A Two-Semester Precalculus/Calculus I Sequence: A Case Study.

ABSTRACT The article begins by highlighting recent trends and concerns in post-secondary Calculus and Precalculus education. The main purpose of the article is to discuss the transition to a new Precalculus/Calculus I two-semester course at Wabash College, a small liberal arts college for men. Three years of data from the earlier, traditional, sequence are compared to two years of preliminary data from the revised sequence. Learning theories are cited to justify the pedagogical value of the revised sequence and a list of possible sequence texts is provided. INTRODUCTION The past 25 years has seen the emergence of a focus on the quality and effectiveness of lower-level mathematics courses such as Calculus and those prior to Calculus. In the 1980's, the remarkable Calculus Reform project was launched - the effects of which are visible in virtually every Calculus text now on the market. The impetus behind the Calculus Reform project was the realization that the way the mathematics world had been teaching Calculus was not producing students who either understood the ideas of Calculus or enjoyed the experience of learning about Calculus. This was clearly evident when looking at the abysmal fraction of Calculus I students who went on to any success in future mathematics classes. The following quote in Dudley [3] by A. Wayne Roberts illustrates the problem: "Far too many students who started the course [Calculus] were failing to complete it with a grade of C or better, and perhaps worse, an embarrassing number who did complete it professed either not to understand it or not to like it, or both. For most students it was not a satisfying culmination of their secondary preparation, and it was not a gateway to future work. It was an exit." The mathematics community now finds itself in a somewhat similar situation with regards to the Precalculus offerings that most U.S. colleges and universities provide. The 2000 CBMS (Conference Board of Mathematical Sciences) survey documents that remedial mathematics enrollment at twoyear and four-year institutions is up 76% since 1980 while Calculus enrollment during that same period remains essentially flat. These numbers indicate that more of our students are spending time in courses designed to prepare them for Calculus, but are not actually getting into, or through, Calculus itself. For a far better summary of this information please see the excellent paper by McGowen [11]. With more and more of the post-secondary student body not yet equipped to take Calculus and with more and more demand for individuals in technical fields whose training requires Calculus, there is a strong need to reform the precalculus offerings of colleges and universities into courses that do in actuality lead to student success in Calculus. This is, of course, nothing new, and the past seven or eight years have seen frequent special sessions and workshops at various MAA (Mathematical Association of America) meetings focusing on the issue of the courses offered below Calculus. In addition, the MAA's 2004 CUPM (Committee on the Undergraduate Program in Mathematics) Curriculum Guide recommends "General education and introductory courses in the mathematical sciences should be designed to provide appropriate preparation for students taking subsequent courses, such as calculus, ..."(p. 31). This 'Precalculus Problem' was seen for many years in miniature at Wabash College and recently we began seeking alternative methods of presenting this type of course. This article will focus on a revised Precalculus/Calculus I sequence that has been in place at Wabash College for two years. The college and sequence will be described and data presented comparing the revised sequence with the three preceding years in which a typical Precalculus/Calculus I sequence was in place. Though two years is perhaps not enough time to arrive at definitive conculsions, the data collected so far indicates the course revision has been a success in terms of several student retention and success measures. …