Espoused faculty epistemologies for engineering mathematics: Towards defining "Mathematical maturity" for engineering

Successful experiences in mathematics courses during the first two years of college are critical to students’ persistence and learning in their engineering studies. Many core engineering courses require long prerequisite chains, delaying students’ deeper engagement in engineering topics and providing many deterrents for student persistence in engineering even before students take their engineering courses. The disconnect between the mathematics sequence and engineering courses makes it harder for students to perceive how their mathematics knowledge supports their engineering learning and for students to transfer and apply their mathematics knowledge to their engineering coursework. Further, with the lack of engagement with engineering tasks and learning early in the curriculum, students fail to develop identities as engineers that support students’ persistence when learning becomes more challenging. The negative effects of these disconnects are amplified for at-risk populations such as women, minorities, and students from low socio-economic status in engineering, increasing attrition of these populations even though they may perform better. These challenges dictate that we need to better understand what engineering faculty believe about the interplay between engineering and mathematics and how those beliefs shape curriculum and teaching practices.

Initial inquiries into the structure of engineering curriculum revealed that faculty frequently claimed that the prerequisite chains were needed to promote students’ “mathematical maturity.” To better understand how to improve engineering curricula, we are engaging faculty to understand their espoused and practiced definitions of “mathematical maturity.” We hope to identify mismatches between these two definitions to identify avenues for change and improvement in mathematics instruction for engineering.

Epistemological beliefs about knowledge have been shown to strongly affect student outcomes in mathematics and consequently their performance and persistence in engineering. Furthermore, the epistemology of teachers has been shown to influence what is learned by students. We will compare the espoused beliefs of engineering faculty about mathematics instruction in engineering to Gainsburg’s concept of ‘skeptical reverence’ describing the mathematical epistemology of veteran practicing engineers. We are interviewing faculty who teach courses that depend on the calculus sequence as a direct prerequisite to describe their espoused epistemologies about mathematics knowledge and instruction. These interviews are being analyzed using qualitative methods with an a priori coding scheme. We are simultaneously exploring faculty’s teaching practices and curricula to explore how those epistemologies are practiced. The results of this study can inform the construction of integrated engineering mathematics courses or how faculty teach and use mathematics in their engineering courses.