A cultural-historical activity theory based analysis of lecturer and student understanding of learning in the Department of Mathematics and Applied Mathematics at the University of Cape Town

Van Heerden, Thomas

A cultural-historical activity theory based analysis of lecturer and student understanding of learning in the Department of Mathematics and Applied Mathematics at the University of Cape Town

Master Thesis

2019

Abstract

Cultural-historical activity theory (CHAT) provides a framework for analysing activity systems. I use that framework to investigate teaching and learning in two first-year university mathematics courses at the University of Cape Town. The focus of this investigation is whether the different subjects of this activity system (i.e. the students and the lecturers) have different conceptions of learning, and what those possible differences mean for teaching and learning. The CHAT framework is well-suited to this type of work. CHAT’s theoretical roots are in Hegel’s dialectics and Vygotsky’s mediation. Teaching and learning are higher-order mental phenomena. Dialectics allow us to aggregate our data to draw conclusions about this type of higher-order phenomenon, and the notion of mediation (extended from Vygotsky’s initial work by Leont’ev and others) provides a means to understand how learning happens. Data are collected both through face-to-face interviews with a small group of subjects (n = 6) and more broadly through an online questionnaire (n = 55). The face-to-face interviews and the questionnaires make it clear that students and lecturers do have different conceptions of learning; in the language of CHAT, there are tensions in the system. These tensions can be categorised into two major themes: what students do and how they do it. These tensions will not be easily resolved; I suggest teaching some meta-cognitive skills rather than only mathematics as a first step.

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