You are here

DRILL 3.1 - Motivation

Vadim Ponomarenko

Calculus and precalculus are the most important subjects taught in mathematics departments at colleges and universities -- a large proportion of all college students take calculus or some sort of precalculus at some point before graduation. This cannot be said of any other subject in the mathematics curriculum. For example, the Trinity University mathematics department in Fall 2003 offers 11 sections of calculus and three sections of precalculus. All other courses together comprise 10 sections. Furthermore, calculus is a prerequisite to many other courses, so an improvement in calculus and precalculus education would benefit almost all students taking mathematics during their undergraduate careers.

Calculus and precalculus education typically attempts to train students in a wide variety of skills. These frequently include the following major goals:

  1. Competence: Achieving fluency in mechanical computation and calculation of formal mathematical exercises.
  2. Modeling: Understanding and practicing the methods by which real-world problems can be modeled with formal mathematics.
  3. Proof: Learning the patterns of thought that allow the construction and comprehension of a mathematical argument.

Each of these has value in its own right, as well as value to support understanding of material learned in subsequent courses, mathematics or otherwise.

Of these three goals, the most basic and easily assessed is the first, Competence. In order to reach this goal, all students must practice. Because of the variation in skill and preparation among students, some will require substantially more practice than others on any given topic. The purpose of DRILL is to assist the instructor to help the students meet this single goal. By mechanizing the practice, it is separated somewhat from the instructor. This allows the instructor to focus more time and effort on other goals.

Vadim Ponomarenko, "DRILL 3.1 - Motivation," Convergence (December 2004)