Instructor, Psychiatry and Behavioral Sciences
PhD, Carnegie Mellon University, Cognitive Psychology (2008)
BS, McGill University, Mathematics (2003)
How the brain develops representations for abstract cognitive problems is a major unaddressed question in neuroscience. Here we tackle this fundamental question using arithmetic problem solving, a cognitive domain important for the development of mathematical reasoning. We first examined whether adults demonstrate common neural representations for addition and subtraction problems, two complementary arithmetic operations that manipulate the same quantities. We then examined how the common neural representations for the two problem types change with development. Whole-brain multivoxel representational similarity (MRS) analysis was conducted to examine common coding of addition and subtraction problems in children and adults. We found that adults exhibited significant levels of MRS between the two problem types, not only in the intraparietal sulcus (IPS) region of the posterior parietal cortex (PPC), but also in ventral temporal-occipital, anterior temporal and dorsolateral prefrontal cortices. Relative to adults, children showed significantly reduced levels of MRS in these same regions. In contrast, no brain areas showed significantly greater MRS between problem types in children. Our findings provide novel evidence that the emergence of arithmetic problem solving skills from childhood to adulthood is characterized by maturation of common neural representations between distinct numerical operations, and involve distributed brain regions important for representing and manipulating numerical quantity. More broadly, our findings demonstrate that representational analysis provides a powerful approach for uncovering fundamental mechanisms by which children develop proficiencies that are a hallmark of human cognition.
View details for DOI 10.1016/j.neuropsychologia.2015.07.005
View details for Web of Science ID 000360596700046
View details for PubMedID 26160287
Developmental dyscalculia (DD) is marked by specific deficits in processing numerical and mathematical information despite normal intelligence (IQ) and reading ability. We examined how brain circuits used by young children with DD to solve simple addition and subtraction problems differ from those used by typically developing (TD) children who were matched on age, IQ, reading ability, and working memory. Children with DD were slower and less accurate during problem solving than TD children, and were especially impaired on their ability to solve subtraction problems. Children with DD showed significantly greater activity in multiple parietal, occipito-temporal and prefrontal cortex regions while solving addition and subtraction problems. Despite poorer performance during subtraction, children with DD showed greater activity in multiple intra-parietal sulcus (IPS) and superior parietal lobule subdivisions in the dorsal posterior parietal cortex as well as fusiform gyrus in the ventral occipito-temporal cortex. Critically, effective connectivity analyses revealed hyper-connectivity, rather than reduced connectivity, between the IPS and multiple brain systems including the lateral fronto-parietal and default mode networks in children with DD during both addition and subtraction. These findings suggest the IPS and its functional circuits are a major locus of dysfunction during both addition and subtraction problem solving in DD, and that inappropriate task modulation and hyper-connectivity, rather than under-engagement and under-connectivity, are the neural mechanisms underlying problem solving difficulties in children with DD. We discuss our findings in the broader context of multiple levels of analysis and performance issues inherent in neuroimaging studies of typical and atypical development.
View details for DOI 10.1111/desc.12216
View details for Web of Science ID 000353054000001
Competency with numbers is essential in today's society; yet, up to 20% of children exhibit moderate to severe mathematical learning disabilities (MLD). Behavioural intervention can be effective, but the neurobiological mechanisms underlying successful intervention are unknown. Here we demonstrate that eight weeks of 1:1 cognitive tutoring not only remediates poor performance in children with MLD, but also induces widespread changes in brain activity. Neuroplasticity manifests as normalization of aberrant functional responses in a distributed network of parietal, prefrontal and ventral temporal-occipital areas that support successful numerical problem solving, and is correlated with performance gains. Remarkably, machine learning algorithms show that brain activity patterns in children with MLD are significantly discriminable from neurotypical peers before, but not after, tutoring, suggesting that behavioural gains are not due to compensatory mechanisms. Our study identifies functional brain mechanisms underlying effective intervention in children with MLD and provides novel metrics for assessing response to intervention.
View details for DOI 10.1038/ncomms9453
View details for PubMedID 26419418
The importance of the hippocampal system for rapid learning and memory is well recognized, but its contributions to a cardinal feature of children's cognitive development-the transition from procedure-based to memory-based problem-solving strategies-are unknown. Here we show that the hippocampal system is pivotal to this strategic transition. Longitudinal functional magnetic resonance imaging (fMRI) in 7-9-year-old children revealed that the transition from use of counting to memory-based retrieval parallels increased hippocampal and decreased prefrontal-parietal engagement during arithmetic problem solving. Longitudinal improvements in retrieval-strategy use were predicted by increased hippocampal-neocortical functional connectivity. Beyond childhood, retrieval-strategy use continued to improve through adolescence into adulthood and was associated with decreased activation but more stable interproblem representations in the hippocampus. Our findings provide insights into the dynamic role of the hippocampus in the maturation of memory-based problem solving and establish a critical link between hippocampal-neocortical reorganization and children's cognitive development.
View details for DOI 10.1038/nn.3788
View details for Web of Science ID 000341125400021
View details for PubMedID 25129076
Autism spectrum disorder (ASD) is a neurodevelopmental disorder characterized by social and communication deficits. While such deficits have been the focus of most research, recent evidence suggests that individuals with ASD may exhibit cognitive strengths in domains such as mathematics.Cognitive assessments and functional brain imaging were used to investigate mathematical abilities in 18 children with ASD and 18 age-, gender-, and IQ-matched typically developing (TD) children. Multivariate classification and regression analyses were used to investigate whether brain activity patterns during numerical problem solving were significantly different between the groups and predictive of individual mathematical abilities.Children with ASD showed better numerical problem solving abilities and relied on sophisticated decomposition strategies for single-digit addition problems more frequently than TD peers. Although children with ASD engaged similar brain areas as TD children, they showed different multivariate activation patterns related to arithmetic problem complexity in ventral temporal-occipital cortex, posterior parietal cortex, and medial temporal lobe. Furthermore, multivariate activation patterns in ventral temporal-occipital cortical areas typically associated with face processing predicted individual numerical problem solving abilities in children with ASD but not in TD children.Our study suggests that superior mathematical information processing in children with ASD is characterized by a unique pattern of brain organization and that cortical regions typically involved in perceptual expertise may be utilized in novel ways in ASD. Our findings of enhanced cognitive and neural resources for mathematics have critical implications for educational, professional, and social outcomes for individuals with this lifelong disorder.
View details for DOI 10.1016/j.biopsych.2013.06.018
View details for Web of Science ID 000329130500011
Baddeley and Hitch's multi-component working memory (WM) model has played an enduring and influential role in our understanding of cognitive abilities. Very little is known, however, about the neural basis of this multi-component WM model and the differential role each component plays in mediating arithmetic problem solving abilities in children. Here, we investigate the neural basis of the central executive (CE), phonological (PL) and visuo-spatial (VS) components of WM during a demanding mental arithmetic task in 7-9 year old children (N=74). The VS component was the strongest predictor of math ability in children and was associated with increased arithmetic complexity-related responses in left dorsolateral and right ventrolateral prefrontal cortices as well as bilateral intra-parietal sulcus and supramarginal gyrus in posterior parietal cortex. Critically, VS, CE and PL abilities were associated with largely distinct patterns of brain response. Overlap between VS and CE components was observed in left supramarginal gyrus and no overlap was observed between VS and PL components. Our findings point to a central role of visuo-spatial WM during arithmetic problem-solving in young grade-school children and highlight the usefulness of the multi-component Baddeley and Hitch WM model in fractionating the neural correlates of arithmetic problem solving during development.
View details for DOI 10.1016/j.dcn.2013.10.001
View details for Web of Science ID 000328298700017
The study of developmental disorders can provide a unique window into the role of domain-general cognitive abilities and neural systems in typical and atypical development. Mathematical disabilities (MD) are characterized by marked difficulty in mathematical cognition in the presence of preserved intelligence and verbal ability. Although studies of MD have most often focused on the role of core deficits in numerical processing, domain-general cognitive abilities, in particular working memory (WM), have also been implicated. Here we identify specific WM components that are impaired in children with MD and then examine their role in arithmetic problem solving. Compared to typically developing (TD) children, the MD group demonstrated lower arithmetic performance and lower visuo-spatial working memory (VSWM) scores with preserved abilities on the phonological and central executive components of WM. Whole brain analysis revealed that, during arithmetic problem solving, left posterior parietal cortex, bilateral dorsolateral and ventrolateral prefrontal cortex, cingulate gyrus and precuneus, and fusiform gyrus responses were positively correlated with VSWM ability in TD children, but not in the MD group. Additional analyses using a priori posterior parietal cortex regions previously implicated in WM tasks, demonstrated a convergent pattern of results during arithmetic problem solving. These results suggest that MD is characterized by a common locus of arithmetic and VSWM deficits at both the cognitive and functional neuroanatomical levels. Unlike TD children, children with MD do not use VSWM resources appropriately during arithmetic problem solving. This work advances our understanding of VSWM as an important domain-general cognitive process in both typical and atypical mathematical skill development.
View details for DOI 10.1016/j.neuropsychologia.2013.06.031
View details for Web of Science ID 000328005500026
Now, more than ever, the ability to acquire mathematical skills efficiently is critical for academic and professional success, yet little is known about the behavioral and neural mechanisms that drive some children to acquire these skills faster than others. Here we investigate the behavioral and neural predictors of individual differences in arithmetic skill acquisition in response to 8-wk of one-to-one math tutoring. Twenty-four children in grade 3 (ages 8-9 y), a critical period for acquisition of basic mathematical skills, underwent structural and resting-state functional MRI scans pretutoring. A significant shift in arithmetic problem-solving strategies from counting to fact retrieval was observed with tutoring. Notably, the speed and accuracy of arithmetic problem solving increased with tutoring, with some children improving significantly more than others. Next, we examined whether pretutoring behavioral and brain measures could predict individual differences in arithmetic performance improvements with tutoring. No behavioral measures, including intelligence quotient, working memory, or mathematical abilities, predicted performance improvements. In contrast, pretutoring hippocampal volume predicted performance improvements. Furthermore, pretutoring intrinsic functional connectivity of the hippocampus with dorsolateral and ventrolateral prefrontal cortices and the basal ganglia also predicted performance improvements. Our findings provide evidence that individual differences in morphometry and connectivity of brain regions associated with learning and memory, and not regions typically involved in arithmetic processing, are strong predictors of responsiveness to math tutoring in children. More generally, our study suggests that quantitative measures of brain structure and intrinsic brain organization can provide a more sensitive marker of skill acquisition than behavioral measures.
View details for DOI 10.1073/pnas.1222154110
View details for Web of Science ID 000319803500056
View details for PubMedID 23630286
Developmental dyscalculia (DD) is a disability that impacts math learning and skill acquisition in school-age children. Here we investigate arithmetic problem solving deficits in young children with DD using univariate and multivariate analysis of fMRI data. During fMRI scanning, 17 children with DD (ages 7-9, grades 2 and 3) and 17 IQ- and reading ability-matched typically developing (TD) children performed complex and simple addition problems which differed only in arithmetic complexity. While the TD group showed strong modulation of brain responses with increasing arithmetic complexity, children with DD failed to show such modulation. Children with DD showed significantly reduced activation compared to TD children in the intraparietal sulcus, superior parietal lobule, supramarginal gyrus and bilateral dorsolateral prefrontal cortex in relation to arithmetic complexity. Critically, multivariate representational similarity revealed that brain response patterns to complex and simple problems were less differentiated in the DD group in bilateral anterior IPS, independent of overall differences in signal level. Taken together, these results show that children with DD not only under-activate key brain regions implicated in mathematical cognition, but they also fail to generate distinct neural responses and representations for different arithmetic problems. Our findings provide novel insights into the neural basis of DD.
View details for DOI 10.1016/j.dcn.2011.09.006
View details for Web of Science ID 000315317400014
View details for PubMedID 22682904
Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-related functional magnetic resonance imaging design, we examined brain responses in 22 adults while they performed magnitude comparisons of negative and positive numbers that were quantitatively near (difference <4) or far apart (difference >6). Reaction times (RTs) for negative numbers were slower than positive numbers, and both showed a distance effect whereby near pairs took longer to compare. A network of parietal, frontal, and occipital regions were differentially engaged by negative numbers. Specifically, compared to positive numbers, negative number processing resulted in greater activation bilaterally in intraparietal sulcus (IPS), middle frontal gyrus, and inferior lateral occipital cortex. Representational similarity analysis revealed that neural responses in the IPS were more differentiated among positive numbers than among negative numbers, and greater differentiation among negative numbers was associated with faster RTs. Our findings indicate that despite negative numbers engaging the IPS more strongly, the underlying neural representation are less distinct than that of positive numbers. We discuss our findings in the context of the two theoretical models of negative number processing and demonstrate how multivariate approaches can provide novel insights into abstract number representation.
View details for DOI 10.3389/fnhum.2012.00007
View details for Web of Science ID 000301116300001
View details for PubMedID 22363276
Early elementary schooling in 2nd and 3rd grades (ages 7-9) is an important period for the acquisition and mastery of basic mathematical skills. Yet, we know very little about neurodevelopmental changes that might occur over a year of schooling. Here we examine behavioral and neurodevelopmental changes underlying arithmetic problem solving in a well-matched group of 2nd (n = 45) and 3rd (n = 45) grade children. Although 2nd and 3rd graders did not differ on IQ or grade- and age-normed measures of math, reading and working memory, 3rd graders had higher raw math scores (effect sizes = 1.46-1.49) and were more accurate than 2nd graders in an fMRI task involving verification of simple and complex two-operand addition problems (effect size = 0.43). In both 2nd and 3rd graders, arithmetic complexity was associated with increased responses in right inferior frontal sulcus and anterior insula, regions implicated in domain-general cognitive control, and in left intraparietal sulcus (IPS) and superior parietal lobule (SPL) regions important for numerical and arithmetic processing. Compared to 2nd graders, 3rd graders showed greater activity in dorsal stream parietal areas right SPL, IPS and angular gyrus (AG) as well as ventral visual stream areas bilateral lingual gyrus (LG), right lateral occipital cortex (LOC) and right parahippocampal gyrus (PHG). Significant differences were also observed in the prefrontal cortex (PFC), with 3rd graders showing greater activation in left dorsal lateral PFC (dlPFC) and greater deactivation in the ventral medial PFC (vmPFC). Third graders also showed greater functional connectivity between the left dlPFC and multiple posterior brain areas, with larger differences in dorsal stream parietal areas SPL and AG, compared to ventral stream visual areas LG, LOC and PHG. No such between-grade differences were observed in functional connectivity between the vmPFC and posterior brain regions. These results suggest that even the narrow one-year interval spanning grades 2 and 3 is characterized by significant arithmetic task-related changes in brain response and connectivity, and argue that pooling data across wide age ranges and grades can miss important neurodevelopmental changes. Our findings have important implications for understanding brain mechanisms mediating early maturation of mathematical skills and, more generally, for educational neuroscience.
View details for DOI 10.1016/j.neuroimage.2011.05.013
View details for Web of Science ID 000292717900015
View details for PubMedID 21620984
Although lesion studies over the past several decades have focused on functional dissociations in posterior parietal cortex (PPC) during arithmetic, no consistent view has emerged of its differential involvement in addition, subtraction, multiplication, and division. To circumvent problems with poor anatomical localization, we examined functional overlap and dissociations in cytoarchitectonically defined subdivisions of the intraparietal sulcus (IPS), superior parietal lobule (SPL) and angular gyrus (AG), across these four operations. Compared to a number identification control task, all operations except addition, showed a consistent profile of left posterior IPS activation and deactivation in the right posterior AG. Multiplication and subtraction differed significantly in right, but not left, IPS and AG activity, challenging the view that the left AG differentially subserves retrieval during multiplication. Although addition and multiplication both rely on retrieval, multiplication evoked significantly greater activation in right posterior IPS, as well as the prefrontal cortex, lingual and fusiform gyri, demonstrating that addition and multiplication engage different brain processes. Comparison of PPC responses to the two pairs of inverse operations: division versus multiplication and subtraction versus addition revealed greater activation of left lateral SPL during division, suggesting that processing inverse relations is operation specific. Our findings demonstrate that individual IPS, SPL and AG subdivisions are differentially modulated by the four arithmetic operations and they point to significant functional heterogeneity and individual differences in activation and deactivation within the PPC. Critically, these effects are related to retrieval, calculation and inversion, the three key cognitive processes that are differentially engaged by arithmetic operations. Our findings point to distribute representation of these processes in the human PPC and also help explain why lesion and previous imaging studies have yielded inconsistent findings.
View details for DOI 10.1016/j.neuropsychologia.2011.04.035
View details for Web of Science ID 000293611600034
View details for PubMedID 21616086
Recent research into math cognition has identified areas of the brain that are involved in number processing (Dehaene, Piazza, Pinel, & Cohen, 2003) and complex problem solving (Anderson, 2007). Much of this research assumes that participants use a single strategy; yet, behavioral research finds that people use a variety of strategies (LeFevre et al., 1996; Siegler, 1987; Siegler & Lemaire, 1997). In the present study, we examined cortical activation as a function of two different calculation strategies for mentally solving multidigit multiplication problems. The school strategy, equivalent to long multiplication, involves working from right to left. The expert strategy, used by "lightning" mental calculators (Staszewski, 1988), proceeds from left to right. The two strategies require essentially the same calculations, but have different working memory demands (the school strategy incurs greater demands). The school strategy produced significantly greater early activity in areas involved in attentional aspects of number processing (posterior superior parietal lobule, PSPL) and mental representation (posterior parietal cortex, PPC), but not in a numerical magnitude area (horizontal intraparietal sulcus, HIPS) or a semantic memory retrieval area (lateral inferior prefrontal cortex, LIPFC). An ACT-R model of the task successfully predicted BOLD responses in PPC and LIPFC, as well as in PSPL and HIPS.
View details for DOI 10.3758/CABN.9.3.270
View details for Web of Science ID 000269190400006
View details for PubMedID 19679763
This article investigates the potential of fMRI to test assumptions about different components in models of complex cognitive tasks. If the components of a model can be associated with specific brain regions, one can make predictions for the temporal course of the BOLD response in these regions. An event-locked procedure is described for dealing with temporal variability and bringing model runs and individual data trials into alignment. Statistical methods for testing the model are described that deal with the scan-to-scan correlations in the errors of measurement of the BOLD signal. This approach is illustrated using a "sacrificial" ACT-R model that involves mapping 6 modules onto 6 brain regions in an experiment from Ravizza, Anderson, and Carter (in press) concerned with equation solving. The model's visual encoding predicted the BOLD response in the fusiform gyrus, its controlled retrieval predicted the BOLD response in the lateral inferior prefrontal cortex, and its subgoal setting predicted the BOLD response in the anterior cingulate cortex. On the other hand, its motor programming failed to predict anticipatory activation in the motor cortex, its representational changes failed to predicted the pattern of activity in the posterior parietal cortex, and its procedural component failed to predict an initial spike in caudate. The results illustrate the power of such data to direct the development of a theory of complex problem solving, both at the level of a specific task model as well as at the level of the cognitive architecture.
View details for DOI 10.1080/03640210802451588
View details for Web of Science ID 000261413600005
View details for PubMedID 21585456