A Review of Fully Online Undergraduate Mathematics Instruction through the Lens of Large-Scale Research (2000-2015)

Abstract

The use of fully online instruction has been proliferating in higher education. In undergraduate mathematics, arguments about the effectiveness of fully online instruction have been met with contrasting claims about its potential. Some assert that fully online instruction can promote a deeper and richer conceptual understanding of mathematical ideas while others claim it is difficult to teach mathematics effectively in a fully online context. The aim of this study is to examine these claims by documenting relevant empirical evidence, the findings of which we hope will inform current efforts, by both faculty and administrators, to improve fully online mathematics instruction.

Keywords:

• Online teaching and learning
• mathematics
• meta-analysis
• review

Notes

1 According to Bernard et al. [5], instruction that is asynchronous occurs where “students are not synchronized with [other] classroom students and communication is largely asynchronous, by e-mail, or through CMC [computer-mediated communication] software.” Where synchronous FO instruction may be considered more “group-based,” asynchronous FO instruction tends to be more “individually-based” with students working “independently or in asynchronous groups, usually with the support of an instructor or tutor” (p. 184). There is some complexity here. In particular, FO instruction does not necessarily exclude the use of synchronous instructional components. For example, FO students may be in contact with the instructor and/or other students in real-time via video-conferencing or chat rooms. We acknowledge, as these issues may suggest, problems around defining the nature of FO instruction present a potential limitation to this kind of research where the use of asynchronous vs. synchronous instruction is often “a matter of degree” [21, p. 52]. Nevertheless, as the literature suggest, most current FO instruction tends to be offered asynchronously [39, 45, 56], as this modality is seen to provide students with a maximum degree of flexibility as they balance, for example, work, family and other commitments [21].

2 One review paper on FO statistics instruction was found. Mills and Raju [40] conducted a 10-year review analysing 20 papers, both reflective and empirical, many of which compared FO to F2F instruction. Despite acknowledging “a need for well-designed studies that control for confounding variables and other challenges related to empirical research” (p. 22), they appeared to make little attempt to distinguish studies apart from their inclusion criteria of selecting only peer-reviewed studies.

3 Apart from Google Scholar, with particular guidance from [7] for identification of relevant meta-analyses.

4 Some meta-analytic research covered in this review focuses separately on instruction that is predominantly asynchronous vs. synchronous. As FO instruction is considered to be offered in a predominantly asynchronous format, any reference we make to FO instruction implies a focus on studies directed at instruction considered to be asynchronous. Also, see footnote 1.

5 Though not surprising given previously discussed issues around disciplinary differences.

Additional information

Notes on contributors

Sven Trenholm

Dr. Sven Trenholm is a lecturer of Mathematics Education at the University of South Australia. He received his Ph.D. (Studentship) from Loughborough University (UK), M.Sc. (Distinction) from the State University of New York at Albany (US) and Graduate Diploma in Teaching as well as B.Sc. from McGill University (Canada). Previously he taught mathematics full-time for more than 13 years, including 11 years as a full-time instructor of mathematics at the community college level within the State University of New York. His research is situated in the intersection between the fields of mathematics education and instructional technology. He is primarily interested in investigating the development of mathematical thinking in fully asynchronous online instructional contexts. He has published in leading international journals in his field, including the NCTM Journal for Research in Mathematics Education.

Julie Peschke

Dr. Julie Peschke is currently an Academic Coordinator of Mathematics at Athabasca University, the first open, online university in Canada. Apart from some asynchronous teaching duties, she is responsible for the design and creation of post-secondary mathematics courses online, as well as a full remedial program with interactive tutorials and self-assessment. She received her Ph.D. from the University of Alberta in 2014. Her research interests include the impact of technology on students’ learning and the core principles of designing digital spaces to promote a deeper understanding of mathematical concepts and the role mathematics plays in our modern world.

Mohan Chinnappan

Professor Mohan Chinnappan is a professor of mathematics education at the University of South Australia. He is a leader in the study of mathematics pedagogy with an international reputation for research on the knowledge base that anchors mathematical understanding and transfer. He has authored more than 100 scientific publications and has won national awards for the impact of his research on teaching mathematics and associated professional development. He is a consultant on projects with a focus on fine-grained analyses of mathematics learning processes and PD in Australia, Indonesia, Thailand, Singapore, Vietnam and Malaysia.