Applications and confidence inventories for assessing curricular change in introductory engineering mathematics instruction

Abstract

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. This paper will summarize the project team's work to develop two instruments - one to gauge students' abilities in using mathematics in engineering contexts; and the other to gauge students' self-efficacy perceptions related to studying engineering and to learning and applying mathematics - that can be used to assess the effects of this innovation and others like it. The paper will report on the processes being used to develop and adapt the two instruments, the Mathematics Applications Inventory (MAI) and the Engineering and Mathematics Perceptions Survey (EMPS). The project is funded by the National Science Foundation, Directorate of Education and Human Resources, Course, Curriculum, and Laboratory Improvement (CCLI) Program, Grant # DUE-0837757. The paper will also report the preliminary results of the pilot administration of both instruments in Fall 2009. A sample of first-year engineering students responded to the online EMPS instrument, completed an initial open-ended version of the MAI, and participated in in-depth interviews about their responses to the MAI. The paper will include preliminary 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. Forthcoming project work includes the use of data from the pre-test and post-test pilot administrations and the in-depth student interviews to inform the development of the MAI into a multiple-choice inventory and to inform any necessary revisions of the EMPS. Administration of both inventories to the full class of first-year engineering students is scheduled for Fall 2010. Findings will be used to help assess the effect that integrating collaborative, applied, problem-solving workshops into the first-semester engineering mathematics course has on students' abilities and attitudes about using mathematics. It is also intended that the resulting developed, tested, and validated instruments will be appropriate for the assessment of related innovations in engineering and mathematics instruction at other institutions. © American Society for Engineering Education, 2010.