Research-informed and collaborative reform in
university mathematics teaching: The case of secondary
to tertiary transition
George Witty, Owen Hooper, Elena Nardi, Irene Biza
To cite this version:
George Witty, Owen Hooper, Elena Nardi, Irene Biza. Research-informed and collaborative reform in university mathematics teaching: The case of secondary to tertiary transition. Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14), Free University of Bozen-Bolzano; ERME, Feb 2025, Bozen-Bolzano, Italy. hal-05314344
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Submitted on 14 Oct 2025

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Research-informed and collaborative reform in university
mathematics teaching: The case of secondary to tertiary transition
George Witty, Owen Hooper, Elena Nardi and Irene Biza
University of East Anglia, Norwich, United Kingdom; g.witty@uea.ac.uk
Keywords: Secondary-tertiary transition, teaching design, teacher-researcher partnerships.
Mathematics students are known to face many difficulties during their transition from secondary to tertiary education (Gueudet, 2008). During the teaching of an introductory course for first-year mathematics students, the first author (Witty) encountered numerous issues which he associated with this transition, particularly related to students’ attempts at mathematical communication, as well as their low engagement levels. For example, it was common to encounter students who would produce solutions that used new mathematical words and symbols, but lacked the rigour he would expect from something ‘mathematical’. Gueudet (2008) states that, when students begin university, they notice the new language used by their teachers and imitate it: this “leads them to produce texts looking like mathematics, focusing sometimes more on the form – many symbols, usual language brought to a minimum – than on the mathematical meaning” (p. 244). Similarly, Sfard (2008) notes that “there are important differences between construction and substantiation routines practiced in colloquial and literary mathematical discourses, and these routines change again in the transition from school discourse to the scholarly discourse of mathematicians” (p. 225). As Witty believed it is important to consider how to assist students in overcoming these differences and difficulties in their first year, he became interested in learning more about changes he could make to help. There have been calls for the design and evaluation of interventions that support students during the secondary-tertiary transition. For example, Biehler et al. (2022) state that “there is a growing interest in teaching practices fostering students’ active engagement” (p. 10) and that research in mathematics education can support teachers at university-level in this aim. With this in mind, Witty embarked on the design, implementation and evaluation of a new set of teaching sessions created for a course on ‘Mathematical Skills’ he leads with the aim of alleviating some of the difficulties of the secondary- tertiary transition. Although this intervention was produced in a partnership between him and mathematics education researchers (Hooper, Nardi, Biza), here he reflects on his own experience, mainly of the design part, through a reflexive autoethnographic approach (Ellis et al., 2010).
In this Year 1 course, students are introduced to core definitions and concepts of pure mathematics, such as properties of sets, numbers, and functions, as well as to mathematical proof. When Witty took on this course, he was given materials used previously which lend themselves to a typical ‘chalk-and- talk’ lecture format. He saw problems in students’ engagement and use of mathematical words and symbols whilst teaching this course, and there were additional issues he encountered with his delivery such as an inability to fully convey passion for the new way of mathematical thinking when consigned to a blackboard. He attempted to fix some of these problems in his second year of teaching the course by introducing quizzes into lectures and moving problem solving activity into lecture time. This improved things, but the lack of a systematic approach and understanding of whether he was changing things in a pedagogically sound way meant he did not feel he was reaching the full potential of moving to a new lecture format. When he was made aware of an opportunity to work with the university’s Mathematics Education research group on a project that would involve redesigning a course to include more interactive elements and use of different methods of teaching, this seemed like a good opportunity to improve and expand on his approach to easing the transition to university mathematics.
The approach to planning and designing the new structure for the course was done through regular meetings with Mathematics Education researchers (mostly Hooper) where Witty provided updates on the content and the aims of the sessions, whilst researchers provided research-informed insight on innovative teaching practices, such as inquiry-based group work with flipped classroom elements and use of online tools, such as Padlet, as means for increasing student engagement and contributions during lectures (Hooper & Nardi, 2024). We created a lesson plan template (Figure 1) to detail timings and use of interactivity during a session, along with an explanation by Witty of why he wanted to deliver each part of the session in this way.

				
Figure 1: Template excerpt for the plan of the beginning of a lecture

The creation of a plan for each session – and its collaborative production with the Mathematics Education research team – is a novelty that we see as of potential pedagogical value to other university mathematics teachers. We see its value in being asked to reflect explicitly on why Witty was choosing a certain method or activity or tool. The poster (https://tinyurl.com/CERME14-Poster-Witty-et-al) presents this design process, highlights of the course implementation and reflections thereof.
References
Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., & Winsløw, C. (Eds) (2022). Practice- Oriented Research in Tertiary Mathematics Education (pp. 1–20). Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1
Ellis, C., Adams, T. E., & Bochner, A. P. (2010). Autoethnography: An Overview. Forum: Qualitative Social Research, 12(1). https://doi.org/10.17169/fqs-12.1.1589
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
Hooper, O., & Nardi, E. (2024). How emergency remote teaching inspired a university mathematics course blended learning, flipped classroom intervention. In A. S. González-Martín, G. Gueudet, I. Florensa, N. Lombard (Eds.), Proceedings of INDRUM2024 (pp. 801–810). https://indrum2024.sciencesconf.org/
Sfard, A. (2008). Thinking as Communicating: Human Development, the Growth of Discourses, and
Mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944