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Secondary-to-tertiary comparison through the lens of ways of doing mathematics in relation to functions: a study in collaboration with teachers

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Abstract

This article addresses the issue of transition from secondary to post-secondary education through collaborative research with teachers from both levels. It takes into account implicit elements in this transition. Research on the transition in mathematics education tends to focus more on the tertiary level, studying difficulties encountered by students or comparing curricula, tasks, and textbooks highlighting disruptions or cultural shifts. However, according to Hall (1959), and Artigue (2004) in a mathematical context, it is the implicit “ways of doing” that lead to the greatest cultural differences. In this article, attention is paid to the particular ways in which teachers’ ways of doing mathematics impact the transition. Ethnomethodology (Garfinkel, 1967) and its central concept of ethnomethods are used as the theoretical framework to conceptualize these ways of doing mathematics. A breaching situation presented to a group of secondary- and tertiary-level teachers engaged in collaborative research (Desgagné et al., 2001) brings to light familiar ways of doing mathematics. Our analysis focuses specifically on a comparison of the ways of doing mathematics related to functions at each level.

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Notes

  1. Comparison between cognitive resources used in the resolution of problems by mathematicians and students.

  2. Translated from French.

  3. Though its name suggests otherwise, ethnomethodology is not a methodological approach but rather a theory of social phenomena (ethnomethodology is the study of ethnomethods).

  4. See Corriveau, 2013 for further information about the use of breach or Herbst and Chazan (2015) who have also use the concept of breaching experiment (from ethnomethodology) in their work.

  5. It may seem difficult to talk about the phenomenon of inter-level transition from an international point of view, since educational institutions, as Gueudet (2008) points out, differ from one country to another.

  6. To design tasks as a basis for discussion, I observed mathematics classes at both levels.

  7. This breaching task could also be used with students entering the tertiary level. In fact, as suggested and used by Praslon (2000), unusual tasks make students sensitive to the gap between the secondary and the tertiary levels.

  8. It is not the case for other themes analyzed in the larger research project, i.e., the use of symbolism and the use of contexts in mathematics. These transversal themes are not as well detailed (as a function, as content) in curricula.

  9. The sessions were carried out in French; the excerpts which follow are translations.

  10. Translation of the French term “domaine de travail.”

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  1. Faculté des Sciences de l’éducation, Université Laval, 2320 rue des Bibliothèques (bur. 1230), Québec, QC, G1V 0A6, Canada

    Claudia Corriveau

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  1. Claudia Corriveau
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Correspondence to Claudia Corriveau.

Appendix A

Appendix A

Students’ solutions

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Corriveau, C. Secondary-to-tertiary comparison through the lens of ways of doing mathematics in relation to functions: a study in collaboration with teachers. Educ Stud Math 94, 139–160 (2017). https://doi.org/10.1007/s10649-016-9719-2

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