Ansari, Daniel

Hyde, Daniel C

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Western University Scholarship@Western Brain and Mind Institute Researchers' Publications Brain and Mind Institute 4-1-2018 Advances in Understanding the Development of the Mathematical Brain Daniel C. Hyde Department of Psychology University of Illinois at Urbana-Champaign. Daniel Ansari University of Western Ontario., daniel.ansari@uwo.ca Follow this and additional works at: https://ir.lib.uwo.ca/brainpub  Part of the Neurosciences Commons, and the Psychology Commons Citation of this paper: Daniel C. Hyde, Daniel Ansari, Advances in Understanding the Development of the Mathematical Brain, Developmental Cognitive Neuroscience, Volume 30, 2018, Pages 236-238, ISSN 1878-9293, https://doi.org/10.1016/j.dcn.2018.04.006. (https://www.sciencedirect.com/science/article/pii/S1878929318300860) Contents lists available at ScienceDirectDevelopmental Cognitive Neurosciencejournal homepage: www.elsevier.com/locate/dcnAdvances in Understanding the Development of the Mathematical BrainMathematical thinking has served as a central test case for theoriesof cognition and cognitive development for decades (e.g., Gelman andGallistel, 1986; Piaget, 1952; Wynn, 1990) and philosophical debateson human nature and the mind for much longer. The theoretical im-plications of understanding the development of mathematics, however,should not overshadow its translational importance. Many childrenstruggle to learn mathematical concepts (see Butterworth et al., 2011).This is problematic, as mathematics is ubiquitous and extremely im-portant to success in modern life. By some estimates, for example,mathematics achievement is a better predictor of life success than lit-eracy (e.g., Duncan et al., 2007). Thus, a better understanding ofmathematical thinking has the potential to inform our understanding ofhuman symbolic learning as well as suggest ways in which we canoptimize it through education.The last few decades of research on mathematical thinking havebuilt a rich foundation on which to investigate the relationships be-tween mathematical thinking, development, and the brain. From pastresearch, we see that a reliable network of brain regions appears to becritical for mathematical thought in educated human adults (e.g.,Arsalidou & Taylor, 2011; Dehaene et al., 2003; Menon, 2015). Someportions of the network, including intraparietal regions, appear to bespecialized for numerical and mathematical thinking (e.g., Amalric &Dehaene, 2016), abnormalities or damage to which impair mathematics(Price et al., 2007, Menon, 2016). Co-activation of other nodes of thenetwork suggests the conditions under which mathematics interfaceswith more general symbolic, language abilities, and executive abilities(e.g., Menon, 2015; Vanbinst & De Smedt, 2016). From behavioral re-search, we also see that early mathematics learning follows a reliabletrajectory (e.g., Libertus & Brannon, 2010; Wynn, 1990) and early in-dividual differences predict later achievement (Duncan et al., 2007;LeFevre et al., 2009; Starr et al., 2013). This trajectory coincides withtremendous gains in linguistic and general executive abilities, un-doubtedly contributing to the capacity to learn more complex mathe-matics (see Blair & Razza, 2007; Chu & Geary, 2015; Fuhs & McNeil,2013; LeFevre et al, 2010). Formal education and informal experience(e.g., such as parental input) have a critical impact on mathematicsproficiency and fluency over development (e.g., Berkowitz et al., 2015;LeFevre et al., 2009). Finally, behavior of human infants and children isguided by basic, non-verbal numerical and mathematical intuitions,evidence that some aspects of mathematical thinking might be presentbefore education or instruction (e.g., Feigenson et al., 2004, Gilmoreet al., 2007). Together, this work has led to a number of prominent andcompeting contemporary theories of mathematics development (Carey,2009; Danker & Anderson, 2007; Siegler, 2016; Spelke, 2003;McClelland et al., 2016).This foundation, as well as technological advances in applying brainmeasures to developmental populations, provides the opportunity togain new insights. This special issue highlights some impressive ex-amples of how developmental cognitive neuroscience is currently beingapplied to further our understanding of the development of the math-ematical brain. We see a few prominent themes are emerging from thislatest work.First, there is starting to be enough accumulated evidence to movebeyond single studies and allow meta-science of the literature. Severalpapers in this special issue provide novel insights into the current lit-erature on the development of the mathematical brain through meta-analytic approaches. Arsalidou, Pawilw-Levac, Sadeghi, andPascual-Leone present a meta-analysis of the regions of the brain as-sociated with calculation in children, providing evidence for both thecommonly known frontal and parietal regions near the cortical surface,as well as lesser recognized regions like the insula, claustrum, andcingulate deeper within the brain. They argue based on their metaanalysis that more attention should be given to these deeper regions,which may be implicated in the motivational aspects of mathematics.Pollack and Ashby used meta-analytic techniques to investigatethe overlap between retrieval-based arithmetic and phonological pro-cessing in adults and children. They find that children engage wide-spread frontal regions and the left fusiform gyrus for both types ofprocessing, whereas activity in adults is more restricted to left later-alized inferior frontal regions as well as inferior parietal regions. Thesesresults suggest substantial overlap in the regions of the brain involvedin phonological and arithmetic fact processing, with a broader en-gagement of domain general and symbolic processing resources inchildren to a more focused processing of symbols and their linguisticreferents in adults.Peters and De Smedt provide a comprehensive narrative review ofliterature to date on the anatomical and function brain correlates ofarithmetic, as well as expert commentary on the way forward. Theyhighlight consistent findings in the literature of interconnected frontal,parietal, temporal regions that engage for children during arithmetic, aswell as various changes in structure, function, and connectivity over asarithmetic develops. They note that these changes broadly correspondto changes in strategy (from calculation to fact retrieval) and compe-tence over development, but that the actual causes of these changes andtheir relationship to disability are not yet understood. They note thatage as a developmental variable needs to be used more carefully, ad-ditionally taking into account the particular tasks, assessments, strate-gies, and instructional environments of the children studied. Based ontheir review, they also admonish those in the field to take advantage ofemerging technologies to further study the entire arithmetic networkhttps://doi.org/10.1016/j.dcn.2018.04.006Developmental Cognitive Neuroscience 30 (2018) 236–2381878-9293/ © 2019 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).Tand its’ interconnections rather than particular nodes, to better un-derstand these issues.Second, current work is moving beyond the role of particular brainregions and attempting to better understand the mathematical brain asa network and dependencies between brain regions in this network.Two papers in this special issue examine the relationship betweenfunctional connectivity and mathematics. Price, Yeo, Wilkey, andCutting examine the relationship between resting state functionalconnectivity of subareas of the intraparietal sulcus (IPS) in 1st gradechildren and arithmetic performance a year later. They find higherinterconnectivity between sub-regions of the IPS during rest is relatedto better arithmetic in children. In contrast, they found higher func-tional connectivity between parietal and frontal and parietal and tem-poral regions at rest to be negatively associated with arithmetic de-velopment. These relationships were robust and appear to be specific toarithmetic, as they held, even after controlling for a variety of othergeneral cognitive and achievement factors. As the authors conclude,there are a number of possible interpretations of these findings andmore work is needed to determine which interpretation is correct.However, given the relative ease of collecting resting-state connectivitydata compared to active task brain imaging data with young children,this paper provides a promising methodological approach for futurework.Michels, O’Gorman, and Kucian used an experimental trainingparadigm to compare functional connectivity of IPS between olderchildren with developmental dyscalculia and typical developing peersbefore and after a number line training intervention. As has been seenbefore, they found more connectivity, or hyper-connectivity, in thosewith developmental dyscalculia. Remarkably, however, both groupswere responsive to the 5-week intervention, with group hyper-con-nectivity disappearing at post-test. These results suggest differences infunctional connectivity may be important to explaining dysfunction,but plasticity in functional connectivity may allow for remediation withproper experience.Third, researchers are seeking out deeper causal explanations bytesting the necessity and role of experience in formation and develop-ment of the brain systems for mathematics through varied and in-novative research designs and populations. Two papers in the specialissue focus on the role of early life experience in mathematical devel-opment. Glenn, Demir-Lira, Gibson, Congdon, and Levine study theeffects of early brain injury on preschool numerical development. Theyshow that children with early brain injury are slightly delayed relativeto neurotypical peers in both learning of early number concepts andpreschool mathematics achievement. Longitudinal data also suggestthat children with early brain injury are slower to move throughcommon developmental stages of numerical development. Despitethese findings, however, the authors provide evidence that the delaysare relatively minor and that numerical experience through parentalnumber talk equally influenced children with and without brain injury.Together, the findings of Glenn and colleagues suggest that mathe-matical development is fairly resilient to early injury and, with properexperience, may be able to somewhat remediated.Amalric, Denghien, and Dehaene investigate the role of visualexperience in the formation of the brain networks supporting high-levelmathematics concepts. They show the engagement of a similar networkcommon to mathematics in sighted mathematicians and a small groupof mathematicians who have been blind from childhood. Furthermore,the engaged network is also similar to that widely found when non-mathematicians perform more basic mathematics, supporting the ideathat visual experience is not necessary for the formation of mathe-matics-specific networks in the brain.Two papers in this special issue report findings from experimentalresearch across different age groups. Mathieu, Epinat-Duclos, Leone,Fayol, Thevenot, and Prado investigate the emergence of spatialmeaning for arithmetic operators and its neural correlates. They findthat around 12-13 years of age, children start to a relationship betweenspatially relevant activity in the hippocampus and the perception of theplus sign (+). Furthermore, this activity increases with age and is re-lated to the degree to which operator priming, or presentation of theplus sign prior to a mathematical problem, facilitated addition. Theyspeculate that these finding may reflect the building of associationsbetween the spatial system and the operation of addition in latechildhood.Park studied the emergence of the direct perception of numerosityin children using visual evoked potentials. He shows that numerosity-specific activity arising from right occipital sites emerges steadily after3 years of age. In contrast, direct perceptual sensitivity to other non-numerical magnitudes is not present (and/or does not increase) inchildhood. These findings contrast with other work with younger po-pulations showing behavioral and neural sensitivity to numerosity andother non-numerical parameters, albeit with less strict and systemiccontrols and contrasts. Park suggests that these new findings maysuggest either earlier numerical competencies may not be as specific tonumber as previous thought or simply computed by other mechanisms(e.g., parietal regions) with direct numerical perception developingonly later. Further work is needed, especially at younger ages to re-concile these findings with the rest of the literature.Together, the articles of this special issue provide a selection ofexciting new work expanding the boundaries of our knowledge of thedevelopment of the mathematical brain.ReferencesAmalric, M., Dehaene, S., 2016. Origins of the brain networks for advanced mathematicsin expert mathematicians. In: Proceedings of the National Academy of Sciences 113(18), 4909–4917.Arsalidou, M., Taylor, M.J., 2011. Is 2 + 2= 4? Meta-analyses of brain areas needed fornumbers and calculations. Neuroimage 54 (3), 2382–2393.Berkowitz, T., Schaeffer, M.W., Maloney, E.A., Peterson, L., Gregor, C., Levine, S.C.,Beilock, S.L., 2015. Math at home adds up to achievement in school. Science 350(6257), 196–198.Blair, C., Razza, R.P., 2007. Relating effortful control, executive function, and false beliefunderstanding to emerging math and literacy ability in kindergarten. ChildDevelopment 78 (2), 647–663.Butterworth, B., Varma, S., Laurillard, D., 2011. Dyscalculia: from brain to education.Science 332 (6033), 1049–1053.Carey, S., 2009. The Origin of Concepts. Oxford University Press.Chu, F.W., Geary, D.C., 2015. Early numerical foundations of young children’s mathe-matical development. J. Exp. Child Psychol. 132, 205–212.Danker, J.F., Anderson, J.R., 2007. The roles of prefrontal and posterior parietal cortex inalgebra problem solving: a case of using cognitive modeling to inform neuroimagingdata. Neuroimage 35 (3), 1365–1377.Dehaene, S., Piazza, M., Pinel, P., Cohen, L., 2003. Three parietal circuits for numberprocessing. Cogn. Neuropsychol. 20 (3-6), 487–506.Duncan, G.J., Dowsett, C.J., Claessens, A., Magnuson, K., Huston, A.C., Klebanov, P.,Sexton, H., 2007. School readiness and later achievement. Dev. Psychol. 43 (6),1428–1446.Feigenson, L., Dehaene, S., Spelke, E., 2004. Core systems of number. Trends Cogn. Sci. 8(7), 307–314.Fuhs, M.W., McNeil, N.M., 2013. ANS acuity and mathematics ability in preschoolersfrom low‐income homes: contributions of inhibitory control. Dev. Sci. 16 (1),136–148.Gelman, R., Gallistel, C.R., 1986. The Child's Understanding of Number. HarvardUniversity Press.Gilmore, C.K., McCarthy, S.E., Spelke, E.S., 2007. Symbolic arithmetic knowledge withoutinstruction. Nature 447 (7144), 589.LeFevre, J.A., Skwarchuk, S.L., Smith-Chant, B.L., Fast, L., Kamawar, D., Bisanz, J., 2009.Home numeracy experiences and children’s math performance in the early schoolyears. Can. J. Behav. Sci. 41 (2), 55.LeFevre, J.A., Fast, L., Skwarchuk, S.L., Smith‐Chant, B.L., Bisanz, J., Kamawar, D.,Penner-Wilger, M., 2010. Pathways to mathematics: longitudinal predictors of per-formance. Child Dev. 81 (6), 1753–1767.Libertus, M.E., Brannon, E.M., 2010. Stable individual differences in number dis-crimination in infancy. Dev. Sci. 13 (6), 900–906.McClelland, J. L., Mickey, K., Hansen, S., Yuan, X., & Lu, Q. (2016). A Parallel-DistributedProcessing Approach to Mathematical Cognition. Manuscript, Stanford University,February 18, 2016.Menon, V., 2015. A neurodevelopmental perspective on the role of memory systems inchildren’s math learning. In: Berch, D.B., Geary, D.C., Mann Koepke, K. (Eds.),In Development of Mathematical Cognition-Neural Substrates and Genetic Influences.Elsevier Press.Menon, V., 2016. Working memory in children's math learning and its disruption indyscalculia. Curr. Opin. Behav. Sci. 10, 125–132.Developmental Cognitive Neuroscience 30 (2018) 236–238237Piaget, J., 1952. The Child’s Concept of Number. Norton, New York.Price, G.R., Holloway, I., Räsänen, P., Vesterinen, M., Ansari, D., 2007. Impaired parietalmagnitude processing in developmental dyscalculia. Curr. Biol. 17 (24),R1042–R1043.Siegler, R.S., 2016. Magnitude knowledge: the common core of numerical development.Dev. Sci. 19, 341–361.Spelke, E.S., 2003. In: Getner, D., Goldin-Meadow, S. (Eds.), What Makes us Smart? CoreKnowledge and Natural Language. In Language in Mind: Advances in theInvestigation of Language and Thought. MIT Press, Cambridge, MA.Starr, A., Libertus, M.E., Brannon, E.M., 2013. Number sense in infancy predicts mathe-matical abilities in childhood. Proc. Natl. Acad. Sci. USA 110 (45), 18116–18120.Vanbinst, K., De Smedt, B., 2016. Individual differences in children's mathematicsachievement: The roles of symbolic numerical magnitude processing and domain-general cognitive functions. In. In: Cappelletti, M., Fias, W. (Eds.), Prog. Brain Res.227. Elsevier, pp. 105–130.Wynn, K., 1990. Children's understanding of counting. Cognition 36 (2), 155–193.Daniel C. HydeDepartment of Psychology University of Illinois at Urbana-ChampaignDaniel AnsariUniversity of Western OntarioDevelopmental Cognitive Neuroscience 30 (2018) 236–238238

Advances in Understanding the Development of the Mathematical Brain

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Advances in Understanding the Development of the Mathematical Brain

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