Abstract:
Past research on mathematical knowledge in teaching has mainly focused on real-time practices of teaching from school settings. These studies provide us with empirical and theoretical conceptualisations that describe the use of mathematical knowledge from a pedagogical perspective. However, researchers also advocate the need to look into mathematical knowledge as held by lecturers. My study uses the context of undergraduate mathematics lecturing in a university setting. The aim is to develop a theoretical framework broadly describing mathematicians’ mathematical knowledge and its use in lecturing. In this research, I conceptualise mathematicians’ mathematical knowledge as having ‘head’ and ‘body’ aspects. The head represented the ‘unseen’ aspect of mathematical knowledge whereas the ‘body’ represented the ‘seen’ aspect. This enabled me to understand nuances of mathematicians’ mathematical knowledge; discarding the dichotomy of theory and practice. This ethnographic study used questionnaires, pre- and post-observation interviews, and lecture observations to collect data from 26 mathematicians. The research design adopted a pilot study followed by the main study. The data analysis made use of thematic analysis and a version of grounded theory to uncover the ‘head’ and the ‘body’ aspects of mathematical knowledge. The head aspect of mathematicians’ mathematical knowledge had explicit and implicit dimensions having conscious and unconscious levels of awareness. Their mathematical knowledge had a cyclic nature characterised by both developing and decreasing knowledge. The body aspect of mathematical knowledge examined the mathematical knowledge enacted in lecturing. The use of a framework of key lecturing practices provided the components and interconnections of mathematical knowledge in lecturing. A theoretical framework is developed showing the ‘head’ and the ‘body’ representing mathematicians’ mathematical knowledge as a single entity devoid of the dichotomy. Thus, this research presents us with a new perspective on mathematical knowledge, viewing mathematical knowledge in a creative cycle having an individual as well as a social implication.