Some Thoughts on a First Course in Linear Algebra at the College Level

This paper has two purposes: to react to the recommendations of the Linear Algebra Curriculum Study Group (LACSG) and of David Carlson (one of the organizers of the LACSG), and to begin consideration of an alternative approach to helping students learn linear algebra. The LACSG eeorts to bring linear algebra into the overall undergraduate curriculum reform movement are laudable. There are some concerns with their approach, however, and this paper attempts to raise some questions concerning the lack of a body of research establishing a need for curriculum reform in linear algebra, the apparent identiication, in the LACSG recommendations , of abstract with useless (and hence, by negation, the equating of concrete with useful) and the assumption that performing calculations with matrices (even intriguing operations) is the same as applying mathematical ideas so as to meet the needs of client departments. The alternative proposed here | not in the spirit of replacement but in the sense of letting one more ower bloom | is an extension to linear algebra of an overall curriculum reform project. This project involves learning mathematics by programming in a mathematical-oriented programming language, extensive use of cooperative learning, and the development of alternatives to the lecture method. The discussion of the alternative in this paper is far from complete. It is, rather, an attempt to make a beginning of mapping out a project that will apply to linear algebra an approach that is having some success in precalculus, calculus, discrete mathematics and abstract algrebra.