1 Derek Holton et al. (ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study. 116. ' 2001 Kluwer Academic Publishers. Printed in the Netherlands. KENNETH C. MILLETT MAKING LARGE LECTURES EFFECTIVE: AN EFFORT TO INCREASE STUDENT SUCCESS 1. INTRODUCTION As is the case with many college and university professors, I regularly teach groups of 100 or more students gathered together several times each week in a lecture hall. More precisely, I give lectures on the relevant material, supervise the work of graduate teaching assistants, and assign course grades intended to indicate the level of achievement of those enrolled in the class. These are to be accomplished in a manner satisfactory to the students, at least as measured by their evaluations of the course or reflected by an absence of complaints to the chair or dean. Without any concrete course goals or departmental standard of achievement, I am the sole arbiter of the grading standard applied in the course. The identification of legitimate and concrete measures of effectiveness with which to evaluate the course is left to me. Since the course product is, arguably, the mathematical achievement of the students, I believe that any measure of success must be principally constructed of measures of student performance. This, then, is where I start in trying to figure out how to teach any course. It is this process that I wish to discuss in this report on my continuing effort to increase the effectiveness of my teaching in large classes, (see Millett, 1996, 1997 and 1999). While the following maxim may be debated by many college and university faculty members, the foundation of my teaching efforts is the statement: If students havent learned, youve not taught. Beginning with an assessment of the context, I try to establish statements of the course goals that are understandable and with which my students and I can determine whether or not they have been achieved. Depending upon these goals and the context, instructional strategies are selected. Of course, these are often modified during the instruction to take experience into account. For this purpose, lots of information is collected throughout the course. The success or failure of the implementation is determined by this data as are the final grades. An analysis of this data and the experience with the students provides the basis of modifications of the course goals and strategies in the future. In this note, I describe the experience with a pre-calculus class during the Winter Quarter period, January through March, 2000, following the approach described in the previous paragraph. Although I had not taught this course for quite a while, I am scheduled to teach it again next year. This course provides the occasion for a review of some strategies applied to large class situations, on one hand, and will allow me to describe how one can try to systematically improve the effectiveness of such courses. First I will describe the context and the goals set for this course. Next I will describe the materials and the instructional strategies