Abstract
This chapter is based on work done for more than 40 years at Université Laval, in mathematics courses for future secondary-level mathematics teachers. This work was initiated by Bernard Hodgson, in collaboration with colleagues in the Department of Mathematics and Statistics. It has been influenced by the long-time involvement of Bernard with the Canadian Mathematics Education Study Group (CMESG) and his subsequent involvement at the international level in mathematics education. Since joining the Department in 1995, I have been responsible for one of these courses, which places a strong emphasis on problem solving, using as an important resource Thinking Mathematically (Mason et al., Thinking Mathematically. Addison-Wesley, 1982). This chapter is based on this course, entitled “Mathématiques fondamentales pour l’enseignement” (Fundamental Mathematics for Teaching).
The description of the course and of its evolution is mostly a personal narrative, as I try to convey how the work done with preservice teachers has been enriched by mathematics education and by conversations with mathematics education researchers and with mathematicians who share a strong interest in mathematics education. The main objectives of the course and of its problem-solving component draw from the idea of doing mathematics. This has major implications about the manner in which we work in class, as we are trying to establish cultural norms which are conductive to an authentic engagement with mathematics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Change history
01 February 2020
The published version of this book included multiple errors in code listings throughout the book. These code listings have now been corrected and text has been updated.
References
Adler, J., Hossain, S., Stevenson, M., Clarke, J., Archer, R., & Grantham, B. (2014). Mathematics for teaching and deep subject knowledge: voices of Mathematics Enhancement Course students in England. Journal of Mathematics Teacher Education, 17, 129. https://doi.org/10.1007/s10857-013-9259-y
Ball, D. L., & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In B. Davis & E. Simmt (Eds.), Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 3–14). Edmonton, AB: CMESG/GCEDM.
Bass, H. (2011). A vignette of doing mathematics: A meta-cognitive tour of the production of some elementary mathematics. Montana Mathematics Enthusiast, 8(1/2), 3.
Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teachers’ College Record, 110(3), 608–645.
Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for a mathematics curriculum. Journal of Mathematical Behavior, 14(4), 375–402.
Gourdeau, F. (2010). Émotion, réflexion et action: Mathématiques et enseignement. In Proceedings of the 2010 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 123–137). Burnaby, BC: CMESG/GCEDM.
Gourdeau, F. (2015). Doing mathematics in teacher preparation: Giving space and time to think, reflect, share and feel. In S. J. Cho (Ed.), Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 223–233). Switzerland: Springer.
Gourdeau, F., & Nolan, K. (2016). Mathematics in Teacher Education: What, How… and Why/Les mathématiques dans la formation des enseignants: quoi, comment… et pourquoi. In S. Oesterle, D. Allan, & L. Holms (Eds.), Proceedings of the 2016 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 137–150). CMESG/GCEDM: Burnaby, BC.
Gourdeau, F., Oesterle, S., & Stordy, M. (2014). Mathematical Habits of Mind/Modes de pensée mahématiques. In S. Oesterle & D. Allan (Eds.), Proceedings of the 2014 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 83–115). Burnaby, BC: CMESG/GCEDM.
Gourdeau, F., & Proulx, J., with Maheux, J.-F., & Hodgson, B. (2012). Formation mathématique pour les enseignants de mathématiques du secondaire: Croisement des regards du mathématicien et du didacticien. In J. Proulx, C. Corriveau, & H. Squalli (Eds.), Formation mathématique pour l’enseignement des mathématiques: Pratiques, orientations et recherches (pp. 201–220). Québec, QC: Presses de l’Université du Québec.
Gourdeau, F., & Proulx, J., with Maheux, J.-F., & Hodgson, B. (2018). Mathematical preparation for secondary-level mathematics teachers: Interweaving perspectives of a mathematician and a mathematics teacher educator. Chroniques – fondements et épistémologie de l’activité mathématique.www.chroniques.uqam.ca
Hattie, J. (2012). Visible learning for teachers. New York, NY: Routledge.
Henderson, D. (1996). Alive Mathematical Reasoning. In Proceedings of the 1996 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 27–33). Halifax, NS: Mount Saint Vincent University Press.
Hodgson, B. (2001). The mathematical education of school teachers: Roles and responsibilities of university mathematicians. In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI Study (pp. 501–518). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Liljedahl, P. (2016). Building thinking classrooms: Conditions for problem solving. In P. Felmer, J. Kilpatrick, & E. Pekhonen (Eds.), Posing and solving mathematical problems: Advances and new perspectives (pp. 361–386). New York, NY: Springer.
Liljedahl, P. (2014). The affordances of using visually random groups in a mathematics classroom. In Y. Li, E. Silver, & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practices. New York, NY: Springer.
Ma, L. (1999), Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. Studies in Mathematical Thinking and Learning Series, Routledge.
Mason, J., Burton, L., & Stacey, K. (1982). Thinking Mathematically. Addison-Wesley.
Thurston, W. (1994). On proof and progress in mathematics. Bulletin of the AMS, 30(2), 161–177.
Zeitz, P. (2006), The Art and Craft of Problem Solving, John Wiley & Sons.
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
Gourdeau, F. (2019). Problem Solving as a Subject and as a Pedagogical Approach, and the Ongoing Dialogue Between Mathematics and Mathematics Education. In: Felmer, P., Liljedahl, P., Koichu, B. (eds) Problem Solving in Mathematics Instruction and Teacher Professional Development. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-29215-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-29215-7_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-29214-0
Online ISBN: 978-3-030-29215-7
eBook Packages: EducationEducation (R0)