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

Abstract

ABSTRACTIn 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.KEYWORDS: e-framesepistemological frameslectureonline homeworkvideo lecture Disclosure statementNo potential conflict of interest was reported by the authors.Notes1 See for a detailed discussion of the PAV feature and how students use it.2 The course did not utilize written homework.3 We note our focus is on student learning from different milieu, not their thinking about vector concepts. Literature about the latter indicates students struggle with computing forces in particular directions, an application of vector components (Barniol & Zavala, Citation2014; van Deventer & Wittman, Citation2007; Zavala & Barniol, Citation2010).4 Because second author taught the course and could not know who participated until after course grades were submitted, the first author (FA) conducted all aspects of data collection. This was a requirement from the Institutional Review Board.5 If this had been the second assessment, an alternative explanation might be that students memorized a formula because they expected procedural exam items. That it was the first exam lowers the tenability of this hypothesis, though students may have had some expectation of procedural items due to their broader mathematics experience; see the discussion section for more.6 This method of obtaining consent for use of students’ written documents was approved by the authors’ IRB. Only the first author had access to the two folders for notes for this assignment, and following the due date, the first author graded the lecture notes so the second author did not know the participants’ identities.7 Names are pseudonyms. Note English was not Henry's first language.8 Tom uploaded a file that was not the notes from the lecture. It was unclear whether this was done purposefully because he did not watch the lecture, or if he accidentally selected the wrong file.9 Hereafter, we refer to this e-frame as H1 for “Henry, e-frame 1.” Later in the paper, S1 indicates “Sarah, e-frame 1” and so on.10 We do not take “added” literally here.11 Note: The direction of a normalized vector and the reason it has length 1 was covered in prior lectures. Cardetti et al. (Citation2014) found one of students’ difficulties with lecture videos was trouble recalling relevant prior knowledge; we see Henry’s questions here as supporting the Cardetti et al. (Citation2014) findings.