24 SES 04, Mathematics Curriculum & Student Experiences
After having analyzed and compared current curricula in mathematics between several French speaking countries (Belgium, France, Canada), we can observe that several key concepts in geometry are set aside from cursus programmes. These concepts rejection occurred despite recommendations previously made by many researchers (e.g. Colmez, 1977; Fey, 1979). More than twenty-five years ago, Bishop (1982) lamented over the fact that arithmetic has too often overshadowed geometry. Years later, in 2002, a similar observation was made in the "Report on the implementation of school success" stating that "numbers were clearly favoured over geometry, shapes and sizes (...)". And yet, researchers know the importance of teaching geometric concepts to promote, afterwards, better learning in mathematics.
In the current perspective, it may be necessary to rewrite curricula, so that they become less overloaded (content depending on the number of hours per week), or coherent and consistent (Duroisin & Soetewey, 2011), as it is actually the case in Belgium. However, authors want to show that it is also very important to take into account the acquisition of basic prerequisite, coming from more simple learning (as geometry) at an early stage, and the developmental psychology of children and adolescents to promote, thereafter, more complex acquisition concepts in mathematics (as arithmetic, calculations and proportions...).
Through the cross-perspective of two researchers and one teacher on a curriculum, the aim of this paper is, first, to highlight that the withdrawal of some geometric contents in mathematics curricula can be observed into several countries curriculum. The second goal is to show that the suppression of those geometric contents is problematic for both teachers and learners. On the one hand, teachers are required to provide the cursus in mathematics without being able to rely on all the necessary students’ prerequisites. On the other hand, removals create gaps in the progression and continuity of geometry learning, placing students into difficulties that may affect the rest of their career (Unesco, 1987 ; Bishop, 1983, p.152).
Audibert, G. (1991). La géométrie dans l’enseignement. Repères. Bishop, A. J. (1983). Space and Geometry. In: R. Lesh et M. Landau (dirs. pub.), Acquisition of Mathematics Concepts and Processes, Academic Press, New York, p. 175-203. Bkouche, R. (2006). La Géométrie entre mathématiques et sciences physiques, Proceedings of 4th International Colloquium on the Didactics of Mathematics, volume II. Clements, D. (2001), Teaching and Learning Geometry. In J. Kilparick (Ed), Research Companion to the NCTM Standards for Mathematics. Reston, VA: NCTM. Colmez, F. 1977. Mathematics Education at Pre-school and Primary Level. In : Athen, H. et Kunle, H. (dirs. pub.), Proceedings of the Third International Congress on Mathematical Education, Karlsruhe, Université de Karlsruhe, p. 142-154. Duroisin, N. & Soetewey, S. (2011). Méthodologie de la recherche. Université de Mons. Fey, J. (1979). Mathematics Teaching Today : Perspectives from Three National Surveys. Mathematics Teacher, Vol. 72, p. 490-504. Unesco (1987). Etudes sur l’enseignement des mathématiques. L’enseignement de la géométrie. Unesco. Volume 5. French, D. (2004). Teaching and learning geometry: issues and methods in mathematical education, Continuum International Publishing Group, New York. Jones, K. (2002). Issues in the teaching and learning of geometry. In, Haggarty, L. (ed.) Aspects of teaching secondary mathematics: Perspectives on practice, Routledge Falmer, London, UK, p. 121-139. Royal Society/ Joint Mathematical Council (2001), Teaching and Learning Geometry, Royal Society/Joint Mathematical Council, London, p. 11-19. Schwartz, J.E. (2008). Elementary Mathematics Pedagogical Content Knowledge: Powerful Ideas for Teachers, edition Allyn & Bacon.
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