Lecturers don’t know everything: students listening to the thought processes of lecturers on unfamiliar ground

Abstract

Due to the nature of the teaching environment, students may often develop perceptions of their lecturers’ ability as mathematicians, based on the pre-prepared and well-rehearsed content they present. In reality, performing mathematical calculations and solving problems is a difficult skill, and students may compare their own experiences unfavourably with the ease they see lecturers display. To interrogate this disparity, an exercise was included in an undergraduate maths session during which lecturers attempted unseen problems from A-level maths papers, so the students could see them describing the process of problem-solving—including making mistakes, applying helpful strategies and techniques, correcting their own errors and identifying gaps in their knowledge. As well as describing these positive behaviours for students, the session aimed to develop the students’ understanding that their own experiences of struggling with maths are normal and healthy. The activity formed part of a broader session on making mistakes in maths, which also included some advice and opportunities to find mistakes in mathematical working-out. The students were invited to participate in questionnaires and focus groups to explore their perceptions and attitudes towards their lecturers’ knowledge and capacity to make mistakes, and in this paper we analyse these responses and consider how this relates to teaching, and to students’ personal development.