Reframing the transition:  a mixed methods case study of mathematical thinking workshops in first-year university mathematics

Mokhithi, Mashudu

Reframing the transition: a mixed methods case study of mathematical thinking workshops in first-year university mathematics

Thesis / Dissertation

2026

Publisher

University of Cape Town

Department

Department of Mathematics and Applied Mathematics

Faculty

Faculty of Science

Abstract

For many students, the transition from school to university mathematics is challenging, especially in systems with persistent inequality, such as South Africa. In South Africa, the transition is further shaped by the enduring effects of apartheid on schooling opportunities and preparation for many learners. Support initiatives exist, but most emphasise procedural skills and content mastery while underemphasising skills essential for university mathematics, such as advanced mathematical thinking and metacognitive strategies. This study examines a theoretically grounded alternative that prioritises higher-order thinking and self-regulation. Specifically, it evaluates a voluntary, supplemental set of Mathematical Thinking Workshops (MTWs), which were offered each semester and consisted of two two-hour sessions per week. The workshops foreground collaborative problem-solving, structured reflection, and the unpacking of conceptual structures, and are grounded in the Zone of Proximal Development (ZPD), Cognitive Load Theory (CLT), and APOS theory, with the aim of cultivating the mathematical thinking and metacognitive abilities of first-year BSc students. A convergent parallel mixed-methods design integrated quantitative and qualitative strands. Quantitatively, propensity score methods were employed to mitigate confounding due to differences in pre-university academic achievement between the treatment (workshop participants) and control groups. The Average Treatment Effect on the Treated (ATT) was then estimated with cluster-robust standard errors and Holm-adjusted p-values. Analyses also examined higher-order performance (HO%) and heterogeneity by NSC Mathematics bands (70–84 vs 85-100), with Rosenbaum bounds used as a sensitivity check for unobserved confounding. Qualitatively, a reflexive thematic analysis of six focus group discussions explored the perceived impacts on mathematical understanding, problem-solving confidence, and learning strategies. Quantitatively, participants outperformed matched non-participants on early first-semester assessments and higher-order tasks, with the effects of the final exams being more minor and more variable under cluster-robust, Holm-adjusted inference. Qualitatively, participants described shifts from procedural to conceptual reasoning, strengthened metacognitive regulation (planning, monitoring, and reflection), increased confidence, and a greater sense of belonging within the mathematical community. Facilitator practices (supportive, low-threat climate) and peer collaboration emerged as key mechanisms for success. Collectively, the findings provide a theoretically informed, evidence-based framework for mathematics support that targets higher-order cognition and metacognition, and identify a subgroup (i.e., students in the 70–84 NSC band) for whom MTWs may be especially beneficial.

Keywords

mathematics

workshops

Reference:

Collections

PhD / Doctoral

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