A National Model for Engineering Mathematics Education: Longitudinal Impact at Wright State University

The inability of incoming students to advance past the traditional first-year calculus sequence is a primary cause of attrition in engineering programs across the country. As a result, this paper will summarize an NSF funded initiative at Wright State University to redefine the way engineering mathematics is taught, with the goal of increasing student retention, motivation and success in engineering. The approach involves the development of EGR 101 a first-year engineering course replacing traditional math prerequisites for core sophomore engineering courses along with a more just-in-time structuring of the required calculus sequence. Since its inception in Fall of 2004, the impact of the Wright State model on student retention, motivation and success has been widely reported. This paper includes results of a recent longitudinal study of program impacts at Wright State University, from student performance in math and engineering to ultimate graduation rates. Results show that the program has substantially mitigated the effect of incoming math preparation on student success in engineering across the entire range of incoming ACT math scores, which has more than doubled the average graduation rate of enrolled students. Moreover, it has done so without watering down the caliber of graduates, who have actually enjoyed a slight (but statistically significant) increase in graduation GPA. Finally, the approach has been shown to have the greatest impact on members of underrepresented groups, for many of whom the traditional engineering curriculum is simply not accessible. The paper concludes with a longitudinal examination of student perception data, which appears to establish a clear link between program impacts on student motivation and self-efficacy and ultimate graduate rates. The Wright State Model It is well known that student success in engineering is highly dependent on student success in math, and perhaps more importantly, on the ability to connect the math to the engineering. However, first-year students typically arrive at the university with virtually no understanding of how their pre-college math background relates to their chosen degree programs, let alone their future careers. And despite the national call to increase the number of graduates in engineering and other STEM disciplines , the inability of incoming students to successfully advance past the traditional freshman calculus sequence remains a primary cause of attrition in engineering programs across the country. As such, there is a drastic need for a proven model which eliminates the first-year mathematics bottleneck in the traditional engineering curriculum, yet can be readily adopted by engineering programs across the country. Such is the focus of this work. The Wright State model begins with the development of a novel first-year engineering math course, EGR 101 Introductory Mathematics for Engineering Applications. Taught by engineering faculty, the course includes lecture, laboratory and recitation components. Using an application-oriented, hands-on approach, the course addresses only the salient math topics actually used in core engineering courses. These include the traditional physics, engineering mechanics, electric circuits and computer programming sequences. The EGR 101 course replaces traditional math prerequisite requirements for the above core courses, so that students P ge 2.76. 2 can advance in the curriculum without first completing a traditional first-year calculus sequence. The Wright State model concludes with a more just-in-time structuring of the required math sequence, in concert with college and ABET requirements. The result has shifted the traditional emphasis on math prerequisite requirements to an emphasis on engineering motivation for math. The EGR 101 lecture sections are completely driven by problem-based learning, while the laboratory and recitation sections offer extensive collaborative learning among the students. As such, the course is strongly supported by the literature on how students learn. Excerpts from the EGR 101 laboratory are shown in Figures 1-2. Indeed, physical measurement of the derivative as the velocity in free-fall (Fig. 1), or of the integral as the area under the force-deflection curve (Fig. 2), provides a much greater conceptual understanding of the mathematical concepts than classroom lecture alone. The Wright State model was first implemented in Fall of 2004, and its effect on student retention, motivation and success in engineering has since been widely reported. The 2007 introduction of EGR 199 as a precursor to EGR 101 for initially underprepared students has further strengthened the approach, and has made Wright State’s core engineering curriculum accessible even to incoming students with math placement scores as low as 3 levels below Calc I. Results of the initial implementation are briefly summarized below. Results of Initial Implementation The EGR 101 course ran for the first time in the Fall of 2004. All eligible incoming students in mechanical engineering, materials science and engineering, electrical engineering, engineering physics, biomedical engineering and industrial and systems engineering were enrolled in the course. Through its first year of implementation, a total of 158 students were enrolled in EGR 101, with over 74% completing the course with a grade of “C” or better. The initial implementation of the program had an immediate and dramatic effect on student retention and success in engineering at Wright State. As shown in Fig. 3, every department requiring EGR 101 saw an increase in first-year retention in 2004-2005, as compared to baseline data averaged over the prior four years. Overall, majors requiring EGR 101 saw first-year retention increase from 68.0% to 78.3%. Figure 1. The Derivative Lab Figure 2. The Integral Lab