We investigated ways in which undergraduates use optional learning resources in a typical blended learning environment. Specifically, we recorded how often students attended live faceto-face lectures, accessed online recorded lectures, and visited a mathematics learning support centre during a multivariate calculus course. Four distinct study strategies emerged, but surprisingly none involved making heavy use of more than one resource. In contrast with some earlier research, the general strategy a student adopted was related to their academic achievement, both in the multivariate calculus course, and in their degree programme more widely. Those students who often accessed online lectures had lower attainment than those who often attended live lectures or the support centre. We discuss the implications of these findings and suggest that 'blended teaching environments' may be a more accurate description for what have previously been called 'blended learning environments'.

The use of recorded lecture videos (RLVs) in mathematics instruction continues to advance. Prior research at the post-secondary level has indicated a tendency for RLV use in mathematics to be negatively correlated with academic performance, though it is unclear whether this is because regular users are generally weaker mathematics students or because RLV use is somehow depressing student learning. Through the lens of cognitive engagement, a quasiexperimental pre-and post-test design study was conducted to investigate the latter possibility. Cognitive engagement was operationalised using the Revised Two-Factor Study Process Questionnaire (R-SPQ-2F), which measures learning approaches on two major scales: surface and deep. In two mathematics courses at two universities, in Australia and the UK, participants were administered the questionnaire near the course start and finish. Overall findings were similar in both contexts: a reduction in live lecture attendance coupled with a dependence on RLVs was associated with an increase in surface approaches to learning. This study has important implications for future pedagogical development and adds to the sense of urgency regarding research into best practices using RLVs in mathematics.

The use of fully online (FO) mathematics teaching has been increasing worldwide. Despite claims and findings that mathematics is more challenging to teach FO than face-to-face (F2F), we know little about FO mathematics teaching. In this paper, we address this gap by working to elucidate the differences between teaching in the FO and F2F modalities. We do this by examining FO and F2F teaching from the perspective of Communities of Practice (Wenger, Social learning systems and communities of practice, 2010) by comparing and contrasting current FO practices (or “ways of doing”) in the general undergraduate education community with current F2F practices in the undergraduate mathematics community. We identify six key differences between the two paradigms, which we recast to spotlight areas for technological and pedagogical development.

Un-proctored fully asynchronous1 online courses now appear to be a reality in all discipline areas. With full degree programs being offered online, it has become a badge of honor, to some colleges, to graduate students that have never stepped foot on the physical college campus nor have never before met any college representative, faculty, or staff. To many involved in managing, teaching, and implementing these online courses, the idea of academic integrity related to courses taught in a fully online un-proctored modality is therefore of great interest and concern. This review represents a deliberate effort to distinguish the issue of academic integrity in fully asynchronous online courses into two categories: “Writing-Based” (WB) vs. “Math or Fact-Based” (MFB) courses. WB courses, which tend to be subjective in nature, include discipline areas such as English, history, psychology… . MFB courses, which emphasize calculation and/or factual recall, have a tendency to be highly objective in nature, and include discipline areas such as math, science, business, computers, medical technology… . While there are certainly significant areas of overlap in how different assessment instruments are administered in these two categories, most math and many science courses, for instance, tend to focus on calculation and fact-based assessment instruments (such as mid-term and final exams) and most English and history courses, for example, tend to focus on writing-based assessment instruments (such as written assignments and term papers). Based on this distinction, the notion that pedagogical mechanisms (apart from proctored assessments) are sufficient to ensure academic integrity in online MFB courses is questioned and challenged. Recommendations are given to advance the use of proctored assessments in online MFB courses through the creation of universal proctoring standards and the expansion of current and new testing center networks.

In this paper we consider the transformation of tertiary mathematics lecture practice. We undertake a focused examination of the related research with two goals in mind. First, we document this research, reviewing the findings of key studies and noting that reflective pieces on individual practice as well as surveys are more prevalent than empirical studies. Second, we investigate issues related to the transformation of lecture practice by the emergence of electures. We discuss the latter in terms of claims about the efficiencies offered by new technologies and contrast these with possible disadvantages in terms of student engagement in a learning community. Overall findings indicate that while survey results appear to trumpet the value of e-lecture provision, empirical study results appear to call that value into question.Two explanatory theoretical frameworks are presented. Issues concerning the instructional context (e.g. the nature of mathematical thinking), inherent complexities and recommendations for implementation are discussed.