Approaching Proof in a Community of Mathematical Practice

Sammanfattning: This thesis aims to describe how students encounter proof in a community of mathematical practice at a mathematics department and how they are drawn to share mathematicians’ views and knowledge of proof. Considering the department as a community of practice where the joint enterprise is learning mathematics in a broad sense made it possible to perceive the newcomers as active participants in the practice. The combination of a socio-cultural perspective, Lave and Wenger’s and Wenger’s social practice theories and theories about proof offers a fresh framework in understanding and describing the diversity of the culture involving such a complex notion as proof. Proof is examined from historical, philosophical and didactical points of view and considered as reification and as an artefact from a socio-cultural perspective. The metaphor of transparency of artefacts that refers to the intricate dilemma about how much to focus on different aspects of proof at a meta-level and how much to work with proof without focusing on it, both from teacher and student perspectives, is a fundamental aspect in the data analysis. The data consists of transcripts of interviews with mathematicians and students as well as survey responses of university entrants, protocols of observations of lectures, textbooks and other instructional material. Both qualitative and quantitative methods were applied in the data analysis. A theoretical model with three different teaching styles with respect to proof could be constructed from the data. The students related positively to proof when they entered the practice. Though the mathematicians had no explicit intention of dealing so much with proof in the basic course, students felt that they were confronted with proof from the very beginning of their studies. Proof was there as a mysterious artefact and a lot of aspects of proof remained invisible as experienced by students when they struggled to find out what proof is and to understand its role and meaning in the practice. The first oral examination in proof seems to be significant in drawing students to the practice of proof.