Abstract
While many current position papers and policy documents advocate making a place for the use of calculators in elementary education and point to their potential to enhance mathematical learning, there is continuing professional uncertainty over how to realize such aspirations. This paper reviews a pioneering effort to craft a calculator-aware number curriculum. It examines pedagogical strategies based on diagnose-explain-reinforce and observe-predict-surpass sequences and the wider use of calculators for purposes of computation implementing, result checking, trial improving, and structure modelling. The paper then reports on research that examined the long-term impact of such a curriculum. It identifies the complexities of supporting students as they develop personal methods of calculation and of systematizing such a curriculum to support progression in children’s learning. Among younger students, an emphasis on investigative and problem-solving tasks produced a greater differentiation of experience among students, creating higher expectations for successful students but requiring strong teacher intervention to structure and support the learning of students making poor progress. The major long-term impact of the curriculum was on students’ attitude to mental calculation and proficiency in it. Students proved more prone to calculate mentally and more liable to adopt relatively powerful and efficient strategies. Analysis of students’ calculator use in tackling a realistic number problem shows how effective use of the machine calls for not only mastery of operating procedures but also a grasp of underlying mathematical ideas and the development of distinctive calculator methods. Finally, implications for policy and practice are suggested, emphasizing that a calculator-aware approach cannot simply be improvised around a conventional curriculum.
Résumé
Bien que de nombreux articles et documents officiels actuels affirment que les calculatrices ont leur place en enseignement primaire et que ces machines sont susceptibles de favoriser l’apprentissage des mathématiques chez les enfants, les spécialistes du domaine continuent de s’interroger sur la meilleure façon d’atteindre cet objectif. Cet article passe en revue une initiative originale visant à mettre au point un curriculum sur les nombres qui tienne compte de l’utilisation des calculatrices à l’école. Il analyse des stratégies pédagogiques fondées sur les séquences diagnostique/explication/renforcement et observation/prédiction/dépassement, de même que sur l’utilisation généralisée des calculatrices pour exécuter des calculs, vérifier les résultats, améliorer les épreuves et modeler les structures. L’article se penche ensuite sur des recherches qui ont analysé les effets à long terme d’un tel curriculum. Il souligne également les difficultés que posent d’une part le respect du développement de méthodes individuelles de calcul chez les élèves, et d’autre part la systématisation d’un tel curriculum dans le but de soutenir la progression dans l’apprentissage des enfants. Chez les élèves les plus jeunes, une analyse centrée sur des tâches visant la résolution de problèmes a mis en évidence une plus grande différenciation dans l’expérience des élèves, ce qui a pour effet de créer des attentes plus élevées pour les élèves qui réussissent le mieux, mais demande une intervention plus soutenue de la part des enseignants pour structurer et favoriser l’apprentissage des élèves qui réussissent moins bien. L’effet à long terme le plus important du curriculum concernait l’attitude et la compétence des élèves pour ce qui est du calcul mental. Il ressort en effet que les élèves étaient plus aptes au calcul mental et plus susceptibles d’adopter des stratégies relativement puissantes et efficaces. Une analyse de la façon dont les élèves utilisent la calculatrice pour tenter de résoudre un problème réel montre que pour utiliser la machine de façon efficace, il est nécessaire non seulement de bien connaître les opérations, mais aussi de bien comprendre les concepts mathématiques qui sous-tendent ces opérations et d’assimiler une méthode qui soit spécifique à l’utilisation de la calculatrice. Enfin, l’article suggère certaines implications de cette expérience pour les politiques et la pratique, soulignant qu’une approche qui tient compte de l’utilisation des calculatrices ne peut simplement s’improviser dans le cadre du curriculum traditionnel.
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References
Bierhoff, H. (1996). Laying the foundations of numeracy: A comparison of primary school textbooks in Britain, Germany and Switzerland. London: National Institute of Economic and Social Research.
Foxman, D. (1996). A comparative review of research on calculator availability and use, ages 5— 14. Unpublished report to the School Curriculum and Assessment Authority, London.
Groves, S., & Stacey, K. (1998). Calculators in primary mathematics: Exploring number before teaching algorithms. In L.J. Morrow (Ed.), The teaching and learning of algorithms in school mathematics (National Council of Teachers of Mathematics Yearbook). Reston, VA: National Council of Teachers of Mathematics.
Hembree, R., & Dessart, D. (1986). Effects of hand-held calculators in precollege mathematics: A meta-analysis. Journal for Research in Mathematics Education, 17(2), 83–99.
Hembree, R., & Dessart, D. (1992). Research on calculators in mathematics education. In J. Fey & C. Hirsch (Eds.), Calculators in mathematics education (National Council of Teachers of Mathematics Yearbook; pp. 23–32). Reston, VA: National Council of Teachers of Mathematics.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. Available: http://www.nap.edu/urlbooks/0309069955/html/ (accessed April 8, 2003).
London Mathematical Society, Royal Statistical Society, & Institute of Mathematics and Its Applications. (1995). Tackling the mathematics problem. London: London Mathematical Society.
National Council of Teachers of Mathematics. (1998). Calculators and the education of youth (position statement). Reston, VA: Author. Available: http://www.nctm.org/about/ position_statements/ (accessed April 8, 2003).
National Council of Teachers of Mathematics. (1999). Calculators—What is their place in mathematics classrooms? Dialogues (May/June issue). Reston VA: Author. Available: http://www.nctm.org/dialogues/ (accessed April 8, 2003).
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston VA: Author. Available: http://standards.nctm.org/ (accessed April 8, 2003).
Ontario Ministry of Education. (2003). Report of the expert panel on early math in Ontario. Available: http://mettowas21.edu.gov.on.ca/eng/document/reports/math/(accessed April 8, 2003).
Plunkett, S. (1979). Decomposition and all that rot. Mathematics in School, 8(3), 2–5.
RAND Mathematics Study Panel, D.L. Ball (Chair). (2002). Mathematical proficiency for all students: Toward a strategic research and development program in mathematics education. Santa Monica CA: RAND. Available: http://www.rand.Org/publications/MR/MR1643.0/ (accessed April 8, 2003).
Ruthven, K. (1998). The use of mental, written and calculator strategies of numerical computation by upper-primary pupils within a ‘calculator-aware’ number curriculum. British Educational Research Journal, 24(1), 21–42.
Ruthven, K. (2001). Towards a new numeracy: The English experience of a ‘calculator-aware’ umber curriculum. In J. Anghileri (Ed.), Principles and practice in arithmetic teaching (pp. 165–188). Buckingham, UK: Open University Press.
Ruthven, K., & Chaplin, D. (1997). The calculator as a cognitive tool: Upper-primary pupils tackling a realistic number problem. International Journal of Computers for Mathematical Learning, 2(2), 93–124.
Ruthven, K., Rousham, L., & Chaplin, D. (1997). The long-term influence of a ’calculator-aware’ number curriculum on pupils’ mathematical attainments and attitudes in the primary phase. Research Papers in Education, 12(3), 249–282.
Shuard, H. (1992). CAN: Calculator use in the primary grades in England and Wales. In J. Fey & C. Hirsch (Eds.), Calculators in mathematics education (Yearbook National Council of Teachers of Mathematics; pp. 33–45). Reston VA: National Council of Teachers of Mathematics.
Shuard, H., Walsh, A., Goodwin, J., & Worcester, V. (1991). Calculators, children and mathematics. London, UK: Simon & Schuster.
van den Brink, J. (1993). Different aspects in designing mathematics education: Three examples from the Freudenthal Institute. Educational Studies in Mathematics, 24(1), 35–64.
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Ruthven, K. Creating a Calculator-Aware Number Curriculum. Can J Sci Math Techn 3, 437–450 (2003). https://doi.org/10.1080/14926150309556581
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DOI: https://doi.org/10.1080/14926150309556581