Sensitivity and challenge in university mathematics tutorial teaching

Data from observations of first year university mathematics tutorials were analyzed to elicit characteristics of teaching using a tool, the teaching triad, developed in earlier research. Analysis explored elements of `sensitivity to students' and `mathematical challenge' in the observed teaching. Initial analyses suggested teaching to consist mainly of tutor exposition and closed questions embodying little challenge for the student. More finely grained analyses provided insights into pedagogic processes relating teaching actions, processes and strategies and their learning outcomes, and providing alternative perspectives on sensitivity and challenge. The research, distinctively, shows approaches to analyzing teaching that start to address tutor-student interactions related to cognitive construction of mathematics (here abstract algebra) by undergraduates within the social dimensions of the tutorial setting.