The challenge of teaching first-year undergraduate mathematics: tutors' reflections on the formal mathematical enculturation of their students

Integrating the findings from a qualitative study of 20 first-year undergraduates' learning difficulties within a tutorial-based pedagogy at Oxford, the tutors'responses to and interpretations of these difficulties were studied in semi-structured interviews. Here the tutors' conceptualisations of the students' difficulties with regard to enculturation into formal mathematical reasoning and their standard teaching practices employed in order to cope with these difficulties are discussed. The conventions of school mathematical writing and journal/textbook/lecture writing and the students' confusion about what knowledge they are allowed to assume (school - university conflict, inter-university course conflict, intra-university course conflict) are identified as major influences on the students' formal mathematical enculturation. The need to transform teaching practices accordingly is highlighted.