Mathematics performance in left and right brain-lesioned children and adolescents

How does hemispheric specialization contribute to human-defining cognition?

Uniquely human cognitive faculties arise from flexible interplay between specific local neural modules, with hemispheric asymmetries in functional specialization. Here, we discuss how these computational design principles provide a scaffold that enables some of the most advanced cognitive operations, such as semantic understanding of world structure, logical reasoning, and communication via language. We draw parallels to dual-processing theories of cognition by placing a focus on Kahneman's System 1 and System 2. We propose integration of these ideas with the global workspace theory to explain dynamic relay of information products between both systems. Deepening the current understanding of how neurocognitive asymmetry makes humans special can ignite the next wave of neuroscience-inspired artificial intelligence.

New insights from children with early focal brain injury: Lessons to be learned from examining STEM-related skills

The study of cognitive development in children with early brain injury reveals crucial information about the developing brain and its plasticity. However, information on long-term outcomes of these children, especially in domains relevant to science, technology, engineering, and math (STEM) remains limited. In the current review, our goal is to address the existing research on cognitive development of children with pre- or perinatal focal brain lesion (PL) as it relates to children's STEM-related skills and suggest future work that could shed further light on the developmental trajectories of children with PL. We argue that examining STEM-related development in children with PL will have broader implications for our understanding of the nature of the plasticity children with PL exhibit as well as address theoretical questions in the field regarding the foundation skills for STEM, including visuospatial and mathematical skills.

Data-driven heterogeneity in mathematical learning disabilities based on the triple code model

Many classifications of heterogeneity in mathematical learning disabilities (MLD) have been proposed over the past four decades, however no empirical research has been conducted until recently, and none of the classifications are derived from Triple Code Model (TCM) postulates. The TCM proposes MLD as a heterogeneous disorder, with two distinguishable profiles: a representational subtype and a verbal subtype. A sample of elementary school 3rd to 6th graders was divided into two age cohorts (3rd - 4th grades, and 5th - 6th grades). Using data-driven strategies, based on the cognitive classification variables predicted by the TCM, our sample of children with MLD clustered as expected: a group with representational deficits and a group with number-fact retrieval deficits. In the younger group, a spatial subtype also emerged, while in both cohorts a non-specific cluster was produced whose profile could not be explained by this theoretical approach.

The language of arithmetic across the hemispheres: An event-related potential investigation

Arithmetic expressions, like verbal sentences, incrementally lead readers to anticipate potential appropriate completions. Existing work in the language domain has helped us understand how the two hemispheres differently participate in and contribute to the cognitive process of sentence reading, but comparatively little work has been done with mathematical equation processing. In this study, we address this gap by examining the ERP response to provided answers to simple multiplication problems, which varied both in levels of correctness (given an equation context) and in visual field of presentation (joint attention in central presentation, or biased processing to the left or right hemisphere through contralateral visual field presentation). When answers were presented to any of the visual fields (hemispheres), there was an effect of correctness prior to the traditional N400 timewindow, which we interpret as a P300 in response to a detected target item (the correct answer). In addition to this response, equation answers also elicited a late positive complex (LPC) for incorrect answers. Notably, this LPC effect was most prominent in the left visual field (right hemisphere), and it was also sensitive to the confusability of the wrong answer - incorrect answers that were closely related to the correct answer elicited a smaller LPC. This suggests a special, prolonged role for the right hemisphere during answer evaluation.

Dyscalculia and the Calculating Brain

Dyscalculia, like dyslexia, affects some 5% of school-age children but has received much less investigative attention. In two thirds of affected children, dyscalculia is associated with another developmental disorder like dyslexia, attention-deficit disorder, anxiety disorder, visual and spatial disorder, or cultural deprivation. Infants, primates, some birds, and other animals are born with the innate ability, called subitizing, to tell at a glance whether small sets of scattered dots or other items differ by one or more item. This nonverbal approximate number system extends mostly to single digit sets as visual discrimination drops logarithmically to "many" with increasing numerosity (size effect) and crowding (distance effect). Preschoolers need several years and specific teaching to learn verbal names and visual symbols for numbers and school agers to understand their cardinality and ordinality and the invariance of their sequence (arithmetic number line) that enables calculation. This arithmetic linear line differs drastically from the nonlinear approximate number system mental number line that parallels the individual number-tuned neurons in the intraparietal sulcus in monkeys and overlying scalp distribution of discrete functional magnetic resonance imaging activations by number tasks in man. Calculation is a complex skill that activates both visual and spatial and visual and verbal networks. It is less strongly left lateralized than language, with approximate number system activation somewhat more right sided and exact number and arithmetic activation more left sided. Maturation and increasing number skill decrease associated widespread non-numerical brain activations that persist in some individuals with dyscalculia, which has no single, universal neurological cause or underlying mechanism in all affected individuals.

Evolution of the cognitive profile in school-aged patients with severe TBI during the first 2 years of neurorehabilitation

OBJECTIVE

Persistent post-injury cognitive, academic and behavioural deficits have been documented in children who sustained severe TBI during the school-age years. The major aim of this study was to examine and follow-up for 2 years the cognitive profile of a sample of post-injured patients (aged 6-16.11), in order to verify to what extent they recovered their intellectual functions after rehabilitation.

METHOD

Twenty-six patients who received a specific neuropsychological treatment and three cognitive evaluations with WISC-III were selected from a pool of 77.

RESULTS

This group of patients showed a mild cognitive deficit at baseline, which improved over the 2 years to a borderline level. Despite the improvement in intellectual quotients and single sub-test scores achieved through rehabilitation, different recovery times were seen according to the function under study. The most common deficits are in processing speed, inferential and lexical-semantic skills.

CONCLUSIONS

Detailed analysis of the WISC-III sub-tests allows for an accurate description of single cognitive functions after TBI. This allows one to make differential diagnoses between functional profiles and plan individualized rehabilitation treatments. Post-injured school-aged patients should receive rehabilitation for a period of at least 2 years, which is the time necessary for an at-least partial reorganization of basic cognitive functions.

Tangram solved? Prefrontal cortex activation analysis during geometric problem solving

Recent neuroimaging studies have implicated prefrontal and parietal cortices for mathematical problem solving. Mental arithmetic tasks have been used extensively to study neural correlates of mathematical reasoning. In the present study we used geometric problem sets (tangram tasks) that require executive planning and visuospatial reasoning without any linguistic representation interference. We used portable optical brain imaging (functional near infrared spectroscopy--fNIR) to monitor hemodynamic changes within anterior prefrontal cortex during tangram tasks. Twelve healthy subjects were asked to solve a series of computerized tangram puzzles and control tasks that required same geometric shape manipulation without problem solving. Total hemoglobin (HbT) concentration changes indicated a significant increase during tangram problem solving in the right hemisphere. Moreover, HbT changes during failed trials (when no solution found) were significantly higher compared to successful trials. These preliminary results suggest that fNIR can be used to assess cortical activation changes induced by geometric problem solving. Since fNIR is safe, wearable and can be used in ecologically valid environments such as classrooms, this neuroimaging tool may help to improve and optimize learning in educational settings.

Three parietal circuits for number processing

Did evolution endow the human brain with a predisposition to represent and acquire knowledge about numbers? Although the parietal lobe has been suggested as a potential substrate for a domain-specific representation of quantities, it is also engaged in verbal, spatial, and attentional functions that may contribute to calculation. To clarify the organisation of number-related processes in the parietal lobe, we examine the three-dimensional intersection of fMRI activations during various numerical tasks, and also review the corresponding neuropsychological evidence. On this basis, we propose a tentative tripartite organisation. The horizontal segment of the intraparietal sulcus (HIPS) appears as a plausible candidate for domain specificity: It is systematically activated whenever numbers are manipulated, independently of number notation, and with increasing activation as the task puts greater emphasis on quantity processing. Depending on task demands, we speculate that this core quantity system, analogous to an internal "number line," can be supplemented by two other circuits. A left angular gyrus area, in connection with other left-hemispheric perisylvian areas, supports the manipulation of numbers in verbal form. Finally, a bilateral posterior superior parietal system supports attentional orientation on the mental number line, just like on any other spatial dimension.

Errors in multi-digit arithmetic and behavioral inattention in children with math difficulties

Errors in written multi-digit computation were investigated in children with math difficulties. Third- and fourth-grade children (n = 291) with coexisting math and reading difficulties, math difficulties, reading difficulties, or no learning difficulties were compared. A second analysis compared those with severe math learning difficulties, low average achievement in math, and no learning difficulties. Math fact errors were related to the severity of the math difficulties, not to reading status. Contrary to predictions, children with poorer reading, regardless of math achievement, committed more visually based errors. Operation switch errors were not systematically related to group membership. Teacher ratings of behavioral inattention were related to accuracy, math fact errors, and procedural bugs. The findings are discussed with respect to hypotheses about the cognitive origins of arithmetic errors and in relation to current discussions about how to conceptualize math disabilities.

Common brain regions underlying different arithmetic operations as revealed by conjunct fMRI-BOLD activation

The issue of how and where arithmetic operations are represented in the brain has been addressed in numerous studies. Lesion studies suggest that a network of different brain areas are involved in mental calculation. Neuroimaging studies have reported inferior parietal and lateral frontal activations during mental arithmetic using tasks of different complexities and using different operators (addition, subtraction, etc.). Indeed, it has been difficult to compare brain activation across studies because of the variety of different operators and different presentation modalities used. The present experiment examined fMRI-BOLD activity in participants during calculation tasks entailing different arithmetic operations -- addition, subtraction, multiplication and division -- of different complexities. Functional imaging data revealed a common activation pattern comprising right precuneus, left and right middle and superior frontal regions during all arithmetic operations. All other regional activations were operation specific and distributed in prominently frontal, parietal and central regions when contrasting complex and simple calculation tasks. The present results largely confirm former studies suggesting that activation patterns due to mental arithmetic appear to reflect a basic anatomical substrate of working memory, numerical knowledge and processing based on finger counting, and derived from a network originally related to finger movement. We emphasize that in mental arithmetic research different arithmetic operations should always be examined and discussed independently of each other in order to avoid invalid generalizations on arithmetics and involved brain areas.

Late intellectual and academic outcomes following traumatic brain injury sustained during early childhood

OBJECT

Although long-term neurological outcomes after traumatic brain injury (TBI) sustained early in life are generally unfavorable, the effect of TBI on the development of academic competencies is unknown. The present study characterizes intelligence quotient (IQ) and academic outcomes an average of 5.7 years after injury in children who sustained moderate to severe TBI prior to 6 years of age.

METHODS

Twenty-three children who suffered inflicted or noninflicted TBI between the ages of 4 and 71 months were enrolled in a prospective, longitudinal cohort study. Their mean age at injury was 21 months; their mean age at assessment was 89 months. The authors used general linear modeling approaches to compare IQ and standardized academic achievement test scores from the TBI group and a community comparison group (21 children). Children who sustained early TBI scored significantly lower than children in the comparison group on intelligence tests and in the reading, mathematical, and language domains of achievement tests. Forty-eight percent of the TBI group had IQs below the 10th percentile. During the approximately 5-year follow-up period, longitudinal IQ testing revealed continuing deficits and no recovery of function. Both IQ and academic achievement test scores were significantly related to the number of intracranial lesions and the lowest postresuscitation Glasgow Coma Scale score but not to age at the time of injury. Nearly 50% of the TBI group failed a school grade and/or required placement in self-contained special education classrooms; the odds of unfavorable academic performance were 18 times higher for the TBI group than the comparison group.

CONCLUSIONS

Traumatic brain injury sustained early in life has significant and persistent consequences for the development of intellectual and academic functions and deleterious effects on academic performance.

A matched lesion analysis of childhood versus adult-onset brain injury due to unilateral stroke: another perspective on neural plasticity and recovery of social functioning

BACKGROUND

The literature on neuroplasticity lacks a direct comparison of chronic neuropsychological and social outcomes following brain damage acquired in childhood versus adulthood, when lesions are matched across adults and children for size and location.

METHODS

We paired adults and children with similar unilateral stroke lesions and then compared chronic neuropsychological and social outcomes. Quantitative comparisons were conducted, as well as qualitative analyses of each subject pair, focusing on specific domains of cognitive impairment and changes in social functioning.

RESULTS

We found that learning and memory impairments were most common in both children and adults. Left hemisphere-lesioned children were normal on speech/language ratings, whereas their adult counterparts were borderline impaired. Impairments in social functioning were highly associated with hemispheric side of damage in adults, but not in children: Specifically, adults with right hemisphere lesions developed social defects much more frequently than adults with left hemisphere lesions, whereas this asymmetry was not evident in the children. Most importantly, though, was the overarching finding of a high degree of similarity between chronic neuropsychological and social function outcomes in adults and children with similarly located brain lesions due to unilateral stroke.

CONCLUSIONS

On balance, the findings suggest that lesion location and size are prepotent factors determining neuropsychological and social recovery from stroke.

Arithmetic skills and their cognitive correlates in children with acquired and congenital brain disorder

Arithmetic skills and their cognitive correlates were studied in 24 children with myelomeningocele and shunted hydrocephalus (MM), 27 children with severe traumatic brain injuries (TBI), and 26 children with orthopedic injuries (OI). Their average age was 11.56 years (SD = 2.36). They completed the WRAT-3 Arithmetic subtest and a subtraction task consisting of 20 problems of varying difficulty, as well as measures of working memory, declarative memory, processing speed, planning skills, and visuospatial abilities. The MM group performed more poorly on the WRAT-3 Arithmetic subtest and the subtraction task than the other two groups, which did not differ from each other on either measure. The groups did not differ in the number of math fact errors or visual-spatial errors on the subtraction task, but the MM group made more procedural errors than the OI group. The five cognitive abilities explained substantial variance in performance on both arithmetic tests; processing speed, working memory, declarative memory, and planning accounted for unique variance. Exploratory analyses showed that the cognitive correlates of arithmetic skills varied across groups and ages. Congenital and acquired brain disorders are associated with distinct patterns of arithmetic skills, which are related to specific cognitive abilities.

Developmental dyscalculia and basic numerical capacities: a study of 8–9-year-old students

Thirty-one 8- and 9-year-old children selected for dyscalculia, reading difficulties or both, were compared to controls on a range of basic number processing tasks. Children with dyscalculia only had impaired performance on the tasks despite high-average performance on tests of IQ, vocabulary and working memory tasks. Children with reading disability were mildly impaired only on tasks that involved articulation, while children with both disorders showed a pattern of numerical disability similar to that of the dyscalculic group, with no special features consequent on their reading or language deficits. We conclude that dyscalculia is the result of specific disabilities in basic numerical processing, rather than the consequence of deficits in other cognitive abilities.

A functional MRI study of simple arithmetic—a comparison between children and adults

The purpose of this study was to examine brain areas involved in simple arithmetic, and to compare these areas between adults and children. Eight children (four girls and four boys; age, 9-14 years) and eight adults (four women and four men; age, 40-49 years) were subjected to this study. Functional magnetic resonance imaging (fMRI) was performed during mental calculation of addition, subtraction, and multiplication of single digits. In each group, the left middle frontal, bilateral inferior temporal and bilateral lateral occipital cortices were activated during each task. The adult group showed activation of the right frontal cortex during addition and multiplication tasks, but the children group did not. Activation of the intraparietal cortex was observed in the adult group during each task. Although, activation patterns were slightly different among tasks, as well as between groups, only a small number of areas showed statistically significant differences. The results indicate that cortical networks involved in simple arithmetic are similar among arithmetic operations, and may not show significant changes in the structure during the second decade of life.

Representation and retrieval of arithmetical facts: developmental difficulties

One form of developmental difficulty with arithmetic affects the storage or retrieval of arithmetical facts, such as tables, which are required to implement arithmetical computations (Temple, 1991, 1994). Such difficulties may arise because of impairment in a specialized system for the storage of arithmetical facts or as a result of causally linked impairment in another cognitive domain. This study explored issues concerning the representation and retrieval of arithmetical facts in children with number fact disorders (NF) and in normal children, in particular the status of hypothesized linked impairments: short-term memory (STM) spans, counting skills, speed of speech, and speed of number fact and lexical retrieval. There was no evidence that NF children had weak STM spans on any span measure or that STM spans related to arithmetical fact skills. There was also no evidence that NF children had weak counting abilities or free counting speeds. The NF children were slower in speeded counting, which also correlated with number fact skill. The significance or not of this is discussed. The NF children were also slower than controls in speed of speech and on some measures of speed of access. However, the absence of correlation with number fact skill, the absence of generality across tasks, and the possibility that delayed speeds in fact retrieval reflect the use of alternative strategies, together suggest that the increased speeds are not causally linked to number fact skill. The results are consistent with modular accounts, in which there is a specialized system for the storage and retrieval of arithmetical facts.

The determinants of arithmetic skills in young children: some observations

The cause or causes of arithmetic difficulties in young children are manifold. The condition has its origins in a set of complex disorders and may be due to genetic factors, developmental delays, experiential limitations, language problems, and perceptual, motor, memory and other cognitive weaknesses. Other factors which may cause the disorder are inappropriate and ineffectual instructional practices. Anxiety and unfavourable attitudes towards the subject may influence mastery of arithmetic attainment in young children.

The calculating brain: an fMRI study

To explore brain areas involved in basic numerical computation, functional magnetic imaging (fMRI) scanning was performed on college students during performance of three tasks; simple arithmetic, numerical magnitude judgment, and a perceptual-motor control task. For the arithmetic relative to the other tasks, results for all eight subjects revealed bilateral activation in Brodmann's area 44, in dorsolateral prefrontal cortex (areas 9 and 10), in inferior and superior parietal areas, and in lingual and fusiform gyri. Activation was stronger on the left for all subjects, but only at Brodmann's area 44 and the parietal cortices. No activation was observed in the arithmetic task in several other areas previously implicated for arithmetic, including the angular and supramarginal gyri and the basal ganglia. In fact, angular and supramarginal gyri were significantly deactivated by the verification task relative to both the magnitude judgment and control tasks for every subject. Areas activated by the magnitude task relative to the control were more variable, but in five subjects included bilateral inferior parietal cortex. These results confirm some existing hypotheses regarding the neural basis of numerical processes, invite revision of others, and suggest productive lines for future investigation.

Numerical and arithmetical cognition: patterns of functions and deficits in children at risk for a mathematical disability

Based on performance on standard achievement tests, first-grade children (mean age = 82 months) with IQ scores in the low-average to high-average range were classified as at risk for a learning disability (LD) in mathematics, reading, or both. These at-risk children (n = 55) and a control group of academically normal peers (n = 35) were administered experimental tasks that assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, and ease of retrieving information from long-term memory. Different patterns of intact cognitive functions and deficits were found for children in the different at-risk groups. As a set, performance on the experimental tasks accounted for roughly 50% and 10% of the group differences in mathematics and reading achievement, respectively, above and beyond the influence of IQ. Performance on the experimental tasks thus provides insights into the cognitive deficits underlying different forms of LD, as well as into the sources of individual differences in academic achievement.

Impairments of number processing induced by prenatal alcohol exposure

Prenatal alcohol exposure causes a variety of cognitive deficits, notably in mathematics and higher order processes such as abstraction. An exploratory battery was developed to examine specific types of number processing impairments in 29 adolescent and adult patients with Fetal Alcohol Syndrome (FAS) and Fetal Alcohol Effects (FAE) relative to controls matched for age, gender, and educational level. The battery included 11 tests: number reading and writing, exact calculation (addition, multiplication, subtraction), approximate calculation (selecting a plausible result for an operation), number comparison, proximity judgment, and cognitive estimation. The results indicated particular difficulties in calculation and estimation tests, with intact number reading and writing ability. The greatest impairment was found in the cognitive estimation test, which is sensitive to frontal lobe lesions. The patterns of deficit described may reflect either the diffuseness of brain damage incurred from prenatal alcohol exposure, or a cumulative deficit in comprehension which may be important for the acquisition of higher-order mathematical abilities.

Retrieval processes in arithmetic production and verification

To investigate whether arithmetic production and verification involve the same retrieval processes, we alternated multiplication production trials (e.g., 9 x 6 = ?) with verification trials (4 x 9 = 36, true or false?) and analyzed positive error priming. Positive error priming is the phenomenon in which errors frequently match correct answers from preceding problems. Production errors were strongly primed by previous production trials (the error-answer matching rate was about 90% greater than expected by chance), but production errors were not strongly primed by previous verification trials (approximately 13% above chance). Conversely, false-verification errors were primed by previous verification trials (approximately 25% above chance), but not by production trials. The results indicated that arithmetic production and verification were mediated by different memory processes and suggest a familiarity-based over a retrieval-based model of arithmetic verification.

Developmental dyscalculia and brain laterality

The correlation between arithmetic dysfunction and brain laterality was studied in 25 children with developmental dyscalculia (DD). The children were tested on a standardized arithmetic battery and underwent a neurological and neuro-psychological evaluation. A diagnosis of left hemisphere dysfunction (n = 13) was based on right side soft neurological signs, performance IQ (PIQ) > verbal IQ (VIQ), dyslexia and intact visuo-spatial functions. The criteria for right hemisphere dysfunction (n = 12) were left body signs, VIQ > PIQ, impaired visuo-spatial functions and normal language skills. The groups were similar for age, gender, and socio-economic status. Our results showed that both groups scored more than 2 SD below the mean adjusted score on the arithmetic battery, but the left group was significantly worse in 3 areas: mastery of addition/subtraction, complex multiplication and division and visuo-spatial errors (p < 0.05). The data indicate that dysfunction of either hemisphere hampers arithmetic acquisition, but arithmetic impairment is more profound with left hemisphere dysfunction.

Calculation abilities in young children with different patterns of cognitive functioning

This study examined the arithmetic calculation abilities of kindergarten and first-grade children with different patterns of cognitive functioning: children with low language but adequate spatial abilities (Low Language; n = 33, male = 42%); children with low spatial but adequate language abilities (Low Spatial; n = 21, male = 42%); children with general delays (Delayed; n = 21, male = 48%); and children with no language or spatial impairments (Nonimpaired; n = 33, male = 48%). Each child was given a series of addition and subtraction calculations presented as nonverbal problems, story problems, and number-fact problems. Story problems and number-fact problems require mastery of conventional verbal symbols, whereas nonverbal problems do not. The findings show that nonverbal, story, and number-fact problem formats are differentially sensitive to variation in cognitive ability. The Low Language group performed significantly worse than the Nonimpaired group on story problems but not on nonverbal problems or number-fact problems. The Delayed group performed significantly worse than the Nonimpaired group on nonverbal problems as well as on story problems but not on number-fact problems. The Low Spatial group did not differ significantly from the Nonimpaired group on any of the three problem types, although the overall performance of these children was weaker. When we adjusted for finger use on number-fact problems, the Nonimpaired group outperformed both the Low Language and the Delayed groups but not the Low Spatial group. Thus, the finding that the Low Language and Delayed groups perform as well as the Nonimpaired group on number-fact problems is attributable to their greater finger use.

Counting knowledge and skill in cognitive addition: a comparison of normal and mathematically disabled children

The relationship between counting knowledge and computational skills (i.e., skill at counting to solve addition problems) was assessed for groups of first-grade normal and mathematically disabled (MD) children. Twenty-four normal and 13 MD children were administered a series of counting tasks and solved 40 computer-administered addition problems. For the addition task, problem-solving strategies were recorded on a trial-by-trial basis. Performance on the counting tasks suggested that the MD children were developmentally delayed in the understanding of essential and unessential features of counting and were relatively unskilled in the detection of certain forms of counting error. On the addition task, the MD children committed many more computational errors and tended to use developmentally immature counting procedures. The immature counting knowledge of the MD children, combined with their relatively poor skills at detecting counting errors, appeared to underlie their poor computational skills on the addition task. Suggestions for future research are presented.