Capturing and communicating advanced mathematical activity

Unlike most other subjects, mathematical activity resides almost entirely within the cognitive processes of a mathematics practitioner and is therefore difficult to characterise. Despite recent interest, the nature of advanced mathematical activity remains something of a black box to educational researchers. In addition, the production of advanced mathematical texts, such as theses or journal articles, is often divorced from mathematiciansââ¬â¢ experiences of creating mathematics which can lead them to a sense of personal alienation from their work. This article proposes four practical techniques for capturing advanced mathematical activity. The timing of the use of these techniques is compared against a model of mathematical creativity and the writing process. The establishment of a new genre for communicating advanced mathematics is proposed which combines the product of the activity with the process of creating it