Carl Winsløw -
Task design and assessment in university level analysis
Abstract. Mathematical Analysis was called “a symphony of the infinite” by one of its 20th century masters, David Hilbert. For many students of pure and applied mathematics, that symphony involves a number of difficult transitions, in part because it draws on almost all the mathematics they have met (more or less successfully) since primary school. For two decades, I have worked with various aspects of these challenges, mostly through interventions designed and tested in collaboration with colleagues teaching the subject at various levels, from the introductory “Calculus” type courses to more advanced courses on topics such as Fourier Analysis and Functional Analysis. A common feature in these projects is the deployment of certain elements from the Anthropological Theory of the Didactic to design and analyse student tasks. I will outline this research programme with a main focus on the transitions involved in passing from (mainly) algebraic work – the Calculus – to more theoretical tasks, where the topology and order structure of the real number field become more visible and crucial. Another important focus is the important alignment between tasks used in course work and in assessment. I will also touch upon recent task design integrating topics from Calculus, Linear Algebra and Engineering.
Biography. Carl Winsløw spent the first decade of his graduate career (1990-2000) working mainly on von Neumann algebra theory, beginning with a master degree at Odense University (supervisor: U. Haagerup) and a PhD on type III subfactors at the University of Tokyo (supervisor: Y. Kawahigashi). From around 1996, he began to take interest also in Didactics of Mathematics, with a main focus on the teaching of Mathematical Analysis at the university level. Since his appointment as full professor at the University of Copenhagen in 2003, this has also officially become his main field of research, which has gradually extended to encompass also other foci, such as mathematics teacher knowledge and various subjects from secondary level mathematics. He has supervised more than 50 master theses and 11 doctoral thesis, while building up the first research group in Didactics of Mathematics at the University of Copenhagen. He has been involved in organizing dozens of conferences in the field and was a co-founder of the International Network for Didactical Research on University Mathematics (INDRUM). Most of his research has drawn upon, and contributed to, the theoretical frameworks of ATD and TDS, founded by the French pioneers in the field, Guy Brousseau and Yves Chevallard.