COPING WITH THE REQUIREMENTS FOR RIGOUR: THE NOVELTY OF UNIVERSITY MATHEMATICS

Given that the first-year mathematics undergraduates enter the university with A-level experiences that do not include any formal introduction to proving, the encounter with their course's requirements for rigour is deeply problematic. Based on the findings from a doctoral research project on the novice mathematician's learning difficulties in the encounter with mathematical abstraction, this paper samples a number of these difficulties: extracts of conversations between Oxford tutors and their students are presented and discussed from the point of view of highlighting the difficulty of switching from informal (school) to formal (university) mathematical thinking. Part I Background and Methodology of a Study of Learning Difficulties at University Level A psychological study oflearning difficulties in mathematics is intrinsically interesting both to psychologists- as a context-specific application and extension ofpsychological theories- and to mathematics educators as a theoretical contribution to the discourse relating to their pedagogical practices (Tall 1991b). In this sense the doctoral study on which this paper is based (Nardi 1996) is an attempt to contribute, in an implicit and theoretical way, to the pedagogical discourse on the teaching of advanced mathematics