Skip to main content
Log in

New insights about the secondary–tertiary transition in mathematics

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

In this concluding commentary, I embed the articles of the special issue “Transition from school into university mathematics: experiences across educational contexts” into the current landscape of research on secondary–tertiary transition, and discuss the advancement they made related to the synthesis published in 2008 by Gueudet. My aim is to elaborate a new synthesis across the topics of affect and the use of sociocultural perspectives that have framed the work of all contributions. For that, I focus on four major themes. First, I consider the complex relationship between affect and socio-cultural dimensions in the papers, which raises the need for theory networking in further research clarifying mutual roles of the two dimensions. Second, international diversity is only partially expressed in the collection of papers, thus should be a major topic of research in future that would provide a more comprehensive view on the transition from school to university mathematics. I thirdly discuss how the collection of papers deepens our understanding of the complexity and diversity related to the students’ experience with the secondary–tertiary transition and its potential impact for teaching. Finally, I propose and justify the need for systematic design and evaluation of interventions targeting a change in students’ affect related to the transition. In sum, the wide range of the significant findings in this special issue and their mutual relations add new perspectives to the research on secondary–tertiary transition and evidence a new spectrum of research directions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Notes

  1. This survey has been organized by the educational committee of the European Mathematical Society.

  2. Research in Undergraduate Mathematics Education, http://sigmaa.maa.org/rume/Site/News.html

  3. See in particular the “Joint statement to reduce reviewer bias” https://mathematicseducationjournals.com/

References

  • Adiredja, A. P., & Andrews-Larson, C. (2017). Taking the sociopolitical turn in postsecondary mathematics education research. International Journal of Research in Undergraduate Mathematics Education, 3(3), 444–465. https://doi.org/10.1007/s40753-017-0054-5

    Article  Google Scholar 

  • Alves Dias, M., Artigue, M., Jahn, A.P., &, Campos, T. (2010). A comparative study of the secondary-tertiary transition. In M.F. Pinto, & T.F. Kawasaki (Eds.), Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 129–136). PME.

  • Artigue, M. (2021). Mathematics education research at university level: Achievements and challenges. In V. Durand-Guerrier, R. Hochmuth, E. Nardi, & C. Winsløw (Eds.), Research and development in university mathematics education (pp. 3–21). Routledge. https://doi.org/10.4324/9780429346859-3

    Chapter  Google Scholar 

  • Barquero, B., & Winsløw, C. (2022). Preservice secondary school teachers revisiting real numbers: A striking instance of Klein’s second discontinuity. In R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, & C. Winsløw (Eds.), Practice-oriented research in tertiary mathematics education. Springer. https://doi.org/10.1007/978-3-031-14175-1_25

    Chapter  Google Scholar 

  • Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., & Winsløw, C. (Eds.). (2022). Practice-oriented research in tertiary mathematics education. Springer. https://doi.org/10.1007/978-3-031-14175-1

    Book  Google Scholar 

  • Bikner-Ahsbahs, A., & Prediger, S. (2010). Networking of theories—An approach for exploiting the diversity of theoretical approaches. In B. Sriraman & L. English (Eds.), Theories of Mathematics Education. Advances in Mathematics Education. Springer. https://doi.org/10.1007/978-3-642-00742-2_46

    Chapter  Google Scholar 

  • Biza, I., Jaworski, B., & Hemmi, K. (2014). Communities in university mathematics. Research in Mathematics Education, 16(2), 161–176. https://doi.org/10.1080/14794802.2014.918351

    Article  Google Scholar 

  • Bosch, M., Fonseca, C., & Gascon, J. (2004). Incompletud de las organizaciones matematicas locales en las instituciones escolares [Incompleteness of the mathematical organizations in school institutions]. Recherches en Didactique des Mathématiques, 24(2–3), 205–250. https://revue-rdm.com/2004/incompletitud-de-las/

  • Chevallard, Y. (1992). Fundamental concepts in didactics: Perspectives provided by an anthropological approach. In R. Douady & A. Mercier (Eds.), Research in didactique of mathematics, selected papers (pp. 131–168). La Pensée Sauvage.

    Google Scholar 

  • Clark, M., & Lovric, M. (2009). Understanding secondary–tertiary transition in mathematics. International Journal of Mathematical Education in Science and Technology, 40(6), 755–776. https://doi.org/10.1080/00207390902912878

    Article  Google Scholar 

  • Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Sciences, 10(1/2), 113–163. http://www.jstor.org/stable/1466831

  • Deshler, J., Fuller, E., & Darrah, M. (2019). Affective states of university developmental mathematics students and their impact on self-efficacy, belonging, career identity, success and persistence. International Journal of Research in Undergraduate Mathematics Education, 5(3), 337–358. https://doi.org/10.1007/s40753-019-00096-3

    Article  Google Scholar 

  • Di Martino, P., Gregorio, F., & Iannone, P. (2022a). The transition from school to university in mathematics education research : New trends and ideas from a systematic literature review. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-022-10194-w

  • Di Martino, P., Gregorio, F., & Iannone, P. (2022b). The transition from school to university mathematics in different contexts : Affective and sociocultural issues in students’ crisis. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-022-10179-9

  • Di Martino, P., & Zan, R. (2010). ‘Me and maths’: Towards a definition of attitude grounded on students’ narratives. Journal of Mathematics Teacher Education, 13, 27–48. https://doi.org/10.1007/s10857-009-9134-z

    Article  Google Scholar 

  • Eichler, A., & Gradwohl, J. (2021). Investigating motivational and cognitive factors which impact the success of engineering students. International Journal of Research in Undergraduate Mathematics Education, 7(3), 417–437. https://doi.org/10.1007/s40753-020-00127-4

    Article  Google Scholar 

  • European Commission, Directorate-General for Education, (2016). Youth, sport and culture, does the EU need more STEM graduates? Final report, Publications Office. https://data.europa.eu/doi/10.2766/000444

  • Geisler, S., Rolka, K., & Rach, S. (2023). Development of affect at the transition to university mathematics and its relation to dropout—Identifying related learning situations and deriving possible support measures. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-022-10200-1

    Article  Google Scholar 

  • González-Martín, A. S., Biza, I., Florensa, I., Gueudet, G., Rasmussen, C., Thoma, A., & Viirman, O. (2022). Introduction to the papers of TWG14: University mathematics education. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.), Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Feb 2022, Bozen-Bolzano, Italy.

  • Grove, M., & Croft, T. (2019). Learning to be a postgraduate tutor in a mathematics support centre. International Journal of Research in Undergraduate Mathematics Education, 5(2), 228–266. https://doi.org/10.1007/s40753-019-00091-8

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Gueudet, G., & Pepin, B. (2018). Didactic contract at the beginning of university : A focus on resources and their use. International Journal of Research in Undergraduate Mathematics Education, 4(1), 56–73. https://doi.org/10.1007/s40753-018-0069-6

    Article  Google Scholar 

  • Holland, D. C., Lachicotte, W., Skinner, D., & Cain, C. (1998). Identity and agency in cultural worlds. Harvard University Press.

    Google Scholar 

  • Johns, C. (2020). Self-regulation in first-semester calculus. International Journal of Research in Undergraduate Mathematics Education, 6(3), 404–420. https://doi.org/10.1007/s40753-020-00114-9

    Article  Google Scholar 

  • Kilpatrick, J. (2019). A double discontinuity and a triple approach: Felix Klein’s perspective on mathematics teacher education. In H.-G. Weigand, W. McCallum, M. Menghini, M. Neubrand, & G. Schubring (Eds.), The legacy of Felix Klein. ICME-13 Monographs. Springer. https://doi.org/10.1007/978-3-319-99386-7_15

  • Klein, F. (1908/1939). Elementary mathematics from an advanced standpoint. Part I: Arithmetic, algebra, analysis. Part II: Geometry. (E. R. Hedrick & C. A. Noble, Trans.). Dover Publications.

  • Kober, L. (2015). Reaching students What research says about effective instruction in undergraduate science and engineering. The National Academies Press. https://doi.org/10.17226/1868

    Book  Google Scholar 

  • Kontorovich, I., & Ovadiya, T. (2023). How narratives about the secondary-tertiary transition shape undergraduate tutors’ sense-making of their teaching. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-023-10211-6

  • Laursen, S. L., & Rasmussen, C. (2019). I on the prize: Inquiry approaches in undergraduate mathematics. International Journal of Research in Undergraduate Mathematics Education, 5(1), 129–146. https://doi.org/10.1007/s40753-019-00085-6

    Article  Google Scholar 

  • Leung, F.K.S, Park, K., Shimizu, Y., & Xu, B. (2015). Mathematics education in East Asia. In S.J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education, (pp. 123–143), Springer. https://doi.org/10.1007/978-3-319-12688-3_11

  • Liang, B., Ng, O.-L., & Chan, Y.-C. (2022). Seeing the continuity behind “double discontinuity”: Investigating Hong Kong prospective mathematics teachers’ secondary–tertiary transition. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-022-10197-7

    Article  Google Scholar 

  • Lim, W., Yoon, H., Bae, Y., & Kwon, O. N. (2023). The development of sociomathematical norms in the transition to tertiary exam-oriented individualistic mathematics education in an East Asian context. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-022-10203-y

  • Nardi, E. (2019). From advanced mathematical thinking to university mathematics education: A story of emancipation and enrichment. In T. Dooley & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Mathematical Society for Research in Mathematics Education, (pp. 9–31). DCU Institute of Education and ERME.

  • OECD. (2022). Education at a glance 2022: OECD Indicators. OECD Publishing. https://doi.org/10.1787/3197152b-en

    Article  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 

  • Pinto, A., & Koichu, B. (2022). Diverse perspectives and experiences of university mathematics teachers on improving the secondary-tertiary transition. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-022-10196-8

    Article  Google Scholar 

  • Prendergast, M., O'Meara, N., O'Hara, C., Harbison, L., & Cantley, I. (2019). Bridging the primary to secondary school mathematics divide: Teachers’ perspectives. Issues In Educational Research, 29(1), 243–260. http://www.iier.org.au/iier29/prendergast.pdf

  • Schukajlow, S., Rakoczy, K., & Pekrun, R. (2017). Emotions and motivation in mathematics education: Theoretical considerations and empirical contributions. ZDM-Mathematics Education, 49, 307–322. https://doi.org/10.1007/s11858-017-0864-6

    Article  Google Scholar 

  • Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944

    Article  Google Scholar 

  • Tall, D. (2008). The transition to formal thinking in mathematics. Mathematics Education Research Journal, 20, 5–24. https://doi.org/10.1007/BF03217474

    Article  Google Scholar 

  • Vieira, D., Mutize, T., & Chinchilla, J. R. (2020). Understanding access to higher education in the last two decades. UNESCO. https://www.iesalc.unesco.org/en/2020/12/23/understanding-access-to-higher-education-in-the-last-two-decades/. Accessed 14 Mar 2023.

  • Viirman, O. (2022). Klein's double discontinuity around the world - The case of calculus. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.), Proceedings of the Twelfth Congress of European Research Society in Mathematics Education (CERME12). Free University of Bozen-Bolzano and ERME.

  • Voigt, M., Rasmussen, C., & Martinez, A. E. (2022). The refiguring of students’ mathematical identities : A mixed methods study of three tailored calculus courses. International Journal of Mathematical Education in Science and Technology53(12), 3286–3306. https://doi.org/10.1080/0020739X.2021.1940331

  • Weller, K., Clark, J., Dubinsky, E., Loch, S., McDonald, M., & Merkovsky, R. (2003). Student performance and attitudes in courses based on APOS theory and the ACE teaching cycle. In A. Selden, E. Dubinsky, G. Harel, & F. Hitt (Eds.), CBMS issues in mathematics education (vol. 12, pp. 97–131). American Mathematical Society. https://doi.org/10.1090/cbmath/012/05

Download references

Acknowledgements

I warmly thank Angelika Bikner-Ahsbahs and Vilma Mesa, whose advice and constructive criticism on previous versions played an essential role in the writing of this article.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ghislaine Gueudet.

Ethics declarations

Competing interests

The author declares no competing interests.

Additional information

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gueudet, G. New insights about the secondary–tertiary transition in mathematics. Educ Stud Math 113, 165–179 (2023). https://doi.org/10.1007/s10649-023-10223-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-023-10223-2

Keywords

Navigation