insights into fine-scale developmental changes in the brain. More generally, our study illustrates how brain imaging and developmental research can be integrated to investigate fundamental aspects of neurocognitive development.     

The link between logic,mathematics and imagination: evidence from children with developmental dyscalculia and mathematically gifted children

This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain‐specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain‐general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief‐laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief‐neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real‐life referents) develops later than the ability to reason about belief‐inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8     

Audio‐visual speech in noise perception in dyslexia

Individuals with developmental dyslexia (DD) may experience, besides reading problems, other speech‐related processing deficits. Here, we examined the influence of visual articulatory information (lip‐read speech) at various levels of background noise on auditory word recognition in children and adults with DD. We found that children with a documented history of DD have deficits in their ability to gain benefit from lip‐read information that disambiguates noise‐masked speech. We show with another group of adult individuals with DD that these deficits persist into adulthood. These deficits could not be attributed to impairments in unisensory auditory word recognition. Rather, the results indicate a specific deficit in audio‐visual speech processing and suggest that impaired multisensory integration might be an important aspect of DD.     

The contribution of working memory to children's mathematical word problem solving

The study explored the contribution of working memory to mathematical word problem solving in children. A total of 69 children in grades 2, 3 and 4 were given measures of mathematical problem solving, reading, arithmetical calculation, fluid IQ and working memory. Multiple regression analyses showed that three measures associated with the central executive and one measure associated with the phonological loop contributed unique variance to mathematical problem solving when the influence of reading, age and IQ were controlled for in the analysis. In addition, the animal dual‐task, verbal fluency and digit span task continued to contribute unique variance when the effects of arithmetical calculation in addition to reading, fluid IQ, and age were controlled for. These findings demonstrate that the phonological loop and a number of central executive functions (shifting, co‐ordination of concurrent processing and storage of information, accessing information from long‐term memory) contribute to mathematical problem solving in children. Copyright © 2006 John Wiley & Sons, Ltd.