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Collaboration Between Secondary and Post-secondary Teachers About Their Ways of Doing Mathematics Using Contexts

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Practice-Oriented Research in Tertiary Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

The transition from secondary to postsecondary mathematics has been studied from various angles. Students encounter difficulties in this transition, but the investigation should not only be restricted to their perspective. In our study, we address the transition with teachers from both levels, fostering a dialog between them. This entry allows to tackle the transition from implicit part of teaching. Indeed, we focus on teachers’ ways of doing mathematics using contexts at each level. We drew on ethnomethodology to conceptualize the object “teachers’ ways of doing.” Adopting a collaborative approach and research-practice partnership principles, we established a study in two phases. Results are presented according to these two phases. From the initial phase arise the reconstitution of ways of doing mathematics using contexts at each level, revealing two different “territories.” The second phase exposes a certain rapprochement of the two levels.

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Notes

  1. 1.

    A French acronym referred to in English as General and Vocational College.

  2. 2.

    Some researchers have drawn on ethnomethodology to study different aspect of mathematics education, especially classroom interactions (see Ingram, 2018; Krummheuer, 2020).

  3. 3.

    Three major themes emerged from phase 1: functions and their representations; the use of contexts and symbolism. Between the two phases presented here, from 2014 to 2017, the question of transitions was brought further by the researcher from the angle of symbolism (see Corriveau & Bednarz, 2016, 2017).

  4. 4.

    We use this metaphor to illustrate that during the research, teachers of a specific level consistently organize a familiar territory about their ways of using contexts in which they recognize themselves (as members). We see it as a space that is continuously undergoing organization.

  5. 5.

    We emphasize in bold the teachers’ ways of doing using context.

  6. 6.

    This schema was also utilized in Phase 1 of the project with a goal of rapprochement, but was handled differently. Throughout the discussions, the teachers remained in their own territory and engaged in dialogue without necessarily entering the territory of the other (Corriveau, 2013).

  7. 7.

    And also from research conducted in situated perspectives (Please see, in particular, Lave, 1988, 1996; Noss, 2002; Noss et al., 1999; Nunès et al., 1993; Traoré & Bednarz, 2009).

  8. 8.

    The reflection would be completely different for mathematics students. New requirements in terms of formalism, proofs, rigor and abstract mathematics in mathematics major programmes have been an important focus to understand the transition and remain very relevant for those students. We chose to focus here on non-mathematics students and on the relationship between mathematics and other disciplines at tertiary level. Indeed, there is an increased interest about the role of mathematics in other disciplines at tertiary level as pointed out by Biza et al. (2016), however one can ask what is the role of other disciplines – and more broadly of contexts – in mathematics courses?

References

  • Artigue, M. (2004). Le défi de la transition secondaire/supérieur: Que peuvent nous apporter les recherches didactiques et les innovations développées dans ce domaine. Communication presented at the first Canada-France mathematics sciences conference. Toulouse.

    Google Scholar 

  • Bednarz, N. (2004). Collaborative research and professional development of teachers in mathematics. In M. Niss & E. Emberg (Eds.), Proceedings of the international conference on mathematics education (CD-ROM). Roskilde University.

    Google Scholar 

  • Biza, I., Giraldo, V., Hochmuth, R., Sadat Khakbaz, A., & Rasmussen, C. (2016). Research on teaching and learning mathematics at the tertiary level. Springer Nature. https://doi.org/10.1007/978-3-319-41814-8_1

  • Bosch, M., Fonseca, C., & Gascon, J. (2004). Incompletitud de las organizaciones matemáticas locales en las instituciones escolares. Recherches en didactique des mathématiques, 24(2–3), 205–250.

    Google Scholar 

  • Cicourel, A. V. (1974). Interpretive procedures and normative rules in the negotiation of status and role. In A. V. Ciccourel (Ed.), Cognitive sociology: Language and meaning in social interaction (pp. 11–41). The Free Press.

    Google Scholar 

  • Coburn, C. E., & Penuel, W. R. (2016). Research–practice partnerships in education: Outcomes, dynamics, and open questions. Educational Researcher, 45(1), 48–54. https://doi.org/10.3102/0013189X16631750

    Article  Google Scholar 

  • Corriveau, C. (2013). Des manières de faire des mathématiques comme enseignants abordées dans une perspective ethnométhodologique pour explorer la transition secondaire collégial. Unpublished doctoral thesis. Université du Québec à Montréal.

    Google Scholar 

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

    Article  Google Scholar 

  • Corriveau, C., & Bednarz, N. (2013). Manières de faire des mathématiques comme enseignants: une perspective ethnométhodologique. For the Learning of Mathematics, 33(2), 24–30.

    Google Scholar 

  • Corriveau, C., & et Bednarz, N. (2016). Transition secondaire postsecondaire abordée sous l’angle de l’harmonisation entre manières de faire des mathématiques comme enseignants entourant le symbolisme. Revue canadienne de l’enseignement des sciences, des mathématiques et des technologies/Canadian Journal of Science, Mathematics and Technology, 16(3), 213–236.

    Google Scholar 

  • Corriveau, C., & Bednarz, N. (2017). The secondary-tertiary transition viewed as a change in mathematical cultures: An exploration concerning symbolism and its use. Educational Studies in Mathematics, 95(1), 1–19. https://doi.org/10.1007/s10649-016-9738-z

    Article  Google Scholar 

  • Corriveau, C., Breuleux, A., Kobiela, M., & Oliveira, I. (2020). Projet ARIM: processus de rapprochement des pratiques d’enseignement de mathématiques pour favoriser un passage plus harmonieux pour les élèves lors de transitions scolaires. Rapport final de recherche pour la subvention no. 2017-PO-202613. Fonds de recherche du Québec Socité Culture, Programme d’actions concertées sur la réussite et la persévérance scolaire (research report).

    Google Scholar 

  • Davis, B. (2005). Trois attitudes de recherche en éducation. Revue des sciences de l’éducation, 31(2), 389–416. https://doi.org/10.7202/012762ar

    Article  Google Scholar 

  • Desgagné, S. (2001). La recherche collaborative: une nouvelle dynamique de recherche en éducation. In M. Anadón (Ed.), Nouvelles dynamiques de recherche en éducation (pp. 51–76). Les presses de l’Université Laval.

    Google Scholar 

  • Di Martino, P., & Gregorio, F. (2019). The mathematical crisis in secondary–tertiary transition. International Journal of Science and Mathematics Education, 17(4), 825–843. https://doi.org/10.1007/s10763-018-9894-y

    Article  Google Scholar 

  • Douady, R. (1986). Jeux de cadres et dialectique outil-objet. Recherches en Didactique des Mathématiques, 7(2), 5–31.

    Google Scholar 

  • Douady, R. (1991). Tool, object, setting, window: Elements for analyzing and constructing didactical situations in mathematics (In mathematical knowledge: Its growth through teaching) (pp. 107–130). Springer. https://doi.org/10.1007/978-94-017-2195-0_6

    Book  Google Scholar 

  • Emerson, L., Kilpin, K., & Feekery, A. (2015). Smoothing the path to transition. Summary Report. Teaching & Learning Research Initiative, 2–17.

    Google Scholar 

  • Garfinkel, H. (1967). Studies in ethnomethodology. Prentice-Hall.

    Google Scholar 

  • Garfinkel, H., & Sacks, H. (1970). On formal structures of practical actions. In J. D. McKinney & E. A. Tiryakian (Eds.), Theoretical sociology (pp. 337–366). Appleton-Century Crofts.

    Google Scholar 

  • Groupe, A. H. A. (1999). Vers l’infini pas à pas-Approche Heuristique de l’Analyse. Manuel de l’élève, De Boeck Wesmael.

    Google Scholar 

  • Gueudet, G. (2004). Rôle du géométrique dans l’enseignement de l’algèbre linéaire. Recherche en didactique des mathématiques, 24(1), 81–114.

    Google Scholar 

  • Gueudet, G. (2008a). La transition secondaire-supérieur: résultats de recherches didactiques et perspectives. In R. Rouchier (Ed.), Actes de la XIIIe école d’été de didactique des mathématiques (CD-ROM). France.

    Google Scholar 

  • Gueudet, G. (2008b). Investigating the secondary-tertiary transition. Educational Studies in Mathematics, 67, 237–254. https://doi.org/10.1007/s10649-007-9100-6

    Article  Google Scholar 

  • Harris, D., Black, L., Hernandez-Martinez, P., Pepin, B., Williams, J., & with the TransMaths Team. (2015). Mathematics and its value for engineering students: What are the implications for teaching? International Journal of Mathematical Education in Science and Technology, 46(3), 321–336. https://doi.org/10.1080/0020739X.2014.979893

    Article  Google Scholar 

  • Heo, G. M., Anderson, D., Goyetche, M. H., Taker, D., & Breuleux, A. (2011). Distributed leadership facilitating collaboration in a teacher community of practice. In M. Koehler & P. Mishra (Eds.), Proceedings of SITE 2011-Society for Information Technology & teacher education international conference (pp. 1529–1534). Association for the Advancement of computing in education (AACE).

    Google Scholar 

  • Hernandez-Martinez, P., Williams, J., Black, L., Davis, P., Pampaka, M., & Wake, G. (2011). Students’ views on their transition from school to college mathematics: Rethinking ‘transition’ as an issue of identity. Research in Mathematics Education, 13(2), 119–130. https://doi.org/10.1080/14794802.2011.585824

    Article  Google Scholar 

  • Hochmuth, R. (2020). Service-courses in university mathematics education. Encyclopedia of Mathematics Education, 770–774.

    Google Scholar 

  • Ingram, J. (2018). Moving forward with ethnomethodological approaches to analysing mathematics classroom interactions. ZDM, 50(6), 1065–1075. https://doi.org/10.1007/s11858-018-0951-3

    Article  Google Scholar 

  • Janvier, C. (1990). Contextualization and mathematics for all. In T. J. Cooney & C. R. Hirsh (Eds.), Teaching and learning mathematics in the 1990s (pp. 183–193). National Council of Teachers of Mathematics.

    Google Scholar 

  • Janvier, C. (1991). Contextualisation et représentation dans l’utilisation des mathématiques. In C. Garnier, N. Bednarz, & I. Ulanovskaya (Eds.), Après Vygotski et Piaget: Perspectives sociale et constructiviste, Écoles russe et occidentale (pp. 129–147). De Boeck.

    Google Scholar 

  • Krummheuer, G. (2020). Interactionist and ethnomethodological approaches in mathematics education. Encyclopedia of mathematics education, 412–415. https://doi.org/10.1007/978-94-007-4978-8_81

  • Liebendörfer, M., & Hochmuth, R. (2013). Interest in mathematics and the first steps at the university. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of the 8th conference of European research in mathematics education (pp. 2386–2395). Middle East Technical University.

    Google Scholar 

  • Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge University Press.

    Book  Google Scholar 

  • Lave, J. (1996). Teaching and learning in practice. Mind, Culture and Activity, 3(3), 149–164.

    Article  Google Scholar 

  • Leviatan, T. (2008). Bridging a cultural gap. Mathematics Education Research Journal, 20(2), 105–116. https://doi.org/10.1007/BF03217480

    Article  Google Scholar 

  • Mathieu-Soucy, S. (2020). Becoming a teacher: A narrative inquiry into the experiences of novice teachers of mathematics in cégep. Unpublished doctoral thesis. Concordia University.

    Google Scholar 

  • McPhail, R. (2015). Pre-university prepared students: A program for facilitating the transition from secondary to tertiary education. Teaching in Higher Education, 20(6), 652–665. https://doi.org/10.1080/13562517.2015.1062360

    Article  Google Scholar 

  • Noss, R. (2002). Mathematical epistemologies at work. For the Learning of Mathematics, 22(2), 2–13.

    Google Scholar 

  • Noss, R., Pozzi, S., & Hoyles, C. (1999). Touching epistemologies: Meanings of average and variation in nursing practice. Educational Studies in Mathematics, 40(1), 25–51. https://doi.org/10.1023/A:1003763812875

    Article  Google Scholar 

  • Nunès, T., Schliemann, A. D., & Carraher, D. (1993). Street mathematics and school mathematics. Cambridge University Press. https://doi.org/10.1111/j.2044-835X.1985.tb00951.x

    Book  Google Scholar 

  • Pepin, B. (2014). Using the construct of the didactic contract to understand student transition into university mathematics education. Policy Futures in Education, 12(5), 646–657. https://doi.org/10.2304/pfie.2014.12.5.646

    Article  Google Scholar 

  • Stadler, E. (2011). The same but different: Novice university students solve a textbook exercise. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of CERME 7 (pp. 2083–2092). University of Rzesvow.

    Google Scholar 

  • Vandebrouck, F. (2011). Students conceptions of functions at the transition between secondary school and university. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of CERME 7 (pp. 2093–2102). University of Rzesvow.

    Google Scholar 

  • De Vleeschouwer, M. (2010). An institutional point of view of the secondary–university transition: The case of duality. International Journal of Mathematical Education in Science and Technology, 41(2), 155–171. https://doi.org/10.1080/00207390903372445

    Article  Google Scholar 

  • Thoma, A., & Nardi, E. (2018). Transition from school to university mathematics: Manifestations of unresolved commognitive conflict in first-year students’ examination scripts. International Journal of Research in Undergraduate Mathematics Education, 4(1), 161–180. https://doi.org/10.1007/s40753-017-0064-3

    Article  Google Scholar 

  • Thomas, M. O., & Klymchuk, S. (2012). The school–tertiary interface in mathematics: Teaching style and assessment practice. Mathematics Education Research Journal, 24(3), 283–300. https://doi.org/10.1007/s13394-012-0051-6

    Article  Google Scholar 

  • Traoré, K., & Bednarz, N. (2009). Mathématiques de la vie quotidienne au Burkina Faso: une analyse de la pratique sociale de comptage et de vente de mangues. Educational Studies in Mathematics, 72(3), 359–378. https://doi.org/10.1007/s10649-009-9200-6

    Article  Google Scholar 

  • Winsløw, C. (2007). Les problèmes de transition dans l’enseignement de l’analyse et la complémentarité des approches diverses de la didactique. Annales de didactique et de sciences cognitives, 12, 195–215.

    Google Scholar 

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Authors and Affiliations

  1. Université Laval, Québec, QC, Canada

    Claudia Corriveau

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  1. Claudia Corriveau
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Correspondence to Claudia Corriveau .

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Editors and Affiliations

  1. Institute of Mathematics, Paderborn University, Paderborn, Nordrhein-Westfalen, Germany

    Rolf Biehler

  2. Institute of Mathematics, Paderborn University, Paderborn, Nordrhein-Westfalen, Germany

    Michael Liebendörfer

  3. University Paris Saclay, Orsay, France

    Ghislaine Gueudet

  4. Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA

    Chris Rasmussen

  5. Faculty of Science, University of Copenhagen, Copenhagen, Denmark

    Carl Winsløw

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Corriveau, C. (2022). Collaboration Between Secondary and Post-secondary Teachers About Their Ways of Doing Mathematics Using Contexts. In: Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., Winsløw, C. (eds) Practice-Oriented Research in Tertiary Mathematics Education. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-14175-1_4

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