An Alternative Calculus I Course

INTRODUCTIONCalculus I at post-secondaiy institutions has historically been perceived as a "filter" that blocks access to professional careers in STEM fields [14]. This perception is further validated when the failure rate in the course is high and experiences are often negative.Failure in Calculus I is commonly identified in the literature as a grade of D or F or a withdrawal from the course. While a grade of D is not a failing grade in the eyes of some institutions it does not indicate that a student is prepared for success in the courses subsequent to Calculus I. Findings from the MAA National Calculus Study have revealed that the DFW rate for Calculus I at research institutions is 25%, which is problematic for STEM majors [3].As Seymour and Hewitt [13] have documented, negative experiences in introductory courses are a contributing factor to students leaving STEM disciplines. This resonates with findings from the recent MAA National Calculus Study. In a survey to colleges and universities, Bressoud and Rasmussen [4] found that Calculus I, an introductory STEM course, lowers confidence, decreases enjoyment of mathematics, and reduces the desire to continue in STEM fields. Poor instruction is often to blame for such experiences [4, 13]. The focus for this paper is on improving success rates in Calculus I for Physical Scientists I courses (referred to as Calculus I in this narrative) offered at our institution and also to discuss strategies for instruction in a Calculus I classroom.CALCULUS I AT OUR INSTITUTIONCalculus I at Colorado State University is comprised primarily of students majoring in engineering, mathematics, physics, computer science, statistics, and chemistry. Total enrollment in Calculus I varies, but usually ranges between 375 and 450 students each semester. Graduate Teaching Assistants (GTAs) typically teach regular sized (30 to 40 students) sections and senior GTAs or experienced instructors teach the large sections (60 to 100 students). Our Precalculus courses are not instructor led, but consists of online, self-paced learning modules.The national failure rate at research universities is much lower than the current DFW rate at our institution, which has historically remained steady at about 40%.Though recent course redesign efforts undertaken by a new course coordinator have started to result in a drop in the DFW rate, more is being done to address this concern. We highlight one of the successful efforts undertaken - a two-semester version of Calculus I.AN ALTERNATIVE VERSION OF CALCULUS ITraditional teacher-centered instruction is one of the contributors to low success rates in Calculus I, and unfortunately the way that mathematics courses are often taught [2]. Teacher-centered instruction, having students sit at their desks while solutions to mathematics problems are constructed on the board, does not lend itself to engaging students in their own learning processes.In addition to the need for improved Calculus I instruction, due to weak algebra, trigonometry and study skills, our students are often not prepared to keep up with the pace of the one-semester (four credit) version of Calculus I. Therefore, we developed and piloted a two-semester (6 credit) version of Calculus I. Students self-selected this course based on a recruitment email, sent to all students registered for Calculus I, that discussed common problems that Calculus I students encounter at our institution and described an alternative course intended to address these obstacles. An excerpt from the recruitment email for the two-semester course is:Specifically, the course will involve an initial review in algebra and trigonometry, and will then explore topics of calculus at a slower rate than a semester long course would do. Additionally, time will be spent honing study skills and doing mathematics in small groups. My goal will be to establish an active, studentcentered learning environment in which we develop, discuss, and deepen our understanding of topics in Calculus. …