Active learning strategies in advanced mathematics classes

ABSTRACT Advanced mathematics and other theoretical sciences are often taught purely using the lecture format, which promotes passivity and isolation in students. This paper advocates the use of certain alternative teaching methods, including co-operative learning in small groups and essay-writing assignments about technical topics. The emphasis throughout is on getting students to participate more, to interact more, and to broaden their perspective. Efforts are described to implement these reforms in upper-division courses in probability theory at the University of Minnesota, and students' anonymous questionnaires are analysed. It is argued that many of these teaching reforms can be implemented quite generally, without huge effort, and without greatly disrupting the normal flow of a course. I hear, I forget; I see, I remember; I do, I understand. (old proverb)