Abstract
In this article, we review the brain and cognitive processes underlying the development of arithmetic skills. This review focuses primarily on the development of arithmetic skills in children, but it also summarizes relevant findings from adults for which a larger body of research currently exists. We integrate relevant findings and theories from experimental psychology and cognitive neuroscience. We describe the functional neuroanatomy of cognitive processes that influence and facilitate arithmetic skill development, including calculation, retrieval, strategy use, decision making, as well as working memory and attention. Building on recent findings from functional brain imaging studies, we describe the role of distributed brain regions in the development of mathematical skills. We highlight neurodevelopmental models that go beyond the parietal cortex role in basic number processing, in favor of multiple neural systems and pathways involved in mathematical information processing. From this viewpoint, we outline areas for future study that may help to bridge the gap between the cognitive neuroscience of arithmetic skill development and educational practice.
Similar content being viewed by others
References
Ackerman, B. P. (1996). Induction of a memory retrieval strategy by young children. Journal of Experimental Child Psychology, 62(2), 243–271.
Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278–291.
Arterberry, M. E., Milburn, M. M., Loza, H. L., & Willert, H. S. (2001). Retrieval of episodic information from memory: Comparisons among 3- and 4-year-olds, 7- and 8-year olds, and adults. Journal of Cognition and Development, 2, 283–305.
Ashcraft, M. H. (1982). The development of mental arithmetic: A chronometric approach. Developmental Review, 2, 213–236.
Baroody, A. J. (1987). The development of counting strategies for single-digit addition. Journal for Research in Mathematics Education, 18, 141–157.
Barth, H., La Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences of the United States of America, 102(39), 14116–14121.
Beilock, S. L., & Carr, T. H. (2005). When high-powered people fail: Working memory and “choking under pressure” in math. Psychological Science, 16(2), 101–105.
Besnon, D. F., & Weir, W. F. (1972). Acalculia: Acquired anarithmetia. Cortex, 8(4), 465–472.
Bruandet, M., Molko, N., Cohen, L., & Dehaene, S. (2004). A cognitive characterization of dyscalculia in Turner syndrome. Neuropsychologia, 42(3), 288–298.
Bull, R., Epsy, K., & Wiebe, S. (2008). Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology, 33(3), 205–208.
Bunge, S. A., & Wright, S. B. (2007). Neurodevelopmental changes in working memory and cognitive control. Current Opinion in Neurobiology, 17(2), 243–250.
Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K. A. (2006). Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology, 4(5), e125.
Cantlon, J. F., Libertus, M. E., Pinel, P., Dehaene, S., Brannon, E. M., & Pelphrey, K. A. (2009). The neural development of an abstract concept of number. Journal of Cognitive Neuroscience, 21(11), 2217–2229.
Casey, B. J., Thomas, K. M., Davidson, M. C., Kunz, K., & Franzen, P. L. (2002). Dissociating striatal and hippocampal function developmentally with a stimulus–response compatibility task. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 22(19), 8647–8652.
Chang, C., Crottaz-Herbette, S., & Menon, V. (2007). Temporal dynamics of basal ganglia response and connectivity during verbal working memory. Neuroimage, 34(3), 1253–1269.
Chochon, F., Cohen, L., van de Moortele, P. F., & Dehaene, S. (1999). Differential contributions of the left and right inferior parietal lobules to number processing. Journal of Cognitive Neuroscience, 11(6), 617–630.
Cohen, L., & Dehaene, S. (2004). Specialization within the ventral stream: The case for the visual word form area. Neuroimage, 22(1), 466–476.
Crottaz-Herbette, S., Anagnoson, R. T., & Menon, V. (2004). Modality effects in verbal working memory: Differential prefrontal and parietal responses to auditory and visual stimuli. Neuroimage, 21(1), 340–351.
Crottaz-Herbette, S., & Menon, V. (2006). Where and when the anterior cingulate cortex modulates attentional response: Combined fMRI and ERP evidence. Journal of Cognitive Neuroscience, 18(5), 766–780.
Cycowicz, Y. M. (2000). Memory development and event-related brain potentials in children. Biological Psychology, 54(1–3), 145–174.
Cycowicz, Y. M., Friedman, D., Snodgrass, J. G., & Duff, M. (2001). Recognition and source memory for pictures in children and adults. Neuropsychologia, 39(3), 255–267.
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20(3/4/5/6), 487–506.
Delazer, M., & Benke, T. (1997). Arithmetic facts without meaning. Cortex: A Journal Devoted to the Study of the Nervous System and Behavior, 33(4), 697–710.
Delazer, M., Domahs, F., Bartha, L., Brenneis, C., Lochy, A., Trieb, T., et al. (2003). Learning complex arithmetic—An fMRI study. Brain Research: Cognitive Brain Research, 18(1), 76–88.
Delazer, M., Domahs, F., Lochy, A., Bartha, L., Brenneis, C., & Trieb, T. (2004). The acquisition of arithmetic knowledge—An fMRI study. Cortex, 40(1).
Delazer, M., Ischebeck, A., Domahs, F., Zamarian, L., Koppelstaetter, F., Siedentopf, C. M., et al. (2005). Learning by strategies and learning by drill—Evidence from an fMRI study. Neuroimage, 25(3), 838–849.
Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience, and education. New York: Psychology Press.
Eichenbaum, H. (2000). Hippocampus: Mapping or memory? Current Biology, 10, R785–R787.
Fuchs, L. S., Compton, D. L., Fuchs, D., Paulsen, K., Bryant, J. D., & Hamlett, C. L. (2005). The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology, 97, 493–513.
Fuchs, L. S., Powell, S. R., Hamlett, C. L., Fuchs, D., Cirino, P. T., & Fletcher, J. M. (2007). Remediating computational deficits at third grade: A randomized field trial. Journal of Research on Educational Effectiveness (in press).
Geary, D. C. (1990). A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology, 49(3), 363–383.
Geary, D. C. (1994). Children’s mathematical development: Research and practical applications. Washington, DC: American Psychological Association.
Geary, D. C., & Brown, S. C. (1991). Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children. Developmental Psychology, 27, 398–406.
Geary, D. C., & Damon, W. (2006). Development of mathematical understanding. In D. Kuhl & R. S. Siegler (Eds.), Handbook of child psychology (Vol. 6). New York: Wiley.
Geary, D. C., Hamson, C. O., & Hoard, M. K. (2000). Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology, 77(3), 236–263.
Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88(2), 121–151.
Geary, D. C., Hoard, M. K., Nugent, L., Byrd-Craven, J., Berch, D. B., & Mazzocco, M. M. (2007). Strategy use, long-term memory, and working memory capacity. In Anonymous (Ed.), Why is math so hard for some children? (pp. 83–105). Baltimore, MD: Paul H. Brookes Publishing Co.
Geary, D. C., Hoard, M. K., & Royer, J. M. (2002). Learning disabilities in basic mathematics: Deficits in memory and cognition. In Anonymous (Ed.), Mathematical cognition (pp. 93–115). Greenwich, CT: Information Age Publishing.
Geary, D. C., Widaman, K. F., & Little, T. D. (1986). Cognitive addition and multiplication: Evidence for a single memory network. Memory and Cognition, 14, 478–487.
Ghilardi, M., Ghez, C., Dhawan, V., Moeller, J., Mentis, M., Nakamura, T., et al. (2000). Patterns of regional brain activation associated with different forms of motor learning. Brain Research, 871(1), 127–145.
Girelli, L., Delazer, M., Semenza, C., & Denes, G. (1996). The representation of arithmetical facts: Evidence from two rehabilitation studies. Cortex: A Journal Devoted to the Study of the Nervous System and Behavior, 32(1), 49–66.
Gogtay, N., Giedd, J. N., Lusk, L., Hayashi, K. M., Greenstein, D., Vaituzis, A. C., et al. (2004). Dynamic mapping of human cortical development during childhood through early adulthood. Proceedings of the National Academy of Sciences of the United States of America, 101(21), 8174–8179.
Grabner, R. H., Ansari, D., Koschutnig, K., Reishofer, G., Ebner, F., & Neuper, C. (2009). To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia, 47(2), 604–608.
Groen, G. J., & Parkman, J. M. (1972). A chronometric analysis of simple addition. Psychological Review, 79(4), 329–343.
Gruber, O., Indefrey, P., Steinmetz, H., & Kleinschmidt, A. (2001). Dissociating neural correlates of cognitive components in mental calculation. Cerebral cortex (New York, N.Y.: 1991), 11(4), 350–359.
Hart, J, Jr., Kraut, M. A., Kremen, S., Soher, B., & Gordon, B. (2000). Neural substrates of orthographic lexical access as demonstrated by functional brain imaging. Neuropsychiatry, Neuropsychology, and Behavioral Neurology, 13(1), 1–7.
Henschen, S. (1920). Klinische und anatomische beitraege sur pathologie des Gehirns. Stockholm, Sweden: Nordiska Bokhandeln.
Hitch, G. J., & McAuley, E. (1991). Working memory in children with specific arithmetical learning difficulties. British Journal of Psychology, 82(3), 375–386.
Ischebeck, A., Zamarian, L., Egger, K., Schocke, M., & Delazer, M. (2007). Imaging early practice effects in arithmetic. Neuroimage, 36(3), 993–1003.
Ischebeck, A., Zamarian, L., Siedentopf, C., Koppelstatter, F., Benke, T., Felber, S., et al. (2006). How specifically do we learn? Imaging the learning of multiplication and subtraction. Neuroimage, 30(4), 1365–1375.
Kahn, H. J., & Whitaker, H. A. (1991). Acalculia: An historical review of localization. Brain and Cognition, 17, 102–115.
Kail, R., & Park, Y. S. (1994). Processing time, articulation time, and memory span. Journal of Experimental Child Psychology, 57(2), 281–291.
Kail, R., & Salthouse, T. A. (1994). Processing speed as a mental capacity. Acta Psychologica, 86(2–3), 199–225.
Kronbichler, M., Hutzler, F., Wimmer, H., Mair, A., Staffen, W., & Ladurner, G. (2004). The visual word form area and the frequency with which words are encountered: Evidence from a parametric fMRI study. Neuroimage, 21(3), 946–953.
Kwon, H., Reiss, A. L., & Menon, V. (2002). Neural basis of protracted developmental changes in visuo-spatial working memory. Proceedings of the National Academy of Sciences of the United States of America, 99(20), 13336–13341.
Lee, K. M. (2000). Cortical areas differentially involved in multiplication and subtraction: A functional magnetic resonance imaging study and correlation with a case of selective acalculia. Annals of Neurology, 48(4), 657–661.
LeFevre, J. A., Bisanz, J., & Mrkonjic, L. (1988). Cognitive arithmetic: Evidence for obligatory activation of arithmetic facts. Memory and Cognition, 16, 45–53.
Lyon, G. R., & Rumsey, J. M. (1996). Neuroimaging: A window to the neurological foundations of learning and behavior in children. Baltimore, MD: Paul H. Brooke.
McCarthy, R. A., & Warrington, E. K. (1988). Evidence for modality-specific meaning systems in the brain. Nature, 334(6181), 428–430.
McCloskey, M., Harley, W., & Sokol, S. M. (1991). Models of arithmetic fact retrieval: An evaluation in light of findings from normal and brain-damaged subjects. Journal of Experimental Psychology: Learning Memory and Cognition, 17(3), 377–397.
McNeil, J. E., & Warrington, E. K. (1994). A dissociation between addition and subtraction with written calculation. Neuropsychologia, 32(6), 717–728.
Menon, V., Boyett-Anderson, J. M., & Reiss, A. L. (2005). Maturation of medial temporal lobe response and connectivity during memory encoding. Cognitive Brain Research, 25(1), 379–385.
Menon, V., Mackenzie, K., Rivera, S. M., & Reiss, A. L. (2002). Prefrontal cortex involvement in processing incorrect arithmetic equations: Evidence from event-related fMRI. Human Brain Mapping, 16(2), 119–130.
Menon, V., Rivera, S. M., White, C. D., Eliez, S., Glover, G. H., & Reiss, A. L. (2000a). Functional optimization of arithmetic processing in perfect performers. Cognitive Brain Research, 9(3), 343–345.
Menon, V., Rivera, S. M., White, C. D., Glover, G. H., & Reiss, A. L. (2000b). Dissociating prefrontal and parietal cortex activation during arithmetic processing. Neuroimage, 12(4), 357–365.
Menon, V., White, C. D., Eliez, S., Glover, G. H., & Reiss, A. L. (2000c). Analysis of a distributed neural system involved in spatial information, novelty, and memory processing. Human Brain Mapping, 11(2), 117–129.
Meyer, M. L., Salimpoor, V. N., Wu, S. S., Geary, D., & Menon, V. (2009). Differential contribution of specific working memory components to mathematical skills in 2nd and 3rd graders. Learning and Individual Differences (in press).
Miller, K., Perlmutter, M., & Keating, D. (1984). Cognitive arithmetic: Comparison of operations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10, 46–60.
Niedeggen, M., Rosler, F., & Jost, K. (1999). Processing of incongruous mental calculation problems: Evidence for an arithmetic N400 effect. Psychophysiology, 36(3), 307–324.
Ofen, N., Kao, Y. C., Sokol-Hessner, P., Kim, H., Whitfield-Gabrieli, S., & Gabrieli, J. D. (2007). Development of the declarative memory system in the human brain. Nature Neuroscience, 10(9), 1198–1205.
Olesen, P. J., Macoveanu, J., Tegnér, J., & Klingberg, T. (2007). Brain activity related to working memory and distraction in children and adults. Cerebral Cortex, 17(5), 1047–1054.
Olesen, P. J., Westerberg, H., & Klingberg, T. (2004). Increased prefrontal and parietal activity after training of working memory. Nature Neuroscience, 7(1), 75–79.
Packard, M. G., & Knowlton, B. J. (2002). Learning and memory functions of the basal ganglia. Annual Review of Neuroscience, 25, 563–593.
Passolunghi, M. C., & Siegel, L. S. (2001). Short-term memory, working memory, and inhibitory control in children with difficulties in arithmetic problem solving. Journal of Experimental Child Psychology, 80(1), 44–57.
Passolunghi, M. C., & Siegel, L. S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88(4), 348–367.
Price, C. J., & Devlin, J. T. (2003). The myth of the visual word form area. Neuroimage, 19(3), 473–481.
Price, C. J., & Devlin, J. T. (2004). The pro and cons of labelling a left occipitotemporal region: “The visual word form area”. Neuroimage, 22(1), 477–479.
Rickard, T. C., & Bourne, L. E. (1996). Some tests of an identical elements model of basic arithmetic skills. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22, 1281–1295.
Rickard, T. C., Romero, S. G., Basso, G., Wharton, C., Flitman, S., & Grafman, J. (2000). The calculating brain: An fMRI study. Neuropsychologia, 38(3), 325–335.
Rivera, S. M., Reiss, A. L., Eckert, M. A., & Menon, V. (2005). Developmental changes in mental arithmetic: Evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex, 15(11), 1779–1790.
Rosenberg-Lee, M., Tsang, J. M., & Menon, V. (2009). Symbolic, numeric, and magnitude representations in the parietal cortex. Behavioral Brain Sciences, 32(3-4), 350–351. discussion 356–373.
Salimpoor, V. N., Chang, C., & Menon, V. (2009). Neural basis of repetition priming during mathematical cognition: Repetition suppression or repetition enhancement? J Cogn Neurosci.
Schacter, D. L., & Wagner, A. D. (1999). Medial temporal lobe activations in fMRI and PET studies of episodic encoding and retrieval. Hippocampus, 9(1), 7–24.
Schneider, W., & Goswami, U. (2002). Memory development in childhood. In Anonymous (Ed.), Blackwell handbook of childhood cognitive development (pp. 236–256). London, UK: Blackwell.
Shaw, P., Kabani, N. J., Lerch, J. P., Eckstrand, K., Lenroot, R., Gogtay, N., et al. (2008). Neurodevelopmental trajectories of the human cerebral cortex. Journal of Neuroscience, 28(14), 3586–3594.
Siegel, L. S., & Ryan, E. B. (1989). The development of working memory in normally achieving and subtypes of learning disabled children. Child Development, 60(4), 973–980.
Siegler, R. S. (1998). Children’s Thinking. New Jersey: Prentice Hall.
Siegler, R. S., & Shrager, J. (1984). Strategy choice in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), Origins of cognitive skills (pp. 229–293). Hillsdale, NJ: Erlbaum.
Siegler, R. S., & Stern, E. (1998). Conscious and unconscious strategy discoveries: A microgenetic analysis. Journal of Experimental Psychology: General, 127(4), 377–397.
Simon, O., Mangin, J. F., Cohen, L., Le Bihan, D., & Dehaene, S. (2002). Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe. Neuron, 33(3), 475–487.
Squire, L. R., Stark, C. E., & Clark, R. E. (2004). The medial temporal lobe. Annual Review of Neuroscience, 27, 279–306.
Supekar, K., Musen, M., & Menon, V. (2009). Development of large-scale functional brain networks in children. PLoS Biology, 7(7), e1000157.
Suzuki, W. A., & Amaral, D. G. (1994). Perirhinal and parahippocampal cortices of the macaque monkey: Cortical afferents. The Journal of Comparative Neurology, 350(4), 497–533.
Swanson, H. L. (1994). Short-term memory and working memory: Do both contribute to our understanding of academic achievement in children and adults with learning disabilities? Journal of Learning Disabilities, 27(1), 34–50.
Swanson, H. L., Cooney, J. B., & Brock, S. (1993). The influence of working memory and classification ability on children’s word problem solution. Journal of Experimental Child Psychology, 55(3), 374–395.
Swanson, H. L., & Sachse-Lee, C. (2001). Mathematical problem solving and working memory in children with learning disabilities: Both executive and phonological processes are important. Journal of Experimental Child Psychology, 79(3), 294–321.
Takayama, Y., Sugishita, M., Akiguchi, I., & Kimura, J. (1994). Isolated acalculia due to left parietal lesion. Archives of Neurology, 51(3), 286–291.
Temple, C. M. (2002). Developmental dyscalculia. In F. B. A. J. Grafman (Ed.), Handbook of Neuropsychology (Vol. 6: Child Psychology, pp. 211–222). North Holland: Elsevier Science Publishers.
van der Sluis, S., van der Leij, A., & de Jong, P. F. (2005). Working memory in Dutch children with reading- and arithmetic-related LD. Journal of Learning Disabilities, 38(3), 207–221.
van Harskamp, N. J., & Cipolotti, L. (2001). Selective impairments for addition, subtraction and multiplication. implications for the organisation of arithmetical facts. Cortex: A Journal Devoted to the Study of the Nervous System and Behavior, 37(3), 363–388.
van Merrienboer, J. J. G., & Sweller, J. (2005). Cognitive load theory and complex learning: Recent developments and future directions. Educational Psychology Review, 17(2), 147–177.
Venkatraman, V., Ansari, D., & Chee, M. W. (2005). Neural correlates of symbolic and non-symbolic arithmetic. Neuropsychologia, 43(5), 744–753.
Warrington, E. K. (1982). The fractionation of arithmetical skills: A single case study. Quarterly Journal of Experimental Psychology, 34, 31–51.
Westerberg, H., & Klingberg, T. (2007). Changes in cortical activity after training of working memory–a single-subject analysis. Physiology & Behavior, 92(1–2), 186–192.
Wilson, K. M., & Swanson, H. L. (2001). Are mathematics disabilities due to a domain-general or a domain-specific working memory deficit? Journal of Learning Disabilities, 34(3), 237–248.
Wu, S. S., Chang, T. T., Majid, A., Caspers, S., Eickhoff, S. B., & Menon, V. (2009). Functional heterogeneity of inferior parietal cortex during mathematical cognition assessed with cytoarchitectonic probability maps. Cereb Cortex.
Wu, S. S., Meyer, M. L., Maeda, U., Salimpoor, V., Tomiyama, S., Geary, D. C., et al. (2008). Standardized assessment of strategy use and working memory in early mental arithmetic performance. Developmental Neuropsychology, 33(3), 365–393.
Zago, L., Pesenti, M., Mellet, E., Crivello, F., Mazoyer, B., & Tzourio-Mazoyer, N. (2001). Neural correlates of simple and complex mental calculation. Neuroimage, 13(2), 314–327.
Zamarian, L., Ischebeck, A., & Delazer, M. (2009). Neuroscience of learning arithmetic-evidence from brain imaging studies. Neuroscience and Biobehavioral Reviews, 33(6), 909–925.
Acknowledgments
It is a pleasure to thank Meghan Meyer, Sarah Wu and Christina B Young for assistance in the preparation of this article, Dr. Mark Eckert for assistance with Fig. 3, and Dr. Miriam Rosenberg-Lee for the insightful comments and feedback. The preparation of this article was made possible by grants from the NIH (HD047520, HD059205) and the National Science Foundation (BCS/DRL 0449927).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Menon, V. Developmental cognitive neuroscience of arithmetic: implications for learning and education. ZDM Mathematics Education 42, 515–525 (2010). https://doi.org/10.1007/s11858-010-0242-0
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11858-010-0242-0