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Is an Inquiry-Based Approach Possible at the Elementary School?

  • Magali HersantEmail author
  • Christine Choquet
Chapter
Part of the ICME-13 Monographs book series (ICME13Mo)

Abstract

In this paper, we focus on the inquiry-based approach at the elementary school when students try to resolve mathematics problems. After a brief survey about problem solving, problem posing and inquiry-based learning, we analyze two case studies in the French context with the framework of the learning by problematization (Fabre & Orange in ASTER 24:37–57, 1997) and the notion of potential of inquiry of a problem that we introduce. This way, we identify some conditions of possibilities of learning mathematics with inquiry at elementary French schools. The design of the situation chosen by the teacher, that must conduct students to doubt and enroll them on inquiry, plays a crucial role. The teacher must also be able to support students’ inquiry activity, which may require developing didactical skills through teachers’ training.

References

  1. Artigue, M. (2011). Les défis de l’enseignement des mathématiques dans l’éducation de base. Paris: Unesco édition.Google Scholar
  2. Artigue, M. (2012). Démarches d’investigation. Réflexions à partir de quelques projets européens. IREM de Lyon. http://www.univirem.fr/IMG/pdf/Demarche_d_investigation_Lyon1_MICHELE_ARTIGUE_11_Juin_2012.pdf.
  3. Bachelard, G. (1970). Le Rationalisme appliqué. Paris: PUF.Google Scholar
  4. Balacheff, N. (1987). Processus de preuve et situations de validation. Educational Studies in Mathematics, 18(2), 147–176.CrossRefGoogle Scholar
  5. Brousseau, G. (1997). Theory of didactical situations. Kluwer Academic Publishers.Google Scholar
  6. Choquet, C. (2014). Une caractérisation des pratiques de professeurs des écoles lors de séances de mathématiques dédiées à l’étude de problèmes ouverts au cycle 3 (Thèse de doctorat, Université of Nantes, France). https://tel.archives-ouvertes.fr/tel-01185671/document.
  7. Dewey, J. (1938). Logic: The theory of inquiry. New York: Henri Holt and Company.Google Scholar
  8. Dewey, J. (2011). Démocratie et éducation suivi de Expérience et éducation. Paris: Armand Colin.Google Scholar
  9. Douady, R. (1986). Jeux de cadres et dialectique outil-objet. Recherches en Didactique des Mathématiques, 7(2), 5–31.Google Scholar
  10. Dorier, J.-L., & Garcia, J. (2013). Challenges and opportunities for the implementation of inquiry-based learning in day-to-day teaching. ZDM Mathematics Education, 45(6), 837–849.CrossRefGoogle Scholar
  11. Engeln, K., Euler, M., & Maaß, K. (2013). Inquiry-based learning in Mathematics and science: A comparative baseline study of teachers’ beliefs and practices across 12 European countries. ZDM Mathematics Education, 45(6), 823–836.CrossRefGoogle Scholar
  12. Erh-Tsung, C., & Fou-Lai, L. (2013). A survey of the practice of a large-scale implementation of inquiry-based mathematics teaching: from Taiwan’s perspective. ZDM Mathematics Education, 45(6), 919–923.CrossRefGoogle Scholar
  13. Fabre, M. (2005). Deux sources de l’épistémologie des problèmes: Dewey et Bachelard. Les Sciences de l’éducation - Pour l’Ère nouvelle, 38(3), 53–67.  https://doi.org/10.3917/lsdle.383.0053.CrossRefGoogle Scholar
  14. Fabre, M., & Orange, C. (1997). Construction des problèmes et franchissements d’obstacles. ASTER, 24, 37–57. http://ife.ens-lyon.fr/publications/edition-electronique/aster/RA024-03.pdf.
  15. Grau, S. (2017). Problématiser en mathématiques: le cas de l’apprentissage des fonctions affines (Thèse de doctorat, Université de Nantes, France).Google Scholar
  16. Hersant, M. (2010). Empirisme et rationalité au cycle 3, vers la preuve en mathématiques. Habilitation à diriger des recherches, Université de Nantes. https://hal.archives-ouvertes.fr/tel-01777604.
  17. Hersant, M. (2014). Facette épistémologique et facette sociale du contrat didactique: une distinction pour mieux caractériser la relation contrat didactique milieu, l’action de l’enseignant et l’activité potentielle des élèves. Recherches en Didactique des Mathématiques, 34(1), 9–31.Google Scholar
  18. Hersant, M., & Orange-Ravachol, D. (2015). Démarche d’investigation et problématisation en mathématiques et en SVT: des problèmes de démarcation aux raisons d’une union. Recherches En Education, 21, 95–108. http://www.recherches-en-education.net/IMG/pdf/REE-no21.pdf.
  19. Hersant, M., & Perrin-Glorian, M.-J. (2005). Characterization of an ordinary teaching practice with the help of the theory of didactic situations. Educational Studies in Mathematics, 59(1), 113–151.  https://doi.org/10.1007/s10649-005-2183-z.CrossRefGoogle Scholar
  20. Hétier, R. (2008). La notion d’expérience chez John Dewey : une perspective éducative. Recherches en Education, 5, 21–32. http://www.recherches-en-education.net/IMG/pdf/REE-no5.pdf.
  21. Inoue, N., & Buczynski, S. (2011). You asked open-ended questions, now What? Understanding the nature of stumbling blocks in teaching inquiry lessons. The Mathematics Educator, 20(2), 10–23.Google Scholar
  22. Kuhn, T. S. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.Google Scholar
  23. Laborde, C., Perrin-Glorian, M.-J., & Sierpinska, A. (Éd.). (2005). Beyond the apparent banality of the mathematics classroom. Boston, MA: Springer.Google Scholar
  24. Linn, M. C., Davis, E. A., & De Bell, P. (2004). Internet environments for science education. Lawrence Erlbaum Associates.Google Scholar
  25. Malaspina, U. (2016). Problem posing: An overview for further progress. In P. Liljedahl, M. Santos-Trigo, U. Malaspina, & R. Bruder (dir.), Problem solving in mathematics education. ICME 13 Topical Surveys. Springer Open.Google Scholar
  26. Maaß, K., & Artigue, M. (2013). Implementation of inquiry-based learning in day-to-day teaching: A synthesis. ZDM Mathematics Education, 45(6), 779–795.CrossRefGoogle Scholar
  27. Orange, C. (2000). Idées et raisons. Habilitation à Diriger des recherches, Université de Nantes.Google Scholar
  28. Orange, C. (2005). Problématisation et conceptualisation en sciences et dans les apprentissages scientifiques. Les sciences de l’éducation pour l’ère nouvelle, 38(3), 70–92.Google Scholar
  29. O’Shea, J., & Leavy, M. (2013). Teaching mathematical problem-solving from an emergent constructivist perspective: The experiences of Irish primary teachers. Journal of Mathematics Teacher Education, 16(4), 293–318.CrossRefGoogle Scholar
  30. Perrin, D. (2007). L’expérimentation en mathématiques. In Actes du 33è colloque de la Copirelem (pp. 37–72). Dourdan. Available at: http://www.math.u-psud.fr/~perrin/Conferences/L_experimentation_en_maths/PetitxDP.pdf.
  31. Poincaré, H. (1970). La valeur de la science. Paris: Champs-Flammarion.Google Scholar
  32. Pólya, G. (1954). Mathematics and plausible reasoning. Princeton University Press.Google Scholar
  33. Pólya, G. (1965). Comment poser et résoudre des problèmes. Paris: Jacques Gabay.Google Scholar
  34. Popper, K. (1972). Objective knowledge: An evolutionary approach. Oxford: OUP.Google Scholar
  35. Rocard, M., Csemely, P., Jorde, D., Lenzen, D., Walberg-Henriksson, H., & Hemmo, V. (2007). Science education now: A renewed pedagogy for the future of Europe. Bruxuelles. http://ec.europa.eu/research/science-society/document_library/pdf_06/report-rocard-on-science-education_en.pdf.
  36. Santos-Trigo, M. (2013). Problem solving in mathematics education. In Lerman, S. (Ed.), Encyclopedia of mathematics education (pp. 496–501).Google Scholar
  37. Schoenfeld, A.-H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.Google Scholar
  38. Schoenfeld, A.-H., & Kilpatrick, J. (2013). A US perspective on the implementation of inquiry-based learning in mathematics. ZDM Mathematics Education, 45, 901–909.CrossRefGoogle Scholar
  39. Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1–7.  https://doi.org/10.1007/s10649-013-9478-2.CrossRefGoogle Scholar
  40. Silver, E.-A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.Google Scholar
  41. Vergnaud, G. (1998). A comprehensive theory of representation for mathematics education. The Journal of Mathematical Behavior, 17(2), 167–181.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.ESPE, Université de NantesNantesFrance

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