Identifying and Removing a Calculus Prerequisite as a Bottleneck in Clemson's General Engineering Curriculum

Journal of Engineering Education, Jul 2004 by Ohland, Matthew W, Yuhasz, Amy G, Sill, Benjamin L

ABSTRACT

A review of prerequisites often reveals that reasons for requiring a prerequisite may no longer prevail due to curriculum or course changes. Based on a study of a curriculum bottleneck unrelated to required mastery, the prerequisite structure in Clemson University's General Engineering curriculum (the common firstyear curriculum for all engineering students) was changed so that Calculus I could be taken in the second semester. Student record analysis shows both the magnitude of the bottleneck prior to the policy change and the effect on student enrollment practices after the policy change. Longitudinal studies show a statistically significant improvement in retention in engineering adding to the body of evidence that indicates that it is important to retention that students start college mathematics at a level for which they are prepared.

Keywords: freshman engineering, longitudinal study, mathematics readiness

I. INTRODUCTION

Students entering the General Engineering program at Clemson University are required to take and pass calculus, which is typical of other engineering programs. Much research has been conducted that affirms the importance of a good experience in the first college mathematics course and its correlation with success in engineering [1, 2]. When it comes to freshman engineering programs, "there is a consensus that math is the largest stumbling block causing dropout in the freshman year" [3]. Because calculus is the first math course in most engineering curricula, there is enormous pressure for students to be calculus ready when they arrive at college. In a study of Purdue engineering students, Budny reported that students succeeding in pre-calculus had retention rates approximately equal to those of students succeeding in calculus [2, 4]. Clemson University's General Engineering program has many requirements that students must complete before they can select an engineering major, and passing Calculus I is a common a barrier to curricular progress. It was hypothesized that if students could start ENGR 120, Introduction to Engineering Problem Solving and Design, before completing Calculus I, students would be able to progress in other parts of their curriculum and higher retention rates would result.

Before Fall 2000, Calculus I was a prerequisite for the second course in Clemson's General Engineering program (ENGR 120) as well as for the first course in physics. This caused a bottleneck in the curriculum-students could not progress in the engineering curriculum until passing Calculus I. Thus, failing or withdrawing from Calculus I, or not being prepared for it, had a much greater effect on a student's progress than failing other required courses. In order for a student to progress with their peers, a student would need to successfully complete three challenging courses (ENGR 120, Calculus II, and Physics) over the summer, a daunting task for students who are generally less prepared academically.

Moreover, students moving into an engineering major from General Engineering after May 15, 1996, have been required to have a grade of C or better in each course in the freshman curriculum except a humanities/social science requirement [S]. This means that, in Clemson's General Engineering curriculum, a grade of D is no better than an F or a W in terms of progress in the curriculum, thus aggravating the calculus bottleneck issue. The bottleneck caused by the calculus prerequisite policy had a number of consequences:

* students who continued in engineering were delayed;

* some students, faced with this fact, left engineering; and

* affected students occupied seats in fall (out-of-sequence) offerings of ENGR 120, causing the enrollment of those sections to be higher than desired.

II. CALCULUS AS A PREREQUISITE

The most obvious reason to designate a course as prerequisite to another is when the courses are in sequence-it certainly makes sense for Calculus I to be a prerequisite for Calculus II. Even across departments, there are cases where one course must be completed in order to begin the material in another. As the material in the two courses changes, however, this relationship may weaken over time.

Another reason to designate a prerequisite is to establish certain checkpoints in a curriculum-this makes for less divergence of student course patterns and prevents a student from making too much progress in a curriculum that he or she is destined to abandon. Across the country, it is common for the first course in the calculus sequence to be a "gateway" to the engineering curriculum. Simply because calculus has such a high failure rate, there is the sense that, if someone is going to fail calculus and leave engineering, it might as well happen sooner rather than later. This appears to be the historical reason for making Calculus I a prerequisite for ENGR 120.

In order to serve students without compromising course objectives, the prerequisites for ENGR 120 and the first course in physics were reviewed in Spring 2000. This review of current instruction in both physics and ENGR 120 indicated that current curriculum expectations required only a co-requisite status of Calculus I, Following this review, a new policy was enacted, Fall 2000, which would allow students to take Calculus I as a co-requisite for ENGR 120 and enroll in physics with the permission of the instructor, which is granted pro forma.