Designing for Improved Success in First-year Mathematics

Designing for Improved Success in First Year MathematicsIn responding to the need to improve retention in the first year of engineering, many institutionshave developed a range of academic support programs, including learning communities, peermentoring, summer bridge programs, tutoring and supplemental instructional workshops.1,2,3,4,5Other institutional efforts are aimed at curricular changes involving new approaches to teachingand learning, such as student-centered pedagogies and design projects in first-year engineeringcourses.6,7 However, students’ difficulties with first year mathematics courses remain awidespread and consistent barrier to success in engineering for many students.8,9 In this paper,we will present the results of research on three programs designed to address student success infirst year mathematics courses. We will also describe the design principles that guided thedevelopment and implementation of these programs.In collaboration with the college of engineering, the department of mathematics designed threechanges in the mathematics program for first year students: (1) a complete restructuring of thesummer bridge program mathematics course; (2) a revision of the pre-calculus course forstudents who would otherwise have been placed in a college algebra course; and (3) theimplementation of a Calculus I course for students who had not taken calculus in high school.The summer bridge program is a six-week residential program that provides pre-freshmen withan opportunity to become familiar with the university’s academic, social, and cultural life. Inprevious years, students taking a mathematics course as part of this program performed a fullletter grade lower in their first semester math course than their peers who did not participate inthe summer program. To address this gap, we completely re-designed the summer mathematicscourse to be organized around a deep understanding of the average rate of change through thehands-on investigation of models of changing phenomena, such as linear motion, light intensity,and exponential growth and decay in simple RC circuits. A focused set of algebra skills wasaddressed in the context of investigating these models. These changes closed the previous gradegap between summer and non-summer students in their first semester mathematics course.While many incoming students enroll in a calculus course, some place into a pre-calculus courseand some into a college algebra course. To address the needs of those students who place intocollege algebra and prepare them for Calculus I in one semester rather than two, we introduced anew 4-credit version of pre-calculus, in which algebra concepts were taught as needed for thepre-calculus topics throughout the semester. The level of difficulty of homework, quizzes, andexams of the new course were identical to the traditional course, which served as our controlgroup. Since the Fall of 2008, student success rate in both versions of the course has beenpractically identical, followed by comparable performance in Calculus I the next semester.Many first year students have had a year of calculus in high school, but for a variety of reasonseither do not take or do not succeed on an examination (such as the AP Calculus exam) so as toearn college credit for Calculus I. Approximately 80% of the students enrolled in Calculus I hadprevious exposure to the procedures and concepts typically taught in the large lecture course, and20% had no calculus background. This difference in background led to a full letter gradedifference in performance on the final exam. To address this gap, we divided this course into twosections, with one section of the course exclusively for those students who have not had calculusin high school. This change closed the full letter grade gap that existed between students whohad taken calculus in high school and those who had not.References[1] Gattis, C., Hill, B., & Lachowsky, A. (2007). A successful engineering peer mentoring program. In American Society for Engineering Education Annual Conference and Exposition, Conference Proceedings.[2] Jones, S., Rusch, K., Waggenspack, W., Seals, R., & Henderson, V. (2010). S-STEM: Eng^2 scholars for success engineering engagement. In American Society for Engineering Education Annual Conference and Exposition, Conference Proceedings.[3] Kukreti, A., Simonson, K., Johnson, K., & Evans, L. (2009). A NSF-supported S-STEM program for recruitment and retention of underrepresented ethnic and women students in engineering. In American Society for Engineering Education Annual Conference and Exposition, Conference Proceedings.[4] Massi, L., Georgiopoulos, M., Young, C., Ducharme, A., Ford, C., Small, K., Lancey, P., & Bhatia, D. (2010). YES: A NSF S-STEM scholarship program experience at the University of Central Florida. In American Society for Engineering Education Annual Conference and Exposition, Conference Proceedings.[5] Russomanno, D., Best, R., Ivey, S., Haddock, J., Franceschetti, D., & Hairston, R. (2010). MemphiStep: A STEM talent expansion program at the University of Memphis. Journal of STEM Education, 11(1 & 2), 69-81.[6] Hoit, M., & Ohland, M. (1998). Impact of a discipline-based introduction to engineering course on improving retention. Journal of Engineering Education, 87(1), 79-85.[7] Kilgore, D., Atman, C. J., Yasuhara, K., Barker, T. J., & Morozov, A. (2007). Considering context: A study of first-year engineering students. Journal of Engineering Education, 96(4), 321-334.[8] Bullock, D., Callahan, J., Ban, Y., Ahlgren, A., & Schrader, C. (2009). The implementation of an online mathematics placement exam and its effects on student success in precalculus and calculus. In American Society for Engineering Education Annual Conference and Exposition, Conference Proceedings.[9] Alkhasawneh, R., & Hobson, R. (2010). Pre-college mathematics preparation: Does it work? In American Society for Engineering Education Annual Conference and Exposition, Conference Proceedings.