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In an online asynchronous vector calculus course, we observed exam answers solved with a formula from online homework instead of the formula from lecture. Our exploratory study investigated (1) why students learned from homework instead of lecture for this topic and (2) their epistemological frames (e-frames) for lecture and homework. Per (1), reasons included studying homework as more efficient than reviewing lectures, difficulty understanding the lecture, and incomplete lecture notes. Per (2), some students see lecture as explaining mathematical meaning and giving them tools to do homework. Students primarily see homework as a space to learn procedures. The results are significant for several reasons. First, they connect homework and lecture learning, rather than treating them separately (as in prior research). A key contribution of the work is both the empirical documentation that students’ lecture and homework learning influence one another, and the implication from this that researchers should attend to learning at the intersections of milieu. A second significance of the work is the preliminary documentation of students’ e-frames for lecture and homework. Characterizing e-frames is important because improvements in student learning may come in part from helping students shift their beliefs about learning and about mathematics as a discipline.

Learning from Lecture and Homework: The Case for Studying Intersections of Milieu