Introduction
In any class, it is terribly frustrating to find that students have somehow managed to pass the course without grasping what would typically be considered fundamental concepts. It is especially frustrating if the course is a prerequisite for another course in which those concepts are vital.
In Calculus 1, it is easily argued that the fundamental concept that every student should grasp is differentiation. During the Spring 1995 semester I decided to try an idea that has been used at other institutions to insure competence in differentiation as a necessary condition for passing the course.
On an e-mail discussion list dealing with Calculus Reform, Lou Talman, of Metropolitan State College of Denver, gave a summary of a battery of what he called gateway tests. Other names are used for the idea. Throughout the remainder of this paper, I will call them skill tests.
Description of Implementation
I decided to essentially mimic Professor Talman's implementation of the skill tests. He graciously sent me a copy of the problems he uses. During the early part of the semester, the list of problems is given to the students. Shortly thereafter they are given skills tests based exactly on problems from the list. Each skills test consists of four problems from the list. One is chosen from problems one through twenty-five. One is chosen from problems twenty-six through fifty. One is chosen from problems fifty-one through seventy-five. Finally one other problem is chosen randomly from the remaining seventy-two. These problems are a good representation of the types of differentiation skills a student should master to be justified in saying they passed Calculus 1.
To pass a skills test, all four problems must be worked perfectly. Skills tests are given in class for four consecutive weeks. To pass the course, it is necessary, though not sufficient, for a student to pass four skills tests. For students who do not pass the four tests given in class, opportunities are given each week thereafter to retake the tests. No credit, other than the opportunity to pass the course, is given for the skills tests.
Back to Fred Worth's Home Page.