Skip to main navigation menu Skip to main content Skip to site footer
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 24 No. 3 (2021): November

DEVELOPMENT OF EARLY NUMERICAL ABILITY: CONTRIBUTIONS FROM COGNITIVE PSYCHOLOGY TO INITIAL MATHEMATICS EDUCATION

DOI
https://doi.org/10.12802/relime.21.2433
Submitted
November 8, 2022
Published
2021-11-30

Abstract

Numerical ability develops in the early years and is at the foundation of later math learning, as well as academic and job success in adulthood. Initial mathematics education has traditionally focused on the teaching of general processes, seeking the development of logical-mathematical thinking and mathematical language. This article seeks to reflect on the importance of training cognitive processes of the specific numerical domain, based on the findings in cognitive psychology. Thus, in this work the latest empirical evidence is reviewed, based on recent studies with behavioral approaches in numerical cognition, focused on the development of early numerical skills. To do this, the main milestones of numerical development are reviewed in relation to the acquisition of later arithmetic, taking into account the intrinsic and extrinsic influences on the individual during the early years.

References

  1. Anders, Y., Rossbach, H. G., Weinert, S., Ebert, S., Kuger, S., Lehrl, S., y von Maurice, J. (2012). Home and preschool learning environments and their relations to the development of early numeracy skills. Early Childhood Research Quarterly, 27(2), 231–244. https://doi.org/10.1016/j.ecresq.2011.08.00
  2. 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
  3. Ansari, D., Garcia, N., Lucas, E., Hamon, K., y Dhital, B. (2005). Neural correlates of symbolic number processing in children and adults. NeuroReport, 16(16), 1769–1773. https://doi.org/10.1097/01.wnr.0000183905.23396.f1
  4. Au, J., Jaeggi, S. M., y Buschkuehl, M. (2018). Effects of non-symbolic arithmetic training on symbolic arithmetic and the approximate number system. Acta Psychologica, 185(April 2017), 1–12. https://doi.org/10.1016/j.actpsy.2018.01.005
  5. Bugden, S., DeWind, N. K., y Brannon, E. M. (2016). Using cognitive training studies to unravel the mechanisms by which the approximate number system supports symbolic math ability. Current Opinion in Behavioral Sciences, 10, 73–80. https://doi.org/10.1016/j.cobeha.2016.05.002
  6. Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry and Allied Disciplines, 46(1), 3–18. https://doi.org/10.1111/j.1469-7610.2004.00374.x
  7. Carey, S. (2004). Susan Carey. Doedalus, Wonter(1), 59–68. https://doi.org/10.1162/001152604772746701
  8. Carey, S. (2009). The Origin of Concepts. The Origin of Concepts, 1–608. https://doi.org/10.1093/acprof:oso/9780195367638.001.0001
  9. Carey, S., y Barner, D. (2019). Ontogenetic Origins of Human Integer Representations. Trends in Cognitive Sciences, 1–13. https://doi.org/10.1016/j.tics.2019.07.004
  10. Chen, Q., y Li, J. (2014). Association between individual differences in non-symbolic number acuity and math performance: A meta-analysis. Acta Psychologica, 148, 163–172. https://doi.org/10.1016/j.actpsy.2014.01.016
  11. Chu, F. W., vanMarle, K., y Geary, D. C. (2015). Early numerical foundations of young children’s mathematical development. Journal of Experimental Child Psychology, 132, 205–212. https://doi.org/10.1016/j.jecp.2015.01.006
  12. Clements, D. H., y Sarama, J. (2008). Experimental Evaluation of the Effects of a Research-Based Preschool Mathematics Curriculum. American Educational Research Journal, 45(2), 443–494. https://doi.org/10.3102/0002831207312908
  13. Crollen, V., Castronovo, J., y Seron, X. (2011). Under- and over-estimation: A bi-directional mapping process between symbolic and non-symbolic representations of number? Experimental Psychology, 58(1), 39–49. https://doi.org/10.1027/1618-3169/a000064
  14. Dehaene, S. (2011). The number sense. New York: Oxford University Press.
  15. Dehaene, S., Piazza, M., Pinel, P., y Cohen, L. (2003). Three Parietal Circuits for Number Processing. Cognitive Neuropsychology, 20(3–6), 487–506. https://doi.org/10.1080/02643290244000239 del Río, M. F., Susperreguy, M. I., Strasser, K., y Salinas, V. (2017). Distinct Influences of Mothers and Fathers on Kindergartners’ Numeracy Performance: The Role of Math Anxiety, Home Numeracy Practices, and Numeracy Expectations. Early Education and Development, 28(8), 939–955. https://doi.org/10.1080/10409289.2017.1331662
  16. Dolscheid, S., Winter, C., Ostrowski, L., y Penke, M. (2017). The many ways quantifiers count: Children’s quantifier comprehension and cardinal number knowledge are not exclusively related. Cognitive Development, 44(August), 21–31. https://doi.org/10.1016/j.cogdev.2017.08.004
  17. Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., ... Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. https://doi.org/10.1037/0012-1649.43.6.1428; 10.1037/0012-1649.43.6.1428.supp (Supplemental)
  18. Ebersbach, M. (2016). Development of Children’s Estimation Skills: The Ambiguous Role of Their Familiarity With Numerals. Child Development Perspectives, 10(2), 116–121. https://doi.org/10.1111/cdep.12172
  19. Ebersbach, M., y Erz, P. (2014). Symbolic versus non-symbolic magnitude estimations among children and adults. Journal of Experimental Child Psychology, 128, 52–68. https://doi.org/10.1016/j.jecp.2014.06.005
  20. Emerson, R. W., y Cantlon, J. F. (2015). Continuity and change in children’s longitudinal neural responses to numbers. Developmental Science, 18(2), 314–326. https://doi.org/10.1111/desc.12215
  21. Feigenson, L., Dehaene, S., y Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314. https://doi.org/10.1016/j.tics.2004.05.002
  22. Fuchs, L. S., Geary, D. C., Fuchs, D., Hamlett, C. L., y Bryant, J. D. (2010). Do Different Types of School Mathematics Development Depend on Different Constellations of Numerical versus General Cognitive Abilities?, 46(6), 1731–1746. https://doi.org/10.1037/a0020662.Do
  23. Fuson, K. C. (1992). Research on whole number addition and subtraction. In Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics. (pp. 243–275). New York, NY, England: Macmillan Publishing Co, Inc.
  24. Gashaj, V., Oberer, N., Mast, F. W., y Roebers, C. M. (2019). Individual differences in basic numerical skills: The role of executive functions and motor skills. Journal of Experimental Child Psychology, 182, 187–195. https://doi.org/10.1016/j.jecp.2019.01.021
  25. Geary, D. C. (1995). Reflections of evolution and culture in children’s cognition. Implications for mathematical development and instruction. American Psychologist, 50(1), 24–37.
  26. Geary, D. C., Nicholas, A., Li, Y., y Sun, J. (2017). Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement : An Eight-Year Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achie. Journal of Educational Psychology, 109(5), 680–693. https://doi.org/10.1037/edu0000159
  27. Gelman, R., y Gallistel, C. R. (1978). The Child’s Understanding of Number. Cambridge, MA: Harvard University Press.
  28. Goffin, C., y Ansari, D. (2016). Beyond magnitude: Judging ordinality of symbolic number is unrelated to magnitude comparison and independently relates to individual differences in arithmetic. Cognition, 150. https://doi.org/10.1016/j.cognition.2016.01.018
  29. Goffin, C., y Ansari, D. (2019). How Are Symbols and Nonsymbolic Numerical Magnitudes Related? Exploring Bidirectional Relationships in Early Numeracy. Mind, Brain, and Education, 13(3), 143–156. https://doi.org/10.1111/mbe.12206
  30. Guillaume, M., Nys, J., Mussolin, C., y Content, A. (2013). Differences in the acuity of the Approximate Number System in adults: The effect of mathematical ability. Acta Psychologica, 144(3), 506–512. https://doi.org/10.1016/j.actpsy.2013.09.001
  31. Holloway, I. D., y Ansari, D. (2009). Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children’s mathematics achievement. Journal of Experimental Child Psychology, 103(1), 17–29. https://doi.org/10.1016/j.jecp.2008.04.001
  32. Hornung, C., Schiltz, C., Brunner, M., y Martin, R. (2014). Predicting first-grade mathematics achievement: The contributions of domain-general cognitive abilities, nonverbal number sense, and early number competence. Frontiers in Psychology, 5(APR). https://doi.org/10.3389/fpsyg.2014.00272
  33. Hyde, D. C., Khanum, S., y Spelke, E. S. (2014). Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 131(1), 92–107. https://doi.org/10.1016/j.cognition.2013.12.007
  34. Jiménez-Lira, C., Carver, M., Douglas, H., y LeFevre, J. A. (2017). The integration of symbolic and non-symbolic representations of exact quantity in preschool children. Cognition, 166, 382–397. https://doi.org/10.1016/j.cognition.2017.05.033
  35. Jordan, N. C., y Levine, S. C. (2009). Socioeconomic variation, number competence, and mathematics learning difficulties in young children. Developmental Disabilities Research Reviews, 15(1), 60–68. https://doi.org/10.1002/ddrr.46
  36. Kaufmann, L., Koppelstaetter, F., Siedentopf, C., Haala, I., Haberlandt, E., Zimmerhackl, L. B., ... Ischebeck, A. (2006). Neural correlates of the number-size interference task in children. NeuroReport, 17(6), 587–591. https://doi.org/10.1097/00001756-200604240-00007
  37. Le Corre, M., y Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition, 105(2), 395–438. https://doi.org/10.1016/j.cognition.2006.10.005
  38. Lefevre, J. A., Fast, L., Skwarchuk, S. L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., y Penner-Wilger, M. (2010). Pathways to Mathematics: Longitudinal Predictors of Performance. Child Development, 81(6), 1753–1767. https://doi.org/10.1111/j.1467-8624.2010.01508.x
  39. Lefevre, J. A., Kwarchuk, S. L., Smith-Chant, B. L., Fast, L., Kamawar, D., y Bisanz, J. (2009). Home numeracy experiences and children’s math performance in the early school years. Canadian Journal of Behavioural Science, 41(2), 55–66. https://doi.org/10.1037/a0014532
  40. Leibovich, T., y Ansari, D. (2016). The symbol-grounding problem in numerical cognition: A review of theory, evidence, and outstanding questions. Canadian Journal of Experimental Psychology/Revue Canadienne de Psychologie Expérimentale, 70(1), 12–23. https://doi.org/10.1037/cep0000070
  41. Leibovich, T., Katzin, N., Harel, M., y Henik, A. (2017). From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition. Behavioral and Brain Sciences, 40. https://doi.org/10.1017/S0140525X16000960
  42. Libertus, M. E. (2015). The role of intuitive approximation skills for school math abilities. Mind, Brain, and Education, 9(2), 112–120. https://doi.org/10.1111/mbe.12072
  43. Libertus, M. E., Odic, D., Feigenson, L., y Halberda, J. (2016). The precision of mapping between number words and the approximate number system predicts children’s formal math abilities. Journal of Experimental Child Psychology, 150. https://doi.org/10.1016/j.jecp.2016.06.003
  44. Lipton, J. S., y Spelke, E. S. (2005). Preschool Children’s Mapping of Number Words to Nonsymbolic Numerosities. Child Development, 76(5), 978–988.
  45. Lyons, I. M., Price, G. R., Vaessen, A., Blomert, L., y Ansari, D. (2014). Numerical predictors of arithmetic success in grades 1-6. Developmental Science, 17(5), 714–726. https://doi.org/10.1111/desc.12152
  46. Lyons, I. M., Vogel, S. E., y Ansari, D. (2016). On the ordinality of numbers: A review of neural and behavioral studies. Progress in Brain Research (1st ed., Vol. 227). Elsevier B.V. https://doi.org/10.1016/bs.pbr.2016.04.010
  47. Lyons, Ian M, y Beilock, S. L. (2013). Ordinality and the Nature of Symbolic Numbers, 33(43), 17052–17061. https://doi.org/10.1523/JNEUROSCI.1775-13.2013
  48. Maertens, B., De Smedt, B., Sasanguie, D., Elen, J., y Reynvoet, B. (2016). Enhancing arithmetic in pre-schoolers with comparison or number line estimation training: Does it matter? Learning and Instruction, 46, 1–11. https://doi.org/10.1016/j.learninstruc.2016.08.004
  49. Manolitsis, G., Georgiou, G. K., y Tziraki, N. (2013). Examining the effects of home literacy and numeracy environment on early reading and math acquisition. Early Childhood Research Quarterly, 28(4), 692–703. https://doi.org/10.1016/j.ecresq.2013.05.004
  50. Matejko, A. A., y Ansari, D. (2016). Trajectories of symbolic and nonsymbolic magnitude processing in the first year of formal schooling. PLoS ONE, 11(3), 1–15. https://doi.org/10.1371/journal.pone.0149863
  51. Mejias, S., y Schiltz, C. (2013). Estimation abilities of large numerosities in Kindergartners. Frontiers in Psychology, 4(August), 1–12. https://doi.org/10.3389/fpsyg.2013.00518
  52. Melhuish, E. C., Phan, M. B., Sylva, K., Sammons, P., Siraj-Blatchford, I., y Taggart, B. (2008). Effects of the home learning environment and preschool center experience upon literacy and numeracy development in early primary school. Journal of Social Issues, 64(1), 95–114. https://doi.org/10.1111/j.1540-4560.2008.00550.x
  53. Merkley, R., y Ansari, D. (2016). Why numerical symbols count in the development of mathematical skills: Evidence from brain and behavior. Current Opinion in Behavioral Sciences, 10, 14–20. https://doi.org/10.1016/j.cobeha.2016.04.006
  54. Moyer, R. S., y Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215, 1519–1520. https://doi.org/10.1038/2151519a0
  55. Mundy, E., y Gilmore, C. K. (2009). Children’s mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology, 103(4), 490–502. https://doi.org/10.1016/j.jecp.2009.02.003
  56. Mussolin, C., Nys, J., Leybaert, J., y Content, A. (2016). How approximate and exact number skills are related to each other across development: A review. Developmental Review, 39, 1–15. https://doi.org/10.1016/j.dr.2014.11.001
  57. Núñez, R. E. (2017). Is There Really an Evolved Capacity for Number? Trends in Cognitive Sciences, 21(6), 409–424. https://doi.org/10.1016/j.tics.2017.03.005
  58. O’Connor, P. A., Morsanyi, K., y McCormack, T. (2018). Young children’s non-numerical ordering ability at the start of formal education longitudinally predicts their symbolic number skills and academic achievement in maths. Developmental Science, 21(5), 1–16. https://doi.org/10.1111/desc.12645
  59. Obersteiner, A., Reiss, K., y Ufer, S. (2013). How training on exact or approximate mental representations of number can enhance first-grade students’ basic number processing and arithmetic skills. Learning and Instruction, 23(1). https://doi.org/10.1016/j.learninstruc.2012.08.004
  60. Odic, D., Le Corre, M., y Halberda, J. (2015). Children’s mappings between number words and the approximate number system. Cognition, 138(May), 102–121. https://doi.org/10.1016/j.cognition.2015.01.008
  61. Paliwal, V., y Baroody, A. J. (2018). Early Childhood Research Quarterly How best to teach the cardinality principle ? Early Childhood Research Quarterly, 44, 152–160. https://doi.org/10.1016/j.ecresq.2018.03.012
  62. Park, J., y Brannon, E. M. (2013). Training the Approximate Number System Improves Math Proficiency. Psychological Science, 24(10). https://doi.org/10.1177/0956797613482944
  63. Park, J., y Brannon, E. M. (2014). Improving arithmetic performance with number sense training: An investigation of underlying mechanism. Cognition, 133(1). https://doi.org/10.1016/j.cognition.2014.06.011
  64. Purpura, D. J., Baroody, A. J., y Lonigan, C. J. (2013). The transition from informal to formal mathematical knowledge: Mediation by numeral knowledge. Journal of Educational Psychology, 105(2), 453–464. https://doi.org/10.1037/a0031753
  65. Reynvoet, B., y Sasanguie, D. (2016). The Symbol Grounding Problem Revisited : A Thorough Evaluation of the ANS Mapping Account and the Proposal of an Alternative Account Based on Symbol – Symbol Associations, 7(October), 1–11. https://doi.org/10.3389/fpsyg.2016.01581
  66. Ritchie, S. J., y Bates, T. C. (2013). Enduring Links From Childhood Mathematics and Reading Achievement to Adult Socioeconomic Status. Psychological Science, 24(7), 1301–1308. https://doi.org/10.1177/0956797612466268
  67. Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J., y De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: a meta-analysis. Developmental Science, 20(3), 1–16. https://doi.org/10.1111/desc.12372
  68. Siegler, R. S., y Ramani, G. B. (2008). Playing linear numerical board games promotes low-income children’s numerical development. Developmental Science, 11(5), 655–661. https://doi.org/10.1111/j.1467-7687.2008.00714.x
  69. Simmons, F., Singleton, C., y Horne, J. (2008). Brief report - Phonological awareness and visual-spatial sketchpad functioning predict early arithmetic attainment: Evidence from a longitudinal study. European Journal of Cognitive Psychology, 20(4), 711–722. https://doi.org/10.1080/09541440701614922.
  70. Skwarchuk, S. L., Sowinski, C., y LeFevre, J. A. (2014). Formal and informal home learning activities in relation to children’s early numeracy and literacy skills: The development of a home numeracy model. Journal of Experimental Child Psychology, 121(1), 63–84. https://doi.org/10.1016/j.jecp.2013.11.006
  71. Sokolowski, H. M., Fias, W., Mousa, A., y Ansari, D. (2017). Common and distinct brain regions in both parietal and frontal cortex support symbolic and nonsymbolic number processing in humans: A functional neuroimaging meta-analysis. NeuroImage, 146(October 2016), 376–394. https://doi.org/10.1016/j.neuroimage.2016.10.028
  72. Spaepen, E., Gunderson, E. A., Gibson, D., Goldin-Meadow, S., y Levine, S. C. (2018). Meaning before order: Cardinal principle knowledge predicts improvement in understanding the successor principle and exact ordering. Cognition, 180(July), 59–81. https://doi.org/10.1016/j.cognition.2018.06.012
  73. Susperreguy, M. I. (2016). Math Talk Between Children and Mothers and Its Connection to Math-Related Practices in the Home Setting. In P. E. Davis-Kean y S. Tang (Eds.), Socializing Children Through Language (pp. 81–109). London, UK: Academic Press. https://doi.org/10.1016/B978-0-12-803624-2.00004-7
  74. Susperreguy, M. I., Douglas, H., Xu, C., Molina-Rojas, N., y LeFevre, J. A. (2018). Expanding the Home Numeracy Model to Chilean children: Relations among parental expectations, attitudes, activities, and children’s mathematical outcomes. Early Childhood Research Quarterly. https://doi.org/10.1016/j.ecresq.2018.06.010
  75. Szkudlarek, E., y Brannon, E. M. (2017). Does the Approximate Number System Serve as a Foundation for Symbolic Mathematics? Language Learning and Development, 00(00), 1–20. https://doi.org/10.1080/15475441.2016.1263573
  76. Teghtsoonian, R. (1973). Range effects in psychophysical scaling and a revision of Steven’s law. The American Journal of Psychology, 86, 3–27.
  77. Träff, U. (2013). The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children. Journal of Experimental Child Psychology, 116(2), 139–156. https://doi.org/10.1016/j.jecp.2013.04.007
  78. Van Herwegen, J., Costa, H. M., Nicholson, B., y Donlan, C. (2018). Improving number abilities in low achieving preschoolers: Symbolic versus non-symbolic training programs. Research in Developmental Disabilities, 77(March), 1–11. https://doi.org/10.1016/j.ridd.2018.03.011
  79. Vanbinst, K., y De Smedt, B. (2016). Individual differences in children’s mathematics achievement: The roles of symbolic numerical magnitude processing and domain-general cognitive functions. Progress in Brain Research, 1–26. https://doi.org/10.1016/bs.pbr.2016.04.001
  80. Wong, T. T. Y., Ho, C. S. H., y Tang, J. (2016). The relation between ANS and symbolic arithmetic skills: The mediating role of number-numerosity mappings. Contemporary Educational Psychology, 46, 208–217. https://doi.org/10.1016/j.cedpsych.2016.06.003
  81. Wynn, R. E. N. (1990). Children’s understanding of counting. Cognition, 36, 155–193.
  82. Xu, F., y Arriaga, R. I. (2007). Number discrimination in 10-month-old infants. British Journal of Developmental Psychology, 25(1), 103–108. https://doi.org/10.1348/026151005X90704

Downloads

Download data is not yet available.

Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.