The organizers of the Thirteenth International Congress on Mathematical Education (ICME-13), held in Hamburg, Germany, July 2016, asked the organizers of its Topic Study Groups (TSGs), of which there were 54, to write topical surveys. The TSGs were where most of the work of the individual ICME-13 participants was carried out. Each TSG had an overall theme — the theme of TSG2 was* Mathematics Education at Tertiary Level*, and this is the associated Topical Survey. In addition, at ICME-13, there were other events, such as plenary lectures, invited specialty lectures, and workshops, that participants could attend. At the time of my writing this, there are 13 Topical Surveys, devoted to ICME-13 TSG themes, listed on the Springer webpage. Each of these can be downloaded for free or a hard copy can be purchased. (Several have been or will be reviewed here; search on "Topical Surveys".)

It turns out that the actual writing of at least this particular topical survey, was done by the five TSG2 organizers — the above named authors — prior to the group’s actual discussions and presentations in July 2016. Personally, I find it somewhat surprising that this topical survey, and perhaps others, were written prior to the actual TSG sessions in Hamburg, rather than being a report on them.

I don’t know what the actual charge to each set of TSG organizers was, but here is what the publisher, Springer, has to say on its website:

Each volume in the series provides a comprehensive and up-to-date survey of a particular topic in mathematics education and reflects the international debate as broadly as possible, while also incorporating insights into lesser-known areas of discussion. As such each volume offers an excellent basis for a meaningful discussion of the ICME-13 conference’s [sic] results.

Since I did not know of the existence of this topical survey until very shortly before traveling to Hamburg for ICME-13, and I doubt many other TSG2 participants did either, it did not form a “basis for meaningful discussion” at the TSG2 sessions. Rather, it seems to represent the views of just its international authors.

This brief 32-page volume has three chapters. In Chapter 1, Introduction, the authors state that this volume concentrates mainly on a description of tertiary mathematics education research outcomes since 2014 because there are three mathematics education research handbooks (whose titles are given) that contain chapters where earlier tertiary mathematics education research results can be found. [N.B. “Tertiary” is the term often used internationally for post-secondary education, and when the authors write of “teachers” in this volume, they are almost always referring to university teachers of mathematics.]

The bulk of this volume is contained in Chapter 2, which is divided into five sections covering “emergent areas of interest”. These are: (1) mathematics teaching at the tertiary level; (2) the role of mathematics in other disciplines taught at the tertiary level; (3) textbooks, assessment and students’ studying practices; (4) transitions to the tertiary level; and (5) theoretical-methodological advances in mathematics education research.

Chapter 3 summarizes what has been written and suggests “under-investigated areas” of tertiary mathematics education research, which would probably be of most interest to other tertiary mathematics education researchers. These are: (1) the transition of mathematics graduates to post-graduate studies; (2) university teachers’ knowledge; and (3) teaching practice development. Finally, there is an extensive 8-page list of reverences that tertiary mathematics education researchers, and perhaps others, would find useful.

I think some, perhaps many, of the research findings discussed briefly in Chapter 2 would be of interest to those who teach mathematics at the tertiary level. For example, one study (conducted in the U.K. by Inglis, et al.) found that university students who most often watched online lectures had lower grades than those who attended actual lectures or made use of their mathematics support center. Another study (conducted in Sweden by Lithner) found that calculus students spent almost all of their homework time on searching for surface similarities to procedures or worked examples in the textbook, with little time spent on justification of their solutions — students considered the textbook’s authority sufficient. Also, Lithner found no evidence that the interviewed students attempted to learn more general ideas or properties associated with the homework problems that they were working.

The above is just a sampling of the briefly discussed research results in Chapter 2 — some perhaps more surprising than others — that a college or university teacher of mathematics could glean from reading this volume.

Annie Selden is Adjunct Professor of Mathematics at New Mexico State University and Professor Emerita of Mathematics from Tennessee Technological University. She regularly teaches graduate courses in mathematics and mathematics education. In 2002, she was recipient of the Association for Women in Mathematics 12th Annual Louise Hay Award for Contributions to Mathematics Education. In 2003, she was elected a Fellow of the American Association for the Advancement of Science. She remains active in mathematics education research and curriculum development.