Abstract
In response to a recent Canada-wide survey, where it was found that mathematicians use computer programming much less in their teaching than in their research, an exploratory study involving 14 Canadian mathematicians sought to gain a deeper understanding of the place of programming in both contexts. To capture the differences in the degree of interaction with programming in various mathematical practices, a scale of six levels has been defined and used. While providing visibility to an aspect of mathematical practice that is often absent from published work, the views of our participants also highlight some important issues that would require attention in order to reduce the identified gap, should that be deemed the favourable direction to take.
Résumé
En réponse à un sondage pancanadien récent, qui révélait que les mathématiciens utilisent beaucoup moins la programmation informatique dans leur enseignement que dans leur recherche, une étude exploratoire auprès de quatorze mathématiciens canadiens a cherché à mieux comprendre la place de la programmation dans ces deux contextes. Une échelle à six niveaux a été définie et utilisée pour caractériser le degré d’interaction avec la programmation dans différentes pratiques mathématiques. Tout en rendant visible un aspect de la pratique mathématique souvent absent des publications, le témoignage des participants à l’étude met en évidence certaines contraintes qu’il conviendrait de revoir si l’on souhaitait réduire l’écart entre les pratiques de recherche et celles qui sont développées dans la formation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The use of quotations here indicates a lack of clarity in the definition of programming. We return to this later. Readers, who are likely to have their own implicit definition, should be aware of a potential ambiguity.
References
Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7, 245–274.
Artigue, M. (2016). Mathematics education research at university level: Achievements and challenges. In E. Nardi, C. Winsløw, & T. Hausberger (Eds.), Proceedings of INDRUM 2016 first conference of the international network for the didactic research in university mathematics (pp. 11–27). Montpellier: University of Montpellier and INDRUM.
Bailey, D. H., & Borwein, J. M. (2005). Experimental mathematics: Examples, methods and implications. Notices of the AMS, 52(5), 502–514.
Broley, L. (2015). La programmation informatique dans la recherche et la formation en mathématiques au niveau universitaire. Université de Montréal, Montréal: Unpublished master’s thesis Available at https://papyrus.bib.umontreal.ca/xmlui/handle/1866/12574.
Broley, L. (2016). The place of computer programming in (undergraduate) mathematical practices. In E. Nardi, C. Winsløw, & T. Hausberger (Eds.), Proceedings of INDRUM 2016 first conference of the international network for the didactic research in university mathematics (pp. 360–369). Montpellier: University of Montpellier and INDRUM.
Burton, L. (2004). Mathematicians as enquirers: Learning about learning mathematics. Norwell: Kluwer Academic Publishers.
Buteau, C., & Muller, E. (2010). Student development process of designing and implementing exploratory and learning objects. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the sixth congress of the European Society for Research in mathematics education (pp. 1111–1120). Lyon: Institut national de recherche pédagogique.
Buteau, C., Jarvis, D., & Lavicza, Z. (2014). On the integration of computer algebra systems (CAS) by Canadian mathematicians: Results of a national survey. Canadian Journal of Science, Mathematics, & Technology. Education, 14(1), 1–23.
Chevallard, Y. (1998). Analyse des pratiques enseignantes et didactique des mathématiques : L'approche anthropologique. Retrieved from http://yves.chevallard.free.fr/spip/spip/IMG/pdf/Analyse_des_pratiques_enseignantes.pdf.
Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15, 375–402.
Francis, K. & Davis, B. (forthcoming). Number, arithmetic, multiplicative thinking and coding. In Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education. Dublin.
Knuth, D. (1985). Algorithmic thinking and mathematical thinking. The American Mathematical Monthly, 92(3), 170–181.
Lagrange, J.-B., & Rogalski, J. (2015). Savoirs, concepts et situations dans les premiers apprentissages en programmation et en algorithmique. In A.-C. Mathé & É. Mounier (Eds.), Actes du séminaire national de didactique des mathématiques (pp. 155–176). Paris: IREM Paris.
Lavicza, Z. (2010). Integrating technology into mathematics teaching at the university level. ZDM. The International Journal on Mathematics Education, 42(1), 105–119.
Leron, U., & Dubinsky, E. (1995). An abstract algebra story. The American Mathematical Monthly, 102(3), 227–242.
Madsen, L. M., & Winsløw, C. (2009). Relations between teaching and research in physical geography and mathematics at research-intensive universities. International Journal of Science and Mathematics Education, 7, 741–763.
Misfeldt, M. & Ejsing-Dunn, S. (2015). Learning mathematics through programming: An instrumental approach to potentials and pitfalls. In K. Krainer & N. Vondrová (Eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 2524–2530). Charles University in Prague, Faculty of Education, and ERME: Prague.
Morrissette, J. (2011). Vers un cadre d'analyse interactionniste des pratiques professionnelles. Recherches qualitatives, 30(1), 10–32.
Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.
Society for Industrial and Applied Mathematics. (2012). Mathematics in industry. Retrieved from http://www.siam.org/reports/mii/2012/report.pdf.
Van der Maren, J.-M. (1996). Le codage et le traitement des données. In Méthodes de recherche pour l'éducation (2nd ed., pp. 427–457). Montréal/Bruxelles: PUM et de Boeck.
Vermersch, P. (2006). L’entretien d’explicitation (5th ed.). Paris: ESF éditeur.
Watson, A. (2008). School mathematics as a special kind of mathematics. For the Learning of Mathematics, 28(3), 3–7.
Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K., Trouille, L., & Wilensky, U. (2016). Defining computational thinking for mathematics and science classrooms. Journal of Science Education and Technology, 25, 127–147.
Winsløw, C. (2015). Mathematics at university: The anthropological approach. In S. J. Cho (Ed.), Selected regular lectures from the 12th international congress on mathematical education (pp. 859–875). Cham: Springer International Publishing.
Winsløw, C., Barquero, B., De Vleeschouwer, M., & Hardy, N. (2014). An institutional approach to university mathematics education: From dual vector spaces to questioning the world. Research in Mathematics Education, 16(2), 95–111.
Acknowledgements
An earlier version of a portion of this paper was presented by Broley at INDRUM 2016 and published in the corresponding proceedings (see Broley 2016). We thank the discussion group on Teachers’ Practices and Institutions for their insightful questions and comments throughout the conference, many of which contributed to our expansion of the paper. We also thank the reviewers and editors for their thoughtful suggestions throughout the review process. The research discussed herein was completed as part of a M.Sc. in mathematics (see Broley 2015 for the complete thesis) at Université de Montréal, with the support of the Social Sciences and Humanities Research Council of Canada.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Broley, L., Caron, F. & Saint-Aubin, Y. Levels of Programming in Mathematical Research and University Mathematics Education. Int. J. Res. Undergrad. Math. Ed. 4, 38–55 (2018). https://doi.org/10.1007/s40753-017-0066-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40753-017-0066-1