Journal of Research in Science, Mathematics and Technology Education

Development of number sense and numeration: a continuum hypothesis

Journal of Research in Science, Mathematics and Technology Education, Volume 6, Issue SI, June 2023, pp. 91-108
OPEN ACCESS VIEWS: 436 DOWNLOADS: 449 Publication date: 15 Jun 2023
ABSTRACT
This text focuses on the development of number sense, specifically addressing the challenges associated with understanding the number system, including the connections to and difficulties in early arithmetic learning. It provides a synthesis of the scientific literature related to this development. It concludes by proposing a hypothesis for the development of number sense, associated with the construction of dynamic and pictorial mental representations. This continuum proposes five key phases: perception of small quantities, additive thinking, multiplicative thinking and pre-place value, passage to tens and passage to hundreds and understanding place value.
KEYWORDS
mathematics, learning difficulty, number sense, numeration, subitizing, groupitizing, mental representation.
CITATION (APA)
Bisaillon, N. (2023). Development of number sense and numeration: a continuum hypothesis. Journal of Research in Science, Mathematics and Technology Education, 6(SI), 91-108. https://doi.org/10.31756/jrsmte.615SI
REFERENCES
  1. Barabé, G. (2011). Une étude du développement professionnel par l’intégration dans la pratique d’une approche visant le développement du potentiel mathématique des élèves. [Mémoire de maitrise]. http://hdl.handle.net/11143/5606
  2. Baroody, A. (2004). The developmental bases for early childhood number and operations standards.
  3. Bednarz, N., et Janvier-Dufour, B. (1984a). La numération : Les difficultés suscitées par son apprentissage. Grand N, 33, 1–11.
  4. Bednarz, N., et Janvier-Dufour, B. (1984b). La numération : Une stratégie didactique cherchant à favoriser une meilleure compréhension. Grand N, 34, 1–17.
  5. Bednarz, N., & Janvier-Dufour, B. (1986). Une étude des conceptions inappropriées développées par les enfants dans l’apprentissage de la numération au primaire. European Journal of Psychology of Education, 1, 17–33. https://doi.org/10.1007/BF03172567
  6. Bergeron, J.-L. (2003). Les cartes à points : Pour une meilleure perception des nombres. Les revues pédagogiques de la Mission laïque française, 50, 11–20.
  7. Bisaillon, N. (2021). Développement du sens du nombre et de la numération : élaboration d’un outil d’évaluation et d’une séquence didactique, [thèse de doctorat, Université de Montréal]. Papyrus. https://doi.org/1866/27259
  8. Bobis, J. (2007). From here to there: The path to computational fluency with multi-digit multiplication. Mathematics: Essentiel for learning, Essentiel for life, 53–59.
  9. Brissiaud, R. (2005). Comment les enfants apprennent à calculer. RETZ.
  10. Case, R., & Okamato, Y. (1996). The role of central conceptual structures in the development of children’s thought. Monographs of the Society for Research in Child Development, 61(1–2), v‑265. https://doi.org/10.1111/j.1540-5834.1996.tb00536.x
  11. Claessens, A., Duncan, G. J., & Egel, M. (2009). Kindergarten skills and fifth-grade achievement : Evidence from the ECLS-K. Economic of Education Review, 28(4), 415–427. https://doi.org/10.1016/j.econedurev.2008.09.003
  12. Clements, D. H. (1999). Subitizing: What is it ? Why teach it? Teaching Children Mathematics, 5(7), Article 7. https://doi.org/10.5951/TCM.5.7.0400
  13. Clark, F. B., & Kamii, C. (1996). Identification of Multiplicative Thinking in Children in Grades 1-5. Journal for Research in Mathematics Education, 27(1), Article 1. https://doi.org/10.2307/749196
  14. Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grows (Éd.), Handbook of research on mathematics teaching and learning, 420–464.
  15. Clements, D. H., & Sarama, J. (2009). Early Childhood Mathematics Education Research. Routledge Edition.
  16. Clements, D. H., Sarama, J., & MacDonald, B. L. (2019). Subitizing: The Neglected Quantifier. In A. Norton & M. W. Alibali (Éds.), Constructing Number: Merging Perspectives from Psychology and Mathematics Education (p. 13–45). Springer International Publishing. https://doi.org/10.1007/978-3-030-00491-0_2
  17. Clements, D., & Sarama, J. (2004). Learning Trajectories in Mathematics Education. Mathematical Thinking and Learning, 6, 81‑89. https://doi.org/10.1207/s15327833mtl0602_1
  18. Dehaene, S. (2001). Précis of the number sense. Mind & Language, 16(1), 16–26. https://doi.org/10.1111/1468-0017.00154
  19. Dehaene, S. (2003). La Bosse des maths. Odile Jacob poche.
  20. Dionne, J. (2007). L’enseignement des mathématiques face aux défis de l’école au Québec: Une cohérence à vivre dans une nécessaire cohésion. Canadian Journal of Science, Mathematics and Technology Education, 7(1), 6‑27. https://doi.org/10.1080/14926150709556717
  21. Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School Readiness and Later Achievement. Developmental Psychology, 43(6), Article 6. https://doi.org/10.1037/0012-1649.43.6.1428
  22. Duval, R. (1996). Quel cognitif retenir en didactique des mathématiques. Recherches En Didactique Des Mathématiques, 16(3), 349–382.
  23. Dyson, N., Jordan, N. C., Beliakoff, A., & Hassinger-Das, B. (2015). A Kindergarten Number-Sense Intervention With Contrasting Practice Conditions for Low-Achieving Children. Journal for Research in Mathematics Education, 46(3), 331‑370. https://doi.org/doi:10.5951/jresematheduc.46.3.0331
  24. Fayol, M. (2012). L’acquisition du nombre. Que sais-je?
  25. Fuson, K. C. (1990). Issues in Place-Value and Multidigit Addition and Substraction Learning and Teaching. Journal for Research in Mathematics Education, 21(4), Article 4. https://doi.org/10.2307/749525f
  26. Geary, D. C. (2000). From infancy to adulthood :the development of numerical abilities. European Child & Adolescent Psychiatry, 9, II/11-II/16. https://doi.org/s007870070004
  27. Greeno, J. G. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22(3), Article 3. https://doi.org/10.2307/749074
  28. Hiebert, J., & Wearne, D. (1992). Links between Teaching and Learning Place Value with Understanding in First Grade. Journal for Research in Mathematics Education, 23(2), Article 2. https://doi.org/10.2307/749496
  29. Houdé, O. (2004). La psychologie de l’enfant. Presses universitaires de France.
  30. Howden, H. (1989). Teaching Number Sense. Arithmetic Teacher, 36(6), Article 6.
  31. Jacob, L., & Willis, S. (2003). The development of multiplicative thinking in young children. Mathematics Education Research: Innovation, Networking, Opportunity: Proceedings of the 26th Annual Conference of the Mathematics Education Research Group of Australia, 460‑467.
  32. Jones, G. A., Thornton, C. A., & Putt, I. J. (1994). A model for Nurturing and Assessing Multidigit Number Sens among First Grade Children. Educational Studies in Mathematics, 27(2), Article 2. https://doi.org/10.1007/BF01278918
  33. Jones, G. A., Thornton, C. A., Putt, I. J., Hill, K. M., Mogill, T., Rich, B. S., & Van Zoest, L. R. (1996). Multidigit Number Sense : A Framework for Instruction and Assessment. Journal for Research in Mathematics Education, 27(3), 310‑336. https://doi.org/10.2307/749367
  34. Jordan, N. C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20(7). https://doi.org/10.1016/j.lindif.2009.07.004
  35. Jordan, N. C., & Dyson, N. (2016). Catching Math Problems Early: Findings From the Number Sens Intervention Project. In Continuous Issues in Numerical Cognition (p. 59–79). Elsevier Inc.
  36. Jordan, N. C., & Levine, S. C. (2009). Socioeconomic Variation, Number Competence, and Mathematics Learning Difficulties in Young Children. Developmental Disabilities Research Reviews, 15, Article 15. https://doi.org/10.1002/ddrr.46
  37. Koudogbo, J. (2013). Portrait actuel des connaissances d’élèves de troisième année de l’ordre primaire et de situations d’enseignement sur la numération de position décimale. Université du Québec à Montréal.
  38. Koudogbo, J. (2013). Portrait actuel des connaissances d’élèves de troisième année de l’orde primaire et de situations d’enseignement sur la numération de position décimale [Université du Québec à Montréal]. http://archipel.uqam.ca/id/eprint/5607
  39. Mary, C., & Squalli, H. (2021). Miser sur le potentiel mathématique des élèves en difficulté : Fondements épistémologiques et didactiques. In La recherche en didactique des mathématiques et les élèves en difficulté (p. 14–30). Les Éditions JDF inc.
  40. McIntosh, A., & Dole, S. (2000). Number sense and mental computation: Implications for numeracy. Improving Numeracy Learning: What Does the Research Tell Us, 34–37.
  41. Pagani, L. S., Fitzpatrick, C., Belleau, L., & Janosz, M. (2011). Prédire la réussite scolaire des enfants en quatrième année à partir de leurs habiletés cognitives, comportementales et motrices à la maternelle. Institut de la statistique du Québec, 6(1), Article 1.
  42. Poirier, L. (2001). Enseigner les maths au primaire. Notes didactiques (ERPI).
  43. Racicot, J. (2008). J’apprends à penser, je réussis mieux. CHU Sainte-Justine.
  44. Reys, B. J. (1994). Promoting Number Sense in the Middle Grades. Mathematics Teaching in the Middle School, 1(22), 114–120. https://doi.org/10.5951/MTMS.1.2.0114
  45. Reys, R. E., & Yang, D.-C. (1998). Relationship between computational performance and number sense among sixth and eighth grade students in Taiwan. Journal for Research in Mathematics Education, 29(2), Article 2. https://doi.org/10.2307/749900
  46. Sayers, J., & Andrews, P. (2015). Foundational number sense:Summarizing the development of an analytical framework. CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education. ERME, Charles University in Prague, Faculty of Education.
  47. Sayers, J., Andrews, P., & Björklund Boistrup, L. (2016). The Role of Conceptual Subitizing in the Development of Foundational Number Sense. In L. Björklund Boistrup & P. Andrews, Mathematics Education in the Early Years (p. 371–394). Springer, Cham.
  48. Schindler, M., Schovenberg, V., & Schabmann, A. (2020). Enumeration processes of children with mathematical difficulties: An explorative eye-tracking study on subitizing, groupitizing, counting, and pattern recognition.
  49. Siegler, R. S. (2010). Enfant et raisonnement, Le développement cognitif de l’enfant. De Boeck.
  50. Starkey, G. S., & McCandliss, B. D. (2014). The emergence of ‘‘groupitizing’’ in children’s numerical cognition. Journal of Experimental Child Psychology, 126, 120–137. https://doi.org/10.1016/j.jecp.2014.03.006
  51. Starkey, P., & Cooper, R. G. (1980). Perception of numbers by human infants. Science, 210, 1033‑1035. https://doi.org/10.1126/science.7434014
  52. Sullivan, P. (2018). Challenging mathematical tasks: Unlocking the potential of all students. Oxford University Press.
  53. Thomas, N. D., & Mulligan, J. (1995). Dynamic Imagery in Children’s Representation of Number. Mathematics Education Research Journal, 7(1), 5–25. https://doi.org/10.1007/BF03217273
  54. Thomas, N. D., Mulligan, J. T., & Goldin, G. A. (2002). Children’s representation and structural development of counting sequence 1–100. Journal of Mathematical Behavior, 21, 117–133. https://doi.org/10.1016/S0732-3123(02)00106-2
  55. Twomey, C., & Dolk, M. (2011). Jeunes mathématiciens en action, construire la multiplication et la division (Vol. 2). Chenelière Éducation.
  56. Witzel, B. S., Ferguson, C. J., & Brown, D. S. (2007). Developing Early Number Sense for Students with Disabilities. LD Online. http://www.ldonline.org/article/14618/
  57. Wynn, K. (1992a). Addition and subtraction by human infants. Nature, 358, 749–750. https://doi.org/10.1038/358749a0
  58. Wynn, K. (1992b). Children’s Acquisition of the Number Words and the Counting System. Cognitive Psychology, 24, 220–251. https://doi.org/10.1016/0010-0285(92)90008-P
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