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This study examined the effect of a professional development training programme on 20 second-year preservice mathematics teachers’ knowledge in foundational mathematical concepts at a rural university in South Africa. The training programme aimed to enhance preservice teachers’ mathematical knowledge for teaching. An embedded mixed-methods case study design was employed. Baseline and endline assessments were administered before and after the training. A participant feedback survey was also administered after the training. Results showed that the training significantly improved the preservice teachers’ understanding and confidence in the selected concepts, despite their low baseline scores. The participants also expressed satisfaction with the knowledge they gained and appreciated the integration of theory and practice in the training. These findings suggest the need for teacher training institutions to ensure that preservice teachers are well versed in both university-level and school-level mathematics. They also support the need for collaboration with other stakeholders to provide preservice teachers with relevant and engaging professional development opportunities that can enhance their mathematical knowledge for teaching.ContributionFindings of this study point to a renewed emphasis on the creation of greater collaborations between institutions of higher learning and other key stakeholders to promote the development of prospective teachers’ knowledge of what they will be expected to teach.

The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look for possible ways for students to develop a way of reasoning to work on problems that involve variational phenomena. Thus, we identified tasks in which calculus students exhibit limited understanding of essential concepts to approach and solve those tasks. The purpose is to illustrate and discuss how the systematic use of a Dynamic Geometry System (DGS) could provide a set of affordances for students to develop ways of thinking to grasp calculus foundational ideas and to study the derivative concept. Here, we relied on Thurston’s seminal work that emphasizes the relevance for learners to identify, connect, and coordinate different dimensions and meanings (intuitive, symbolic, algorithmic, geometric, physical, and formal) to construct, understand, and apply the concept of derivative.