Impact of Collaborative Problem-solving Workshops in Engineering Calculus Course on Applied Mathematical

This project stems from a collaborative effort by engineering and mathematics faculty at a research university to enhance engineering students’ abilities to transfer and apply mathematics to solve problems in engineering contexts. A recent curriculum innovation resulting from these efforts involves the integration of collaborative, applied, problem-solving workshops into the first-semester engineering mathematics course. In the first year of the assessment project, the project team developed two instruments one to gauge students’ abilities in using mathematics in engineering contexts, the Mathematics Applications Inventory (MAI); and the other to gauge students' self-efficacy perceptions related to studying engineering and to learning and applying mathematics, the Engineering and Mathematics Perceptions Survey (EMPS). In this second year of the project we will use the instruments to detect effects of the workshop innovation. The project is funded by the National Science Foundation, Directorate of Education and Human Resources, Course, Curriculum, and Laboratory Improvement (CCLI) Program, Grant # DUE0837757. This paper reports the results of the full administration of both instruments in Fall 2010 to all first-year engineering students at our institution (approximately 820). Slightly less than half enroll in the first calculus course in the engineering mathematics sequence, which covers single variable calculus and includes the collaborative problem-solving workshop innovation. The other first-year students have obtained advanced standing through prior coursework or credit on Advanced Placement exams, and the majority of these enroll in the second course in the sequence, which covers multivariable calculus and does not include the workshop component. All students in each course will complete the MAI as a paper-and-pencil exam during class time at the outset of the semester and again at the end of the semester. All students will also be asked to complete the online EMPS survey at both preand post-semester. This paper includes analyses of the resulting data, including associations between EMPS responses and MAI performance, patterns in students’ responses to the problems on the MAI, common areas of difficulty related to the application of specific mathematical topics, and patterns of responses and performance by other background and status variables such as gender, race, SAT scores, and level of mathematics preparation. Comparisons of responses preand post-semester, as well as comparisons across courses, will help determine impacts of the workshop innovation. We expect that students’ experiences in the workshops will improve their general abilities to apply the mathematics they have learned to engineering-related problems, and will have positive effects on their self-efficacy perceptions related to succeeding in the engineering curriculum. Our findings will help determine whether positive impacts on student skill and self-efficacy are indeed occurring in ways we are able to detect with the use of these instruments. P ge 22798.2

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