Joint math-engineering projects to facilitate calculus success in first year students

Abstract

It has been observed that most first year engineering students seem to enjoy and often perform well in their project and project-oriented freshman engineering course, but seem to have difficulty and often perform poorly in their first calculus course. Working from the perception that first year engineering students do not make the connection between what they learn in calculus and the problems they solve in freshman engineering, the faculty who teach the engineering sections of first semester calculus and the faculty who teach freshman engineering worked together to define projects that span both classes. The primary goal of these projects was to show students how the concepts and techniques they were learning in math class were relevant to their future career in engineering. It was proposed and believed that if the students understood the connection between the two subjects, they would understand both subjects better and be motivated to work diligently in both subjects. Since students historically perform well in freshman engineering, the expected result, if this experiment is successful, would be improved grades in calculus. In this experiment, three joint projects were defined to illustrate the following math concepts: (1) functions, composition of functions, discrete and continuous variables; (2) exponential growth and decay; and (3) rate of change, specifically focusing on Newton's Law of Cooling. Each project presents a fictitious real world problem that puts the students in the context of being the consulting group that needs to develop the solution to the problem. The problem must be understood analytically (the part done in math recitation and continued for homework) as well as experimentally (the part done in and for the engineering class). The students, working in small groups, must create a solution as well as write a technical report and present the problem and their solution to the class. Approximately 130 students participated in these joint math-engineering projects. Their performance, primarily in calculus, was measured and compared to historical performance data as well as to calculus classes without the joint projects. Preliminary data suggests that these projects result in improved grades in calculus. Additionally, the student enthusiasm for these hands on projects has increased as well. While improved student performance in calculus was the primary objective of this effort, the experience of developing and implementing the math-engineering joint projects has resulted in improved communication between both departments and has helped the math faculty see how students work in groups to discuss and solve problems and to create reports and presentations of their work. The interactive nature of these problems, couched in engineering terms, is resulting in more student discussion of mathematics, a more interesting teaching experience for the instructors, and improved student performance. © American Society for Engineering Education, 2010.