Abstract
Arithmetic development is quintessential for learning more advanced mathematics. A key aspect of arithmetic development is a shift from calculation-based procedural strategies to memory-based fact retrieval. For example, children start to learn 3 × 4 by adding 4 + 4 + 4, which is an example of a procedure. After enough repetitions, this becomes an arithmetic fact. This chapter will review the scarce but growing evidence on how arithmetic strategy development in primary school children is reflected in the brain and how its functional networks change over development. The brain network in children recruited for doing arithmetic includes frontal, parietal, occipital-temporal and medial-temporal areas, with different foci depending on the strategy. We discuss studies that have compared different ages as well as longitudinal research. We review the results of brain imaging research that has examined the effects of educational interventions and experimental manipulations of arithmetic strategy on children’s brain activity. Such intervention and experimental studies are critical to unravel the brain mechanisms underlying the successful learning of arithmetic. On a broader note, such studies are able to assess the impact of real-world learning on brain activity patterns and therefore provide an excellent foundation to further the field of educational neuroscience.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278–291. https://doi.org/10.1038/nrn2334
Ansari, D. (2010). Neurocognitive approaches to developmental disorders of numerical and mathematical cognition: The perils of neglecting the role of development. Learning and Individual Differences, 20(2), 123–129. https://doi.org/10.1016/j.lindif.2009.06.001
Arsalidou, M., & Taylor, M. J. (2011). Is 2 + 2 = 4? Meta-analyses of brain areas needed for numbers and calculations. NeuroImage, 54, 2382–2393. https://doi.org/10.1016/j.neuroimage.2010.10.009
Arsalidou, M., Pawliw-Levac, M., Sadeghi, M., & Pascual-Leone, J. (2018). Brain areas associated with numbers and calculations in children: Meta-analyses of fMRI studies. Developmental Cognitive Neuroscience, 30, 239–250. https://doi.org/10.1016/j.dcn.2017.08.002
Bailey, D. H., Littlefield, A., & Geary, D. C. (2012). The codevelopment of skill at and preference for use of retrieval-based processes for solving addition problems: Individual and sex differences from first to sixth grades. Journal of Experimental Child Psychology, 113, 78–92. https://doi.org/10.1016/j.jecp.2012.04.014
Baroody, A. J. (1983). The development of procedural knowledge: An alternative explanation for chronometric trends of mental arithmetic. Developmental Review, 3(2), 225–230. https://doi.org/10.1016/0273-2297(83)90031-X
Baroody, A. J. (1994). An evaluation of evidence supporting fact-retrieval models. Learning and Individual Differences, 6(1), 1–36. https://doi.org/10.1016/1041-6080(94)90013-2
Barrouillet, P., & Fayol, M. (1998). From algorithmic computing to direct retrieval: Evidence from number and alphabetic arithmetic in children and adults. Memory & Cognition, 26(2), 355–368. https://doi.org/10.3758/BF03201146
Barrouillet, P., & Thevenot, C. (2013). On the problem-size effect in small additions: Can we really discard any counting-based account? Cognition, 128(1), 35–44. https://doi.org/10.1016/j.cognition.2013.02.018
Barrouillet, P., Mignon, M., & Thevenot, C. (2008). Strategies in subtraction problem solving in children. Journal of Experimental Child Psychology, 99(4), 233–251. https://doi.org/10.1016/j.jecp.2007.12.001
Blankenship, T. L., Keith, K., Calkins, S. D., & Bell, M. A. (2018). Behavioral performance and neural areas associated with memory processes contribute to math and reading achievement in 6-year-old children. Cognitive Development, 45, 141–151. https://doi.org/10.1016/j.cogdev.2017.07.002
Bloechle, J., Huber, S., Bahnmueller, J., Rennig, J., Willmes, K., Cavdaroglu, S., Moeller, K., & Klein, E. (2016). Fact learning in complex arithmetic—The role of the angular gyrus revisited. Human Brain Map**, 37(9), 3061–3079. https://doi.org/10.1002/hbm.23226
Bugden, S., Price, G. R., McLean, D. A., & Ansari, D. (2012). The role of the left intraparietal sulcus in the relationship between symbolic number processing and children’s arithmetic competence. Developmental Cognitive Neuroscience, 2(4), 448–457. https://doi.org/10.1016/j.dcn.2012.04.001
Campbell, J. I. D., & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130(2), 299–315. https://doi.org/10.1037/0096-3445.130.2.299
Chang, T.-T., Lee, P., & Metcalfe, A. W. S. (2018). Intrinsic insula network engagement underlying children ’ s reading and arithmetic skills. NeuroImage, 167(64), 162–177. https://doi.org/10.1016/j.neuroimage.2017.11.027
Chang, H., Rosenberg-Lee, M., Qin, S., & Menon, V. (2019). Faster learners transfer their knowledge better: Behavioral, mnemonic, and neural mechanisms of individual differences in children’s learning. Developmental Cognitive Neuroscience, 40, 100719. https://doi.org/10.1016/j.dcn.2019.100719
Cho, S., Ryali, S., Geary, D. C., & Menon, V. (2011). How does a child solve 7 + 8? Decoding brain activity patterns associated with counting and retrieval strategies. Developmental Science, 14(5), 989–1001. https://doi.org/10.1111/j.1467-7687.2011.01055.x
Cho, S., Metcalfe, A. W. S., Young, C. B., Ryali, S., Geary, D. C., & Menon, V. (2012). Hippocampal–prefrontal engagement and dynamic causal interactions in the maturation of childrenʼs fact retrieval. Journal of Cognitive Neuroscience, 24(9), 1849–1866.
Craig, A. D. (2002). How do you feel? Interoception: the sense of the physiological condition of the body. Nature Reviews Neuroscience, 3, 655–666.
De Smedt, B. (2018). Applications of cognitive neuroscience in educational research. In G. Noblit (Ed.), Oxford handbook of educational research. Oxford University Press. https://doi.org/10.1093/acrefore/9780190264093.013.69
De Smedt, B., Holloway, I. D., & Ansari, D. (2011). Effects of problem size and arithmetic operation on brain activation during calculation in children with varying levels of arithmetical fluency. NeuroImage, 57(3), 771–781. https://doi.org/10.1016/j.neuroimage.2010.12.037
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487–506. https://doi.org/10.1080/02643290244000239
Delazer, M., Domahs, F., Bartha, L., Brenneis, C., Lochy, A., Trieb, T., & Benke, T. (2003). Learning complex arithmetic—An fMRI study. Cognitive Brain Research, 18, 76–88. https://doi.org/10.1016/j.cogbrainres.2003.09.005
Delazer, M., Ischebeck, A., Domahs, F., Zamarian, L., Koppelstätter, F., Siedentopf, C., Kaufmann, L., Benke, T., & Felber, S. (2005). Learning by strategies and learning by drill—Evidence from an fMRI study. NeuroImage, 25, 838–849. https://doi.org/10.1016/j.neuroimage.2004.12.009
Ehri, L. C. (2005). In M. J. Snowling & C. Hulme (Eds.), Development of sight word reading: Phases and findings. Blackwell Publisching.
European Education and Culture Executive Agency, Eurydice, Ranguelov, S., Motiejunaite, A., & Kerpanova, V. (2015). Mathematics education in. Common Challenges and National Policies. https://doi.org/10.2797/72660
Fias, W., Lammertyn, J., Reynvoet, B., Dupont, P., & Orban, G. A. (2003). Parietal representation of symbolic and nonsymbolic magnitude. Journal of Cognitive Neuroscienceo, 15(1), 47–56. https://doi.org/10.1162/089892903321107819
Fias, W., Menon, V., & Szucs, D. (2013). Multiple components of developmental dyscalculia. Trends in Neuroscience and Education, 2, 43–47. https://doi.org/10.1016/j.tine.2013.06.006
Froyen, D. J. W., Bonte, M. L., Van Atteveldt, N., & Blomert, L. (2009). The long road to automation: Neurocognitive development of letter-speech sound processing. Journal of Cognitive Neuroscience, 21(3), 567–580. https://doi.org/10.1162/jocn.2009.21061
Geary, D. C., Bow-Thomas, C. C., & Yao, Y. (1992). Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children. Journal of Experimental Child Psychology, 54, 372–391.
Grabner, R. H., Ischebeck, A., Reishofer, G., Koschutnig, K., Delazer, M., Ebner, F., & Neuper, C. (2009). Fact learning in complex arithmetic and figural-spatial tasks: The role of the angular gyrus and its relation to mathematical competence. Human Brain Map**, 30(9), 2936–2952. https://doi.org/10.1002/hbm.20720
Howard-Jones, P. A., Ansari, D., Butterworth, B., De Smedt, B., Laurillard, D., Thomas, M. S. C., & Sashank, V. (2016). The principles and practices of educational neuroscience: Comment on bowers. Psychological Review, 123(5), 620–627.
Imbo, I., & Vandierendonck, A. (2008). Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: Differences between children and adults? Psychological Research, 72(3), 331–346. https://doi.org/10.1007/s00426-007-0112-8
Ischebeck, A., Zamarian, L., Siedentopf, C., Koppelstätter, F., Benke, T., Felber, S., & Delazer, M. (2006). How specifically do we learn? Imaging the learning of multiplication and subtraction. NeuroImage, 30, 1365–1375. https://doi.org/10.1016/j.neuroimage.2005.11.016
Iuculano, T., Rosenberg-Lee, M., Richardson, J., Tenison, C., Fuchs, L., Supekar, K., & Menon, V. (2015). Cognitive tutoring induces widespread neuroplasticity and remediates brain function in children with mathematical learning disabilities. Nature Communications, 6, 1–10. https://doi.org/10.1038/ncomms9453
Johnson, M. H. (2011). Developmental cognitive neuroscience interactive specialization : A domain-general framework for human functional brain development ? Accident Analysis and Prevention, 1(1), 7–21. https://doi.org/10.1016/j.dcn.2010.07.003
Jolles, D. D., Supekar, K., Richardson, J., Tenison, C., Ashkenazi, S., Rosenberg-Lee, M., Fuchs, L., & Menon, V. (2016). Reconfiguration of parietal circuits with cognitive tutoring in elementary school children. Cortex, 83, 231–245. https://doi.org/10.1016/j.cortex.2016.08.004
Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85(2), 103–119. https://doi.org/10.1016/S0022-0965(03)00032-8
Lemaire, P. (2018). Lifespan cognitive development: The role of strategies. In P. Lemaire (Ed.), Cognitive development from a strategy perspective (pp. 30–42). Routledge. https://doi.org/10.4324/9781315200446
Martin, A., Schurz, M., Kronbichler, M., & Richlan, F. (2015). Reading in the brain of children and adults: A meta-analysis of 40 functional magnetic resonance imaging studies. Human Brain Map**, 36(5), 1963–1981. https://doi.org/10.1002/hbm.22749
Menon, V. (2015). Arithmetic in the child and adult brain. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition (pp. 502–530). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.041
Menon, V., & Chang, H. (2021). Emerging neurodevelopmental perspectives on mathematical learning. Developmental Review, 60, 100964. https://doi.org/10.1016/j.dr.2021.100964
Metcalfe, A. W. S., Ashkenazi, S., Rosenberg-Lee, M., & Menon, V. (2013). Fractionating the neural correlates of individual working memory components underlying arithmetic problem solving skills in children. Developmental Cognitive Neuroscience, 6, 162–175. https://doi.org/10.1016/j.dcn.2013.10.001
Moscovitch, M., Cabeza, R., Winocur, G., & Nadel, L. (2016). Episodic memory and beyond: The hippocampus and neocortex in transformation. Annual Review of Psychology, 67(1), 105–134. https://doi.org/10.1146/annurev-psych-113011-143733
Peters, L., & De Smedt, B. (2018). Arithmetic in the develo** brain: A review of brain imaging studies. Developmental Cognitive Neuroscience, 30, 265–279. https://doi.org/10.1016/j.dcn.2017.05.002
Peters, L., Polspoel, B., Op de Beeck, H., & De Smedt, B. (2016). Brain activity during arithmetic in symbolic and non-symbolic formats in 9–12 year old children. Neuropsychologia, 86, 19–28. https://doi.org/10.1016/j.neuropsychologia.2016.04.001
Piazza, M., Pinel, P., Le Bihan, D., & Dehaene, S. (2007). A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron, 53, 293–305. https://doi.org/10.1016/j.neuron.2006.11.022
Polspoel, B., Peters, L., Vandermosten, M., & De Smedt, B. (2017). Strategy over operation: Neural activation in subtraction and multiplication during fact retrieval and procedural strategy use in children. Human Brain Map**, 38(9), 4657–4670. https://doi.org/10.1002/hbm.23691
Prado, J., Mutreja, R., & Booth, J. R. (2014). Developmental dissociation in the neural responses to simple multiplication and subtraction problems. Developmental Science, 17(4), 537–552. https://doi.org/10.1111/desc.12140
Qin, S., Cho, S., Chen, T., Rosenberg-Lee, M., Geary, D. C., & Menon, V. (2014). Hippocampal-neocortical functional reorganization underlies children’s cognitive development. Nature Neuroscience, 17(9), 1263–1269. https://doi.org/10.1038/nn.3788
Raichle, M. E. (2015). The brain’s default mode network. Annual Review of Neuroscience, 38, 433–447. https://doi.org/10.1146/annurev-neuro-071013-014030
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, 1779–1790. https://doi.org/10.1093/cercor/bhi055
Rosenberg-Lee, M. (2018). Training studies: An experimental design to advance educational neuroscience. Mind, Brain, and Education, 12(1), 12–22. https://doi.org/10.1111/mbe.12166
Rosenberg-Lee, M., Barth, M., & Menon, V. (2011). What difference does a year of schooling make? Maturation of brain response and connectivity between 2nd and 3rd grades during arithmetic problem solving. NeuroImage, 57, 796–808. https://doi.org/10.1016/j.neuroimage.2011.05.013
Rosenberg-Lee, M., Ashkenazi, S., Chen, T., Young, C. B., Geary, D. C., & Menon, V. (2015). Brain hyper-connectivity and operation-specific deficits during arithmetic problem solving in children with developmental dyscalculia. Developmental Science, 18(3), 351–372. https://doi.org/10.1111/desc.12216
Rosenberg-Lee, M., Iuculano, T., Bae, S. R., Richardson, J., Qin, S., Jolles, D. D., & Menon, V. (2018). Short-term cognitive training recapitulates hippocampal functional changes associated with one year of longitudinal skill development. Trends in Neuroscience and Education, 10(June 2017), 19–29. https://doi.org/10.1016/j.tine.2017.12.001
Siegler, R. S. (1996). Emerging minds : The process of change in children’s thinking. Oxford University Press.
Siegler, R. S., & Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), Origins of cognitive skills (pp. 229–293). Lawrence Erlbaum.
Soltanlou, M., Artemenko, C., Ehlis, A.-C., Huber, S., Fallgatter, A. J., Dresler, T., & Nuerk, H.-C. (2018). Reduction but no shift in brain activation after arithmetic learning in children: A simultaneous fNIRS-EEG study. Scientific Reports, May, 2017, 1–15. https://doi.org/10.1038/s41598-018-20007-x
Supekar, K., Swigart, A. G., Tenison, C., Jolles, D. D., Rosenberg-Lee, M., Fuchs, L., Menon, V., Posner, M., & by I. (2013). Neural predictors of individual differences in response to math tutoring in primary-grade school children. PNAS, 110(20), 8230–8235. https://doi.org/10.1073/pnas.1222154110
Thomason, M. E., Race, E., Burrows, B., Whitfield-Gabrieli, S., Glover, G. H., & Gabrieli, J. D. E. (2009). Development of spatial and verbal working memory capacity in the human brain. Journal of Cognitive Neuroscience, 21(2), 316–332. https://doi.org/10.1162/jocn.2008.21028
Torbeyns, J., De Smedt, B., Stassens, N., Ghesquiere, P., & Verschaffel, L. (2009). Solving subtraction problems by means of indirect addition. Mathematical Thinking and Learning, 11(1–2), 79–91. https://doi.org/10.1080/10986060802583998
Tschentscher, N., & Hauk, O. (2014). How are things adding up ? Neural differences between arithmetic operations are due to general problem solving strategies. NeuroImage, 92, 369–380. https://doi.org/10.1016/j.neuroimage.2014.01.061
Uddin, L. Q., Kinnison, J., Pessoa, L., & Anderson, M. L. (2014). Beyond the tripartite cognition-emotion-interoception model of the human insular cortex. Journal of Cognitive Neuroscience, 26(1), 16–27. https://doi.org/10.1162/jocn
Uittenhove, K., Thevenot, C., & Barrouillet, P. (2016). Fast automated counting procedures in addition problem solving: When are they used and why are they mistaken for retrieval? Cognition, 146, 289–303. https://doi.org/10.1016/j.cognition.2015.10.008
Van Opstal, F., Verguts, T., Orban, G. A., & Fias, W. (2008). A hippocampal-parietal network for learning an ordered sequence. NeuroImage, 40(1), 333–341. https://doi.org/10.1016/j.neuroimage.2007.11.027
Vanbinst, K., Ghesquière, P., & De Smedt, B. (2012). Representations and individual differences in children’s arithmetic strategy use. Mind, Brain, and Education, 6(3), 129–136.
Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557–628). Information Age Publishing.
Yeo, D. J., Wilkey, E. D., & Price, G. R. (2017). The search for the number form area : A functional neuroimaging meta-analysis. Neuroscience and Biobehavioral Reviews, 78(April), 145–160. https://doi.org/10.1016/j.neubiorev.2017.04.027
Zamarian, L., & Delazer, M. (2015). Arithmetic learning in adults: Evidence from brain imaging. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition. Oxford University Press.
Acknowledgement
This work has been supported by a research grant of the Fund for Scientific Research Flanders FWO (grant G.0638.17).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Declercq, M., Fias, W., De Smedt, B. (2023). The Development of Arithmetic Strategy Use in the Brain. In: Robinson, K.M., Dubé, A.K., Kotsopoulos, D. (eds) Mathematical Cognition and Understanding. Springer, Cham. https://doi.org/10.1007/978-3-031-29195-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-031-29195-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-29194-4
Online ISBN: 978-3-031-29195-1
eBook Packages: EducationEducation (R0)