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Diverse perspectives and experiences of university mathematics teachers on improving the secondary-tertiary transition

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Abstract

This study explores the diversity of university mathematics teachers’ perspectives and experiences in relation to the secondary-tertiary transition (STT). Data for this study consist of responses of 310 university mathematics teachers from 30 countries to a survey. The survey design and data analysis are informed by an adaptation of a theory of improvement for education and by four idealized approaches for improving STT as identified in the literature: jump-oriented, enculturation-oriented, diversity-oriented, and cross-community-oriented. We characterize the diversity of perspectives and experiences in the data and examine ideas for future projects in light of these four approaches. We conclude that while jump-oriented approaches for improving STT are still the most prevalent, in part due to a persistent perspective of STT as a “deficit,” university mathematics teachers’ discourse on STT is becoming more diverse and nuanced. We find it particularly promising that participants’ suggestions for future action are aligned with the four approaches, and most notably, with the cross-community approach expressing the emergent need for greater communication between the secondary and tertiary mathematics education communities.

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Data availability

The data that support the findings of this study is not publicly available due to privacy restrictions. Data are available from the corresponding author upon reasonable request and with the permission of the EMS Education Committee.

Notes

  1. A copy of the questionnaire is available as supplementary material.

References

  • Adiredja, A. P., & Zandieh, M. (2020). The lived experience of linear algebra: A counter-story about women of color in mathematics. Educational Studies in Mathematics, 104(2), 239–260. https://doi.org/10.1007/s10649-020-09954-3

    Article  Google Scholar 

  • Alcock, L. (2010). Mathematicians’ perspectives on the teaching and learning of proof. In F. Hitt, D. Holton, & P. Thompson (Eds.), Research in collegiate mathematics education, VII (pp. 63–91). MAA. https://repository.lboro.ac.uk/articles/chapter/Mathematicians_perspectives_on_the_teaching_and_learning_of_proof/9372596

  • Artigue, M. (2004). Le défi de la transition secondaire/supérieur: Que peuvent nous apporter les recherches didactiques et les innovations développées dans ce domaine. Paper presented at the 1st Canada/France Meeting in the Mathematical Sciences, Toulouse.

  • Artigue, M. (2016). Mathematics education research at university level: achievements and challenges. In E. Nardi, C. Winsløw & T. Hausberger (Eds.), Proceedings of the First Conference of the International Network for Didactic Research in University Mathematics (pp. 11–27). University of Montpellier and INDRUM. https://doi.org/10.4324/9780429346859-3

  • Artigue, M., Batanero, C., & Kent, P. (2007). Mathematics thinking and learning at post-secondary level. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1011–1049). Information Age.

    Google Scholar 

  • Bardelle, C., & Di Martino, P. (2012). E-learning in secondary–tertiary transition in mathematics: For what purpose? ZDM-Mathematics Education, 44(6), 787–800. https://doi.org/10.1007/s11858-012-0417-y

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

    Article  Google Scholar 

  • Biza, I., González-Martín, A. S., & Pinto, A. (2022). ‘Scaffolding’ or ‘filtering’: A review of studies on the diverse roles of calculus courses for students, professionals and teachers. International Journal of Research in Undergraduate Mathematics Education. https://doi.org/10.1007/s40753-022-00180-1

    Article  Google Scholar 

  • Bryk, A. S., Gomez, L. M., Grunow, A., & LeMahieu, P. G. (2015). Learning to improve: How America’s schools can get better at getting better. Harvard Education Press.

  • Cai, J., & Hwang, S. (2021). Teachers as redesigners of curriculum to teach mathematics through problem posing: Conceptualization and initial findings of a problem‑posing project. ZDM-Mathematics Education, 53, 1403–1416. https://doi.org/10.1007/s11858-021-01252-3

  • 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 

  • 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 

  • Cronin, A., & Meehan, M. (2021). The utility of mathematics support centre feedback to lecturers of large first-year university mathematics courses. International Journal of Mathematical Education in Science and Technology, 52(10), 1–19.

  • Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. The Journal of Mathematical Behavior, 15(4), 375–402.

    Article  Google Scholar 

  • Dawkins, P. C., & Weber, K. (2017). Values and norms of proof for mathematicians and students. Educational Studies in Mathematics, 95(2), 123–142. https://doi.org/10.1007/s10649-016-9740-5

    Article  Google Scholar 

  • De Guzmán, M., Hodgson, B. R., Robert, A., & Villani, V. (1998). Difficulties in the passage from secondary to tertiary education. In A. Louis, U. Rehmann & P. Schneider (Eds.), Proceedings of the International Congress of Mathematicians (Vol. 3, pp. 747–762). Documenta Mathematica.

  • 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 

  • Edwards, B. S., Dubinsky, E., & McDonald, M. A. (2005). Advanced mathematical thinking. Mathematical Thinking and Learning, 7(1), 15–25. https://doi.org/10.1207/s15327833mtl0701_2

    Article  Google Scholar 

  • Ellis, J., Kelton, M., & Rasmussen, C. (2014). Student perceptions of pedagogy and associated persistence in calculus. ZDM-Mathematics Education, 46(4), 661–673. https://doi.org/10.1007/s11858-014-0577-z

    Article  Google Scholar 

  • Good, C., Aronson, J., & Harder, J. A. (2008). Problems in the pipeline: Stereotype threat and women’s achievement in high level math courses. Journal of Applied Developmental Psychology, 29(1), 17–28. https://doi.org/10.1016/j.appdev.2007.10.004

    Article  Google Scholar 

  • Güçler, B. (2013). Examining the discourse on the limit concept in a beginning-level calculus classroom. Educational Studies in Mathematics, 82(3), 439–453. https://doi.org/10.1007/s10649-012-9438-2

    Article  Google Scholar 

  • Güçler, B. (2016). Making implicit metalevel rules of the discourse on function explicit topics of reflection in the classroom to foster student learning. Educational Studies in Mathematics, 91(3), 375–393. https://doi.org/10.1007/s10649-015-9636-9

    Article  Google Scholar 

  • Gueudet, G. (2008). Investigating the secondary–tertiary transition. Educational Studies in Mathematics, 67(3), 237–254. https://doi.org/10.1007/s10649-007-9100-6

    Article  Google Scholar 

  • Gueudet, G., Bosch, M., DiSessa, A. A., Kwon, O. N., & Verschaffel, L. (2016). Transitions in mathematics education. ICME-13 Topical Surveys. Springer. https://doi.org/10.1007/978-3-319-31622-2

  • Hernandez-Martinez, P. (2016). “Lost in transition”: Alienation and drop out during the transition to mathematically-demanding subjects at university. International Journal of Educational Research, 79, 231–239. https://doi.org/10.1016/j.ijer.2016.02.005

    Article  Google Scholar 

  • Hochmuth, R., Broley, L., & Nardi, E. (2021). Transitions to, across and beyond university. In V. Durand-Guerrier, R., E. Nardi, and C. Winsløw (Eds.), Research and development in university mathematics education (pp. 191–215). Routledge. https://doi.org/10.4324/9780429346859

  • Iannone, P., & Nardi, E. (2005). On the pedagogical insight of mathematicians: ‘Interaction’and ‘transition from the concrete to the abstract.’ The Journal of Mathematical Behavior, 24(2), 191–215. https://doi.org/10.1016/j.jmathb.2005.03.005

    Article  Google Scholar 

  • Koichu, B., & Pinto, A. (on behalf of EMS Education Committee). (2019). The secondary-tertiary transition in mathematics: What are our current challenges and what can we do about it? EMS Newsletter, 112, 34–35.

  • Lawson, D., Grove, M., & Croft, T. (2022). The development of mathematics support: Teaching and learning practices, scholarship, and communities. EpiDEMES. https://doi.org/10.46298/epidemes-9097

  • LeMahieu, P. G., Edwards, A. R., & Gomez, L. M. (2015). At the nexus of improvement science and teaching: Introduction to a special section of the Journal of Teacher Education. Journal of Teacher Education, 66(5), 446–449. https://doi.org/10.1177/0022487115602125

    Article  Google Scholar 

  • Leyva, L. A., Quea, R., Weber, K., Battey, D., & López, D. (2021). Detailing racialized and gendered mechanisms of undergraduate precalculus and calculus classroom instruction. Cognition and Instruction, 39(1), 1–34. https://doi.org/10.1080/07370008.2020.1849218

    Article  Google Scholar 

  • Lew, K., Fukawa-Connelly, T. P., Mejía-Ramos, J. P., & Weber, K. (2016). Lectures in advanced mathematics: Why students might not understand what the mathematics professor is trying to convey. Journal for Research in Mathematics Education, 47(2), 162–198. https://doi.org/10.5951/jresematheduc.47.2.0162

    Article  Google Scholar 

  • Lewis, C. (2015). What is improvement science? Do we need it in education? Educational Researcher, 44(1), 54–61. https://doi.org/10.3102/0013189X15570388

    Article  Google Scholar 

  • Louie, N., Adiredja, A. P., & Jessup, N. (2021). Teacher noticing from a sociopolitical perspective: the FAIR framework for anti-deficit noticing. ZDM-Mathematics Education53(1), 95–107. https://doi.org/10.1007/s11858-021-01229-2

  • Matthews, J., Croft, T., Lawson, D., & Waller, D. (2013). Evaluation of mathematics support centres: A literature review. Teaching Mathematics and Its Applications: International Journal of the IMA, 32(4), 173–190. https://doi.org/10.1093/teamat/hrt013

    Article  Google Scholar 

  • Mitchell, M., & Jolley, J. (2010). Research design explained. WCL.

  • Nardi, E., Ryve, A., Stadler, E., & Viirman, O. (2014). Commognitive analyses of the learning and teaching of mathematics at university level: The case of discursive shifts in the study of Calculus. Research in Mathematics Education, 16(2), 182–198. https://doi.org/10.1080/14794802.2014.918338

    Article  Google Scholar 

  • Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish KOM project. In A. Gagatsis & S. Papastavridis (Eds.), Proceedings of the 3rd Mediterranean Conference on Mathematics Education (pp. 115–124). Hellenic MS.

  • Peck, F. (2021). Towards anti-deficit education in undergraduate mathematics education: How deficit perspectives work to structure inequality and what can be done about it. Primus, 31(9), 940–961. https://doi.org/10.1080/10511970.2020.1781721

    Article  Google Scholar 

  • Perla, R. J., Provost, L. P., & Parry, G. J. (2013). Seven propositions of the science of improvement: Exploring foundations. Quality Management in Healthcare, 22(3), 170–186. https://doi.org/10.1097/QMH.0b013e31829a6a15

    Article  Google Scholar 

  • Peurach, D., Russell, J., Cohen-Vogel, L., & Penuel, W. (Eds.) (2022). The foundational handbook on improvement research in education. Rowman & Littlefield.

  • President’s Council of Advisors on Science and Technology (PCAST) (2012). Engage to excel: Producing one million additional college graduates with degrees in Science, Technology, Engineering, and Mathematics. The White House.

  • Pinto, A. (2019). Variability in the formal and informal content instructors convey in lectures. The Journal of Mathematical Behavior, 54, 100680. https://doi.org/10.1016/j.jmathb.2018.11.001

    Article  Google Scholar 

  • Pinto, A., & Karsenty, R. (2018). From course design to presentations of proofs: How mathematics professors attend to student independent proof reading. The Journal of Mathematics Behavior, 49, 129–144. https://doi.org/10.1016/j.jmathb.2017.11.008

    Article  Google Scholar 

  • Pinto, A., & Karsenty, R. (2020). Norms of proof in different pedagogical contexts. For the Learning of Mathematics, 40(1), 22–27.

    Google Scholar 

  • Rach, S., & Heinze, A. (2017). The transition from school to university in mathematics: Which influence do school-related variables have? International Journal of Science and Mathematics Education, 15(7), 1343–1363. https://doi.org/10.1007/s10763-016-9744-8

    Article  Google Scholar 

  • Russell, J. L., & Penuel, W. R. (2022). In D. Peurach, J. Russell, L. Cohen-Vogel, and W. Penuel (Eds.) Introducing improvement research in education. The foundational handbook on improvement research in education (pp. 1–20). Rowman & Littlefield.

  • Sabbah, S., & Heyd-Metzuyanim, E. (2021). Integration of Arab female students at a technological university—Narratives of identity in figured worlds. International Journal of Science and Mathematics Education, 19(5), 977–996.

  • Schürmann, M., Gildehaus, L., Liebendörfer, M., Schaper, N., Biehler, R., Hochmuth, R., Kuklinski, C., & Lankeit, E. (2020). Mathematics learning support centres in Germany – An overview. Teaching Mathematics and Its Applications: An International Journal of the IMA, 40(2), 99–113. https://doi.org/10.1093/teamat/hraa007

    Article  Google Scholar 

  • Selden, A. (2005). New developments and trends in tertiary mathematics education: Or, more of the same? International Journal of Mathematical Education in Science and Technology, 36(2–3), 131–147. https://doi.org/10.1080/00207390412331317040

    Article  Google Scholar 

  • Selden, A. (2012). Transitions and proof and proving at tertiary level. In G. Hanna & M. de Villiers (Eds.), Proof and proving in mathematics education (pp. 391–420). Springer. https://doi.org/10.1007/978-94-007-2129-6_17

  • Selden, A., & Selden, J. (2001). Tertiary mathematics education research and its future. In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 237–254). Springer.

    Google Scholar 

  • Sfard, A. (2014). University mathematics as a discourse–why, how, and what for? Research in Mathematics Education, 16(2), 199–203. https://doi.org/10.1080/14794802.2014.918339

    Article  Google Scholar 

  • Tall, D. (1991). Advanced mathematical thinking. Kluwer.

    Book  Google Scholar 

  • Thomas, M. O., de Freitas Druck, I., Huillet, D., Ju, M. K., Nardi, E., Rasmussen, C., & Xie, J. (2015). Key mathematical concepts in the transition from secondary school to university. In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 265–284). Springer. https://doi.org/10.1007/978-3-319-12688-3_18

  • 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 

  • Watson, A. (2008). School mathematics as a special kind of mathematics. For the Learning of Mathematics28(3), 3–7. https://www.jstor.org/stable/40248612

  • Weber, K. (2004). Traditional instruction in advanced mathematics courses: A case study of one professor’s lectures and proofs in an introductory real analysis course. The Journal of Mathematical Behavior, 23(2), 115–133. https://doi.org/10.1016/j.jmathb.2004.03.001

    Article  Google Scholar 

  • Weber, K. (2010). Mathematics majors’ perceptions of conviction, validity, and proof. Mathematical Thinking and Learning, 12(4), 306–336. https://doi.org/10.1080/10986065.2010.495468

    Article  Google Scholar 

  • Weber, K. (2012). Mathematicians’ perspectives on their pedagogical practice with respect to proof. International Journal of Mathematical Education in Science and Technology, 43(4), 463–482. https://doi.org/10.1080/0020739X.2011.622803

    Article  Google Scholar 

  • Wood, L. (2001). The secondary-tertiary interface. In D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss, & A. Schoenfeld (Eds.), The teaching and learning of mathematics at university level (pp. 87–98). Springer.

    Google Scholar 

  • Wu, H. (2011). The mis-education of mathematics teachers. Notices of the AMS, 58(3), 372–384.

    Google Scholar 

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Acknowledgements

This research is based on the data collected in a survey initiated by the EMS Education Committee in 2019. The authors are grateful to the Committee for granting access to these data. In addition, our thanks go to Hadas Levi Gamlieli for her assistance with the initial analysis of the survey results.

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Correspondence to Alon Pinto.

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Pinto, A., Koichu, B. Diverse perspectives and experiences of university mathematics teachers on improving the secondary-tertiary transition. Educ Stud Math 113, 147–164 (2023). https://doi.org/10.1007/s10649-022-10196-8

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