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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Artigue, M. (2011). Les défis de l’enseignement des mathématiques dans l’éducation de base. Paris: Unesco édition.
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.
Bachelard, G. (1970). Le Rationalisme appliqué. Paris: PUF.
Balacheff, N. (1987). Processus de preuve et situations de validation. Educational Studies in Mathematics, 18(2), 147–176.
Brousseau, G. (1997). Theory of didactical situations. Kluwer Academic Publishers.
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.
Dewey, J. (1938). Logic: The theory of inquiry. New York: Henri Holt and Company.
Dewey, J. (2011). Démocratie et éducation suivi de Expérience et éducation. Paris: Armand Colin.
Douady, R. (1986). Jeux de cadres et dialectique outil-objet. Recherches en Didactique des Mathématiques, 7(2), 5–31.
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.
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.
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.
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.
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.
Grau, S. (2017). Problématiser en mathématiques: le cas de l’apprentissage des fonctions affines (Thèse de doctorat, Université de Nantes, France).
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.
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.
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.
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.
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.
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.
Kuhn, T. S. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.
Laborde, C., Perrin-Glorian, M.-J., & Sierpinska, A. (Éd.). (2005). Beyond the apparent banality of the mathematics classroom. Boston, MA: Springer.
Linn, M. C., Davis, E. A., & De Bell, P. (2004). Internet environments for science education. Lawrence Erlbaum Associates.
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.
Maaß, K., & Artigue, M. (2013). Implementation of inquiry-based learning in day-to-day teaching: A synthesis. ZDM Mathematics Education, 45(6), 779–795.
Orange, C. (2000). Idées et raisons. Habilitation à Diriger des recherches, Université de Nantes.
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.
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.
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.
Poincaré, H. (1970). La valeur de la science. Paris: Champs-Flammarion.
Pólya, G. (1954). Mathematics and plausible reasoning. Princeton University Press.
Pólya, G. (1965). Comment poser et résoudre des problèmes. Paris: Jacques Gabay.
Popper, K. (1972). Objective knowledge: An evolutionary approach. Oxford: OUP.
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.
Santos-Trigo, M. (2013). Problem solving in mathematics education. In Lerman, S. (Ed.), Encyclopedia of mathematics education (pp. 496–501).
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.
Schoenfeld, A.-H., & Kilpatrick, J. (2013). A US perspective on the implementation of inquiry-based learning in mathematics. ZDM Mathematics Education, 45, 901–909.
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.
Silver, E.-A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
Vergnaud, G. (1998). A comprehensive theory of representation for mathematics education. The Journal of Mathematical Behavior, 17(2), 167–181.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Hersant, M., Choquet, C. (2019). Is an Inquiry-Based Approach Possible at the Elementary School?. In: Liljedahl, P., Santos-Trigo, M. (eds) Mathematical Problem Solving. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-10472-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-10472-6_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-10471-9
Online ISBN: 978-3-030-10472-6
eBook Packages: EducationEducation (R0)