Exploring and enhancing accessibility of abstract mathematics at third-level

This case study seeks to explore and evaluate an approach to the teaching and learning of a core third-year undergraduate pure mathematics module. Within such a context, the key questions driving the study are: 1. What does a typical third year student of mathematics understand as their role in the learning of advanced abstract mathematics? 2. How well prepared are students of mathematics when they undertake an abstract analytic module in their third undergraduate year? In particular, how well developed are their skills in forming valid persuasive argument (aka proof) at this stage of their development? 3. Can this approach (to teaching and learning) foster engagement and a greater sense of independent thinking and learning? 4. How can one incorporate and deliver on an insistence on (student) thinking for oneself at this level? 5. What is the student perception on the role and value of assessment within the learning experience? Does assessment that is terminal and exam-based provide a meaningful learning outcome? The research methodology involved semi-structured interviews with students over a two-year period, and included an embedded mathematical exercise. Preliminary analysis confirms and illuminates the extent to which the ability of students to construct proof is underdeveloped and potentially undermined. It further suggests that the impact and effect of the teaching approach used may counteract this trend and subsequently enable and enrich the overall learning experience. This research offers a contribution to the area of advanced mathematical thinking within the Irish context. This area of mathematics education is well established internationally (see Tall, Dreyfuss, Dubinsky for example) and is gaining in momentum in Ireland. This is the first study of its kind at an advanced undergraduate level in Ireland.