Proof as a threshold concept for university mathematics : an exploration of student identity and transition
This paper was presented as part of a symposium at BERA 2009. The symposium was organised by Dr Paul Hernandez-Martinez and was entitled “Transition in mathematics education: practices and identity”. The accepted summary of the symposium is attached below:
The four papers in this symposium reveal contours, problems and opportunities for mathematics education in transitions (a) between compulsory/school and post-compulsory/college education (Hernandez-Martinez et al) and (b) between college/pre-university and university mathematics education (Davis et al, Harris et al and Jooganah).
Hernandez-Martinez et al identify contradictions in the value given to mathematics between “feeder” institutions (schools) and “user” institutions (colleges). They theorise these contradictions from a Cultural-Historical Activity Theory (CHAT) perspective and analyse students’ narratives as accounts of their identities as “boundary crossers” and how, for some students, the institutional contradictions allow for the possibility of developing new identities as “grown up” adults.
Davis et al, using also a CHAT framework, analyse the different pedagogical and performativity discourses used by two universities and how these discourses mediate students’ identities as users of mathematics in STEM (Science, Technology, Engineering and Mathematics areas) as they transit into their first year at university. For example, they highlight how a pedagogical discourse of sociality might be critical in offering students an opportunity to engage with mathematics during their transition.
Harris et al focus their attention on one transitional practice used by three engineering departments at different universities. They analyse how a mathematics diagnostic test for first year engineering students mediate their identification with mathematics in different ways. So, for example, as a result of this test some students might feel marginalised from mathematics because they have been labelled as “less well-prepared” or as a “struggling” student. In this case, a practice originally design to help students might become for some a problem rather than a solution.
Finally, Jooganah centres her paper on the importance of “proof” for the transition of students into mathematics programmes at university. She analyses how this threshold concept “serves as a focus for student-lecturer (and institutionally, school-university) engagement, conflict, and transition”.