Abstract

Research on future teachers’ geometrical knowledge mainly focused on comparing their knowledge against a reference body of knowledge. Consequently, these studies were categorized into deficit (what is lacking) and affordance (what knowledge enables) approaches. Yet, research literature is very scarce on what future teachers’ geometry knowledge is: what is its content and structure.
In research, under the term of personal epistemology are regrouped studies on people’s perceptions on the nature of knowledge and knowing, in particular those of future or in-service teachers. The main research tool of these studies is a closed item questionnaire with questions usually targeting four aspects of knowledge: certainty, simplicity, source, and justification of knowledge. A shortcoming of this approach is in the difference between professed and enacted epistemologies: the questionnaires measure professed epistemologies, yet these can differ from what is manifested in a spontaneous manner, for example during classroom instruction. A different line of research, pertinent to this thesis, is on teachers’ conceptions of teaching and learning. Several studies suggest that teachers’ conceptions rely on their epistemic beliefs. Both aspects are comprised in the term of teachers’ epistemology, introduced by Brousseau (1987). In brief, teachers’ epistemology comprises aspects of what, why and how to teach.
The aim of the thesis is to construct a praxeological model of future elementary teacher’s envisioned practice of teaching geometric transformations. These praxeologies comprise the tasks future teachers would use in their classroom to teach the topic, as well the techniques they envision students should learn. Along with these elements, we describe the theory underlying the techniques. The theory is the expression of future teachers’ geometric knowledge. In addition, by analyzing future teachers’ lesson plans, we identify manifestations of their spontaneous, enacted epistemology. By extrapolating from the detailed findings about their praxeologies, a broader characterization of future teachers’ epistemology is proposed.
The thesis discusses the potential implications of future teachers’ praxeologies for students’ learning of mathematics and proposes some recommendations for the preparation of teachers to teach mathematics.