Juxtaposing faculty's espoused and practiced epistemologies about mathematics and engineering to catalyze curriculum reform
Successful experiences in mathematics courses during the first two years of college are critical to studentsﾒ persistence and learning in engineering. Engineering courses typically require long prerequisite chains, delaying studentsﾒ engagement in engineering topics and deterring studentsﾒ 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. The negative effects of these disconnects are amplified for at-risk populations, increasing attrition. We need a deeper understanding of barriers to implementing evidence-based instructional strategies to accelerate curriculum reform that address these problems.
Our overarching goal is to explore a new research-based method for executing develop-disseminate-based changes in teaching practice and document why the change strategy is successful or not. Our first sub-goal is to construct an understanding of mathematical maturity that faculty accept yet will challenge their belief that the status quo of non-integrated mathematics and engineering is adequate. This understanding will inform the construction of our change narrative.
Our project is informed by organizational justice theory, arguing that change processes must begin by articulating a narrative for change that aligns with stakeholderﾒs values and reveals why the status quo is inadequate. Until this narrative is crafted, data supporting the proposed change will be dismissed by stakeholders and increase their resistance to change. To create this narrative, we are interviewing faculty to document their espoused epistemologies about the relationship between engineering and mathematics. To show that the status quo is inadequate, we are simultaneously documenting facultyﾒs practiced epistemologies by studying course artifacts such as course syllabi, assignments, and outcomes. These analyses will reveal a disconnect between what faculty say they want students to learn and how they structure their courses and curriculum. This disconnect provides the thesis for our narrative for change.
Traditional mathematics instruction leads students to believe that mathematics has no bearing outside the classroom. They further believe that mathematics is a solitary activity composed of simple problems, solvable in a few minutes. These beliefs undermine students� use of mathematics in engineering to communicate about engineering concepts and models. Engineers possess a �skeptical reverence� of mathematics, believing that mathematics provides compelling evidence and processes for engineering knowledge, but must be checked and questioned. Students� counter-productive epistemological beliefs about mathematics are a product of instruction and provide one possible avenue for effecting change.
Aside from working with faculty at our institution to negotiate change, we are engaging community colleges in our change efforts. We are designing a pilot for an integrated engineering mathematics course for traditionally underprepared community college students, creating new pathways into engineering for these students.
One of our Co-PIs changed departments and could no longer provide access to specific student populations. We have renegotiated access to these students by recruiting the Co-PI's replacement. We will likely request a change in PIs to more fully incorporate this new person into the project.
Herman, G. L., Faulkner, B. (submitted). Espoused faculty epistemologies for engineering mathematics: Towards defining ﾓmathematical maturityﾔ for engineering. In Proceedings of the 2016 ASEE Annual Conference and Exposition. New Orleans, LA, June 26-29.