This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida.

Many factors are involved in the ongoing of how and what to teach in the first linear algebra course, but important among them are the related issues of the audience and the intended purpose. Both have noticeably changed - and become less clear - in the last 30+ year history of the elementary course in the undergraduate curriculum. The audience has become not only larger, but broader in almost every respect. Partly as a result, we have perceived increasingly many purposes for the course. We offer some thoughts on these trends and their influence on the discussion of the elementary course.

Charles R. Johnson, College of William & Mary