Arithmetic in the developing brain: A review of brain imaging studies

Brain imaging studies on academic achievement offer an exciting window on experience-dependent cortical plasticity, as they allow us to understand how developing brains change when children acquire culturally transmitted skills. This contribution focuses on the learning of arithmetic, which is quintessential to mathematical development. The nascent body of brain imaging studies reveals that arithmetic recruits a large set of interconnected areas, including prefrontal, posterior parietal, occipito-temporal and hippocampal areas. This network undergoes developmental changes in its function, connectivity and structure, which are not yet fully understood. This network only partially overlaps with what has been found in adults, and clear differences are observed in the recruitment of the hippocampus, which are related to the development of arithmetic fact retrieval. Despite these emerging trends, the literature remains scattered, particularly in the context of atypical development. Acknowledging the distributed nature of the arithmetic network, future studies should focus on connectivity and analytic approaches that investigate patterns of brain activity, coupled with a careful design of the arithmetic tasks and assessments of arithmetic strategies. Such studies will produce a more comprehensive understanding of how the arithmetical brain unfolds, how it changes over time, and how it is impaired in atypical development.

[1]  S. E. Henschen Über sprach-, musik- und rechenmechanismen und ihre lokalisationen im großhirn , 1919 .

[2]  Wim Fias,et al.  Multiple components of developmental dyscalculia , 2013, Trends in Neuroscience and Education.

[3]  Catherine Lebel,et al.  Brain microstructure is related to math ability in children with fetal alcohol spectrum disorder. , 2010, Alcoholism, clinical and experimental research.

[4]  Kaustubh Supekar,et al.  Reconfiguration of parietal circuits with cognitive tutoring in elementary school children , 2016, Cortex.

[5]  B. De Smedt,et al.  Individual differences in children's mathematics achievement: The roles of symbolic numerical magnitude processing and domain-general cognitive functions. , 2016, Progress in brain research.

[6]  B. Boets,et al.  Phonological processing and arithmetic fact retrieval: Evidence from developmental dyslexia , 2010, Neuropsychologia.

[7]  Christa Neuper,et al.  Individual differences in mathematical competence predict parietal brain activation during mental calculation , 2007, NeuroImage.

[8]  J. Gabrieli,et al.  Functional and morphometric brain dissociation between dyslexia and reading ability , 2007, Proceedings of the National Academy of Sciences.

[9]  B. Smedt Individual Differences in Arithmetic Fact Retrieval , 2016 .

[10]  R. Siegler The perils of averaging data over strategies: An example from children's addition. , 1987 .

[11]  M. Catani,et al.  Can spherical deconvolution provide more information than fiber orientations? Hindrance modulated orientational anisotropy, a true‐tract specific index to characterize white matter diffusion , 2013, Human brain mapping.

[12]  Baxter P. Rogers,et al.  Aberrant functional activation in school age children at-risk for mathematical disability: A functional imaging study of simple arithmetic skill , 2009, Neuropsychologia.

[13]  Tanya M. Evans,et al.  Brain Structural Integrity and Intrinsic Functional Connectivity Forecast 6 Year Longitudinal Growth in Children's Numerical Abilities , 2015, The Journal of Neuroscience.

[14]  P. Paquier,et al.  Neural Differences in Bilingual Children's Arithmetic Processing Depending on Language of Instruction , 2011 .

[15]  J. Booth,et al.  The Differential Role of Verbal and Spatial Working Memory in the Neural Basis of Arithmetic , 2014, Developmental neuropsychology.

[16]  Allan L Reiss,et al.  Changes in frontal-parietal activation and math skills performance following adaptive number sense training: Preliminary results from a pilot study , 2011, Neuropsychological rehabilitation.

[17]  J. Gerstmann SYNDROME OF FINGER AGNOSIA, DISORIENTATION FOR RIGHT AND LEFT, AGRAPHIA AND ACALCULIA: LOCAL DIAGNOSTIC VALUE , 1940 .

[18]  A. Rocha,et al.  Brain mappings of the arithmetic processing in children and adults. , 2005, Brain research. Cognitive brain research.

[19]  Avishai Henik,et al.  Meta-Analyses of Developmental fMRI Studies Investigating Typical and Atypical Trajectories of Number Processing and Calculation , 2011, Developmental neuropsychology.

[20]  Daniel Ansari,et al.  Drawing connections between white matter and numerical and mathematical cognition: A literature review , 2015, Neuroscience & Biobehavioral Reviews.

[21]  J. Booth,et al.  Developmental dissociation in the neural responses to simple multiplication and subtraction problems. , 2014, Developmental science.

[22]  Bert De Smedt,et al.  Brain activity during arithmetic in symbolic and non-symbolic formats in 9–12 year old children , 2016, Neuropsychologia.

[23]  Michael von Aster,et al.  Optimized voxel-based morphometry in children with developmental dyscalculia , 2008, NeuroImage.

[24]  Alan H. Schoenfeld,et al.  What Doesn’t Work: The Challenge and Failure of the What Works Clearinghouse to Conduct Meaningful Reviews of Studies of Mathematics Curricula , 2006 .

[25]  Brian Butterworth,et al.  Developmental trajectories of grey and white matter in dyscalculia , 2013, Trends in Neuroscience and Education.

[26]  J. Booth,et al.  Children with mathematical learning disability fail in recruiting verbal and numerical brain regions when solving simple multiplication problems , 2014, Cortex.

[27]  K. M. Robinson,et al.  Stability and change in children's division strategies. , 2006, Journal of experimental child psychology.

[28]  Guinevere F. Eden,et al.  An Investigation into the Origin of Anatomical Differences in Dyslexia , 2014, The Journal of Neuroscience.

[29]  L. Fuchs,et al.  Neural predictors of individual differences in response to math tutoring in primary-grade school children , 2013, Proceedings of the National Academy of Sciences.

[30]  Lieven Lagae,et al.  The arithmetic problem size effect in children: an event-related potential study , 2014, Front. Hum. Neurosci..

[31]  G. Glover,et al.  Dissociating Prefrontal and Parietal Cortex Activation during Arithmetic Processing , 2000, NeuroImage.

[32]  B. Butterworth,et al.  Age-independent and age–dependent neural substrate for single-digit multiplication and addition arithmetic problems , 2009, NeuroImage.

[33]  Margarete Delazer,et al.  Learning by strategies and learning by drill—evidence from an fMRI study , 2005, NeuroImage.

[34]  L. Lagae,et al.  Arithmetic difficulties in children with mild traumatic brain injury at the subacute stage of recovery , 2015, Developmental medicine and child neurology.

[35]  Nikolaus Kriegeskorte,et al.  Frontiers in Systems Neuroscience Systems Neuroscience , 2022 .

[36]  Rebecca Bull,et al.  Executive Functioning and Mathematics Achievement , 2014 .

[37]  R. Grabner,et al.  Applications of Neuroscience to Mathematics Education , 2015 .

[38]  Bert De Smedt,et al.  Effects of problem size and arithmetic operation on brain activation during calculation in children with varying levels of arithmetical fluency , 2011, NeuroImage.

[39]  J. Booth,et al.  Neural Correlates of Math Gains Vary Depending on Parental Socioeconomic Status (SES) , 2016, Front. Psychol..

[40]  Jamie I. D. Campbell,et al.  Cognitive arithmetic across cultures. , 2001 .

[41]  J. Stein What is Developmental Dyslexia? , 2018, Brain sciences.

[42]  Margot J. Taylor,et al.  Is 2+2=4? Meta-analyses of brain areas needed for numbers and calculations , 2011, NeuroImage.

[43]  Caitlin Tenison,et al.  Weak task-related modulation and stimulus representations during arithmetic problem solving in children with developmental dyscalculia , 2012, Developmental Cognitive Neuroscience.

[44]  J. Wouters,et al.  Neuroscience and Biobehavioral Reviews a Qualitative and Quantitative Review of Diffusion Tensor Imaging Studies in Reading and Dyslexia , 2022 .

[45]  D. Ansari Neurocognitive approaches to developmental disorders of numerical and mathematical cognition: The perils of neglecting the role of development , 2010 .

[46]  Soohyun Cho,et al.  How does a child solve 7 + 8? Decoding brain activity patterns associated with counting and retrieval strategies. , 2011, Developmental science.

[47]  Brain activity. , 2014, Nature nanotechnology.

[48]  André Knops Numerical Cognition: The Basics , 2019 .

[49]  Daniel Ansari,et al.  Why Mental Arithmetic Counts: Brain Activation during Single Digit Arithmetic Predicts High School Math Scores , 2013, The Journal of Neuroscience.

[50]  B. Pennington,et al.  Developmental dyslexia , 2012, The Lancet.

[51]  Jeffrey Bisanz,et al.  Selection of Procedures in Mental Addition: Reassessing the Problem Size Effect in Adults , 1996 .

[52]  F. Hoeft,et al.  Integrating MRI brain imaging studies of pre-reading children with current theories of developmental dyslexia: a review and quantitative meta-analysis , 2016, Current Opinion in Behavioral Sciences.

[53]  N. A. Laskaris,et al.  Transition dynamics of EEG-based network microstates during mental arithmetic and resting wakefulness reflects task-related modulations and developmental changes , 2015, Cognitive Neurodynamics.

[54]  R. Siegler,et al.  Four aspects of strategic change: contributions to children's learning of multiplication. , 1995, Journal of experimental psychology. General.

[55]  Bert De Smedt,et al.  Neurophysiological evidence for the validity of verbal strategy reports in mental arithmetic , 2011, Biological Psychology.

[56]  Daniel Ansari,et al.  Symbolic magnitude processing is as important to arithmetic development as phonological awareness is to reading , 2016 .

[57]  Guinevere F. Eden,et al.  The functional anatomy of single-digit arithmetic in children with developmental dyslexia , 2014, NeuroImage.

[58]  J. Booth,et al.  Distinct representations of subtraction and multiplication in the neural systems for numerosity and language , 2011, Human brain mapping.

[59]  V Menon,et al.  Cerebral Cortex doi:10.1093/cercor/bhi055 Developmental Changes in Mental Arithmetic: Evidence for Increased Functional Specialization in the Left Inferior Parietal Cortex , 2005 .

[60]  Angela R. Laird,et al.  Behavior, sensitivity, and power of activation likelihood estimation characterized by massive empirical simulation , 2016, NeuroImage.

[61]  Charles H. Hillman,et al.  The influence of cardiorespiratory fitness on strategic, behavioral, and electrophysiological indices of arithmetic cognition in preadolescent children , 2014, Front. Hum. Neurosci..

[62]  Hiroshi Fukuda,et al.  A functional MRI study of simple arithmetic--a comparison between children and adults. , 2004, Brain research. Cognitive brain research.

[63]  Sridar Narayanan,et al.  White matter integrity and math performance in pediatric multiple sclerosis: a diffusion tensor imaging study , 2011, Neuroreport.

[64]  John C Gore,et al.  An fMRI study of magnitude comparison and exact addition in children. , 2010, Magnetic resonance imaging.

[65]  Sarit Ashkenazi,et al.  Brain hyper-connectivity and operation-specific deficits during arithmetic problem solving in children with developmental dyscalculia. , 2014, Developmental science.

[66]  Margarete Delazer,et al.  Arithmetic Learning in Adults , 2015 .

[67]  D. Geary Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study. , 2011, Developmental psychology.

[68]  Daniel Ansari,et al.  Individual differences in left parietal white matter predict math scores on the Preliminary Scholastic Aptitude Test , 2013, NeuroImage.

[69]  L. Fuchs,et al.  Plasticity of left perisylvian white-matter tracts is associated with individual differences in math learning , 2015, Brain Structure and Function.

[70]  Guinevere F. Eden,et al.  Functional neuroanatomy of arithmetic and word reading and its relationship to age , 2016, NeuroImage.

[71]  R. Siegler Emerging Minds: The Process of Change in Children's Thinking , 1996 .

[72]  Bruce D. McCandliss,et al.  White matter microstructures underlying mathematical abilities in children , 2008, Neuroreport.

[73]  Gavin R. Price,et al.  Impaired parietal magnitude processing in developmental dyscalculia , 2007, Current Biology.

[74]  E. Ceulemans,et al.  Profiles of children's arithmetic fact development: a model-based clustering approach. , 2015, Journal of experimental child psychology.

[75]  D. Geary,et al.  Cognitive and brain systems underlying early mathematical development. , 2016, Progress in brain research.

[76]  Nancy C. Jordan,et al.  Journal of Experimental , 2002 .

[77]  Vinod Menon,et al.  What Difference Does a Year of Schooling Make? Maturation of Brain Response and Connectivity between 2nd and 3rd Grades during Arithmetic Problem Solving , 2022 .

[78]  F. Xu,et al.  Age Difference in Numeral Recognition and Calculation: An Event-related Potential Study , 2007, Child neuropsychology : a journal on normal and abnormal development in childhood and adolescence.

[79]  André Vandierendonck,et al.  The development of strategy use in elementary school children: working memory and individual differences. , 2007, Journal of experimental child psychology.

[80]  R. Shalev,et al.  Developmental Dyscalculia , 2004, Journal of child neurology.

[81]  D. Geary,et al.  Counting Knowledge and Skill in Cognitive Addition: a Comparison of Normal and Mathematically Disabled Children , 2022 .

[82]  Pierre Barrouillet,et al.  Strategies in subtraction problem solving in children. , 2008, Journal of experimental child psychology.

[83]  Nadja Tschentscher,et al.  How are things adding up? Neural differences between arithmetic operations are due to general problem solving strategies , 2014, NeuroImage.

[84]  Feiyan Chen,et al.  Individual structural differences in left inferior parietal area are associated with schoolchildrens' arithmetic scores , 2013, Front. Hum. Neurosci..

[85]  Kaustubh Supekar,et al.  Cognitive tutoring induces widespread neuroplasticity and remediates brain function in children with mathematical learning disabilities , 2015, Nature Communications.

[86]  J. Rapoport,et al.  Structural MRI of Pediatric Brain Development: What Have We Learned and Where Are We Going? , 2010, Neuron.

[87]  Vinod Menon,et al.  Development of common neural representations for distinct numerical problems , 2015, Neuropsychologia.

[88]  Bruce D. McCandliss,et al.  Development of neural systems for reading. , 2007, Annual review of neuroscience.

[89]  Jan Wouters,et al.  A DTI tractography study in pre-readers at risk for dyslexia , 2015, Developmental Cognitive Neuroscience.

[90]  Guinevere F. Eden,et al.  Meta-Analysis of the Functional Neuroanatomy of Single-Word Reading: Method and Validation , 2002, NeuroImage.

[91]  Vinod Menon,et al.  Arithmetic in the Child and Adult Brain , 2015 .

[92]  Bert De Smedt,et al.  Left fronto-parietal white matter correlates with individual differences in children's ability to solve additions and multiplications: A tractography study , 2014, NeuroImage.

[93]  John C Gore,et al.  The neural correlates of calculation ability in children: an fMRI study. , 2009, Magnetic resonance imaging.

[94]  Hans P. Op de Beeck,et al.  The neural representation of Arabic digits in visual cortex , 2015, Front. Hum. Neurosci..

[95]  C. Gallistel,et al.  Mathematical Cognition , 2005 .

[96]  Kaustubh Supekar,et al.  Dissociable connectivity within human angular gyrus and intraparietal sulcus: evidence from functional and structural connectivity. , 2010, Cerebral cortex.

[97]  L. Fuchs,et al.  Pathways to Third-Grade Calculation Versus Word-Reading Competence: Are They More Alike or Different? , 2016, Child development.

[98]  A. De Visscher,et al.  Similarity interference in learning and retrieving arithmetic facts. , 2016, Progress in brain research.

[99]  Vinod Menon,et al.  Hippocampal–Prefrontal Engagement and Dynamic Causal Interactions in the Maturation of Children's Fact Retrieval , 2012, Journal of Cognitive Neuroscience.

[100]  Jamie I. D. Campbell,et al.  Cognitive arithmetic across cultures. , 2001, Journal of experimental psychology. General.

[101]  M. Delazer,et al.  Neuroscience of learning arithmetic—Evidence from brain imaging studies , 2009, Neuroscience & Biobehavioral Reviews.

[102]  D. Geary Mathematical disabilities: cognitive, neuropsychological, and genetic components. , 1993, Psychological bulletin.

[103]  Andreas Obersteiner,et al.  Arithmetic tasks in different formats and their influence on behavior and brain oxygenation as assessed with near-infrared spectroscopy (NIRS): a study involving primary and secondary school children , 2009, Journal of Neural Transmission.

[104]  Daniel Ansari,et al.  How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children's mathematical skills? A review of evidence from brain and behavior , 2013, Trends in Neuroscience and Education.

[105]  Lucina Q. Uddin,et al.  Neuroanatomical Correlates of Developmental Dyscalculia: Combined Evidence from Morphometry and Tractography , 2009, Front. Hum. Neurosci..

[106]  Chris Singleton,et al.  Do weak phonological representations impact on arithmetic development? A review of research into arithmetic and dyslexia. , 2008, Dyslexia.

[107]  F. Jones,et al.  Qualitative and Quantitative , 2014 .

[108]  D. Geary International Differences in Mathematical Achievement , 1996 .

[109]  Alice De Visscher,et al.  The interference effect in arithmetic fact solving: An fMRI study , 2015, NeuroImage.

[110]  Stanislas Dehaene,et al.  Arithmetic and the Brain This Review Comes from a Themed Issue on Cognitive Neuroscience Edited the Intraparietal Sulcus and Number Sense Number Sense in the Animal Brain , 2022 .

[111]  D. Ansari Effects of development and enculturation on number representation in the brain , 2008, Nature Reviews Neuroscience.

[112]  James R. Booth,et al.  How number line estimation skills relate to neural activations in single digit subtraction problems , 2015, NeuroImage.

[113]  F. Ramus Neurobiology of dyslexia: a reinterpretation of the data. , 2004, Trends in neurosciences.

[114]  M. Snowling Dyslexia, 2nd ed. , 2000 .

[115]  Sean M. Polyn,et al.  Beyond mind-reading: multi-voxel pattern analysis of fMRI data , 2006, Trends in Cognitive Sciences.

[116]  Vinod Menon,et al.  Working memory in children's math learning and its disruption in dyscalculia , 2016, Current Opinion in Behavioral Sciences.

[117]  D G Gadian,et al.  Calculation difficulties in children of very low birthweight: a neural correlate. , 2001, Brain : a journal of neurology.

[118]  Jun Won Kim,et al.  Desynchronization of Theta-Phase Gamma-Amplitude Coupling during a Mental Arithmetic Task in Children with Attention Deficit/Hyperactivity Disorder , 2016, PloS one.

[119]  Daniel Ansari,et al.  Second revision : Supplementary Material Linking brain-wide multivoxel activation patterns to behaviour : examples from language and math , 2010 .

[120]  Hui Zhao,et al.  Parietal hyper-connectivity, aberrant brain organization, and circuit-based biomarkers in children with mathematical disabilities. , 2016, Developmental science.

[121]  James L. McClelland,et al.  Why there are complementary learning systems in the hippocampus and neocortex: insights from the successes and failures of connectionist models of learning and memory. , 1995, Psychological review.

[122]  S. Dehaene,et al.  Cultural Recycling of Cortical Maps , 2007, Neuron.

[123]  R. Wagner,et al.  The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: a longitudinal study from second to fifth grades. , 2001, Journal of experimental child psychology.

[124]  A. Dowker Individual Differences in Arithmetic , 2012 .

[125]  A. Karmiloff-Smith Neuroimaging of the developing brain: Taking “developing” seriously , 2010, Human brain mapping.

[126]  Michael Schneider,et al.  Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: a meta-analysis. , 2017, Developmental science.

[127]  Roland Bammer,et al.  Arithmetic ability and parietal alterations: a diffusion tensor imaging study in velocardiofacial syndrome. , 2005, Brain research. Cognitive brain research.

[128]  A. Henik,et al.  Double Dissociation of Functions in Developmental Dyslexia and Dyscalculia , 2006 .

[129]  A. Connelly,et al.  White matter fiber tractography: why we need to move beyond DTI. , 2013, Journal of neurosurgery.

[130]  D. Geary,et al.  Predicting Children's Reading and Mathematics Achievement from Early Quantitative Knowledge and Domain-General Cognitive Abilities , 2016, Front. Psychol..

[131]  Larry R Squire,et al.  Medial Temporal Lobe Activity during Retrieval of Semantic Memory Is Related to the Age of the Memory , 2009, The Journal of Neuroscience.

[132]  Antony D. Passaro,et al.  Aberrant spatiotemporal activation profiles associated with math difficulties in children: a magnetic source imaging study. , 2008, Neuropsychology.

[133]  Stavros Dimitriadis,et al.  Simple and difficult mathematics in children: A minimum spanning tree EEG network analysis , 2014, Neuroscience Letters.

[134]  Jeannette E. Fleischner,et al.  Automatization and Basic Fact Performance of Normal and Learning Disabled Children , 1983 .

[135]  David C. Geary,et al.  Hippocampal-neocortical functional reorganization underlies children's cognitive development , 2014, Nature Neuroscience.

[136]  M. Pavlova,et al.  Arithmetic and brain connectivity: Mental calculation in adolescents with periventricular lesions , 2009, Neuropsychologia.

[137]  M. Barnes,et al.  A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics , 2016 .

[138]  Janet B W Williams,et al.  Diagnostic and Statistical Manual of Mental Disorders , 2013 .

[139]  Klarissa Ting-Ting Chang,et al.  Heterogeneous and nonlinear development of human posterior parietal cortex function , 2016, NeuroImage.

[140]  Mario Rodríguez-Camacho,et al.  Event-related potentials findings differ between children and adults during arithmetic-fact retrieval , 2010, Neuroscience Letters.

[141]  R. Siegler,et al.  Conscious and unconscious strategy discoveries: a microgenetic analysis. , 1998, Journal of experimental psychology. General.

[142]  K. Eklund,et al.  Counting and RAN: Predictors of Arithmetic Calculation and Reading Fluency. , 2013 .

[143]  Daniel Ansari,et al.  How is phonological processing related to individual differences in children's arithmetic skills? , 2010, Developmental science.

[144]  Bert De Smedt,et al.  Numerical Magnitude Representations and Individual Differences in Children's Arithmetic Strategy Use , 2012 .

[145]  Bert De Smedt,et al.  Does numerical processing uniquely predict first graders’ future development of single-digit arithmetic? , 2015 .

[146]  Darren J. Yeo,et al.  The relation between 1st grade grey matter volume and 2nd grade math competence , 2016, NeuroImage.

[147]  Brian A Wandell,et al.  Frontoparietal white matter diffusion properties predict mental arithmetic skills in children , 2009, Proceedings of the National Academy of Sciences.

[148]  A. Anastasi Individual differences. , 2020, Annual review of psychology.

[149]  H. V. Van Mier,et al.  The Contribution of Numerical Magnitude Comparison and Phonological Processing to Individual Differences in Fourth Graders’ Multiplication Fact Ability , 2016, PloS one.

[150]  Jeremy Kilpatrick,et al.  Adding It Up: Helping Children Learn Mathematics , 2013 .

[151]  Benoit M Dawant,et al.  Relation between brain architecture and mathematical ability in children: a DBM study. , 2013, Magnetic resonance imaging.

[152]  Christa Neuper,et al.  To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving , 2009, Neuropsychologia.

[153]  Karin Kucian,et al.  Development of Neural Networks for Exact and Approximate Calculation: A fMRI Study , 2008, Developmental neuropsychology.