Innovations in Teaching Abstract Algebra

Abstract of article: Six first-year college students are recruited to take part in an experimental class that uses neither lectures nor books. The intent is to have them build abstract structures to account for concrete experiences. From flipping simple objects such as a penny or a piece of paper, they come up with some specific groups. From a special deck of 16 cards they come up with something akin to linear operators on a vector space, except the field is replaced by a semiring. Part of the fun of proceeding in this way is that the participants get to invent the notation and the names of things, which keep changing as the systems evolve and new ideas emerge.

About the author: Paul Fjelstad helped design St. Olaf's Paracollege, which started in 1969 with the goal of encouraging students to take the initiative in designing their education and to experiment with learning styles in the process. His graduate work was in physics (Harvard Ph.D., 1962), where the concrete and abstract work on each other intermittently. In interacting with students, he prefers asking questions to giving answers.