Greg Oates

Effective tutorial programmes in tertiary mathematics

Papers presented at earlier Delta conferences reported on the use of collaborative tutorials and peer-tutors in undergraduate mathematics courses at The University of Auckland. This paper reports on significant developments within the Departments programmes, including the extension of the collaborative small-class tutorials to cover all first-year undergraduate courses in the department. It provides evidence of the effectiveness of the tutorial programme, as gauged from a survey of students’ perceptions. Many of the students enrolled in the Tutoring in Mathematics course that initially trains and provides the peer-group tutors continue on as tutors in other mathematics courses within the Department. Some subsequently enrol in the Universitys Graduate Diploma in Teaching (Secondary). The effects of the tutoring course on tutors continuing to tutor at higher levels, and their performances as novice teachers in the Diploma course are examined.

Undergraduate mathematics students’ reasons for attending live lectures when recordings are available

With the proliferation of new affordable recording technologies, many universities have begun offering students recordings of live lectures as a part of the course resources. We conducted a survey to investigate why some students choose to attend lectures in person rather than simply watching the recordings online, and how students view the two types of lectures. Students attending live lectures in five large undergraduate mathematics lecture streams were invited to respond to the survey. A significant number of respondents viewed recorded lecture as superfluous to their needs which were met upon attending live lecture. Surprisingly, however, an equally large number of students described compelling reasons for watching both live and recorded lectures. A number of factors were identified as determining students’ perceptions of live and recorded lectures as competing or complementary: personal learning styles, study habits, esteem for the lecturer, and the possibility of interaction in the lecture.

Tertiary Mathematics Education

Mathematical and statistical education research relevant to students in tertiary settings is reviewed. This is an expanding field and is evolving as researchers shift their attention from the reporting of innovations in lecturing practice and course design to include a deeper consideration of the experiences of educators and learners in this space. The purposeful inclusion of group work and discussion, focus on concepts, authentic problem solving, interactions in lectures with student response systems and online learning are all changing the way mathematics and statistics are taught at this level. The authors note that traditional measures of achievement in the form of exam marks are still relied upon, and call for theory-based and theory-building research including investigations of depth of understanding, and of transfer of knowledge and skills to new situations. An emphasis on the learner’s experience and the employment of cross-disciplinary teams of researchers are further suggestions.

Seeing Things From Others’ Points of View: Collaboration in Undergraduate Mathematics

Abstract We report on three approaches taken to incorporate collaborative activities into undergraduate mathematics classes. There is strong evidence from research in K-12 classrooms that these, and similar, approaches support a range of positive learning outcomes for students. Despite the potential benefits the cited studies have shown, research into the use of such methods at the tertiary level is limited. We describe the ways in which we have implemented research projects, collaborative tutorials, and team-based learning in a range of undergraduate mathematics classes in two countries. We present quantitative and qualitative evidence from these teaching experiences to support our claim that there is a definite mandate for significant opportunities within our courses for students to work cooperatively, talk together, and argue about mathematics.

Mathematics in a dynamic environment

This is the third special issue of iJMEST to feature selected papers from the Delta Symposium series, and as such, extends a valuable relationship for the dissemination of significant issues and co...

Innovative uses of digital technology in undergraduate mathematics

The ways in which digital technology is often used in university teaching of mathematics can be quite different from how it is employed in schools. This has the potential to form a discontinuity between school and university, making the transition less than smooth for students. In this chapter we consider several examples of how digital technology has been used with first year mathematics students in both New Zealand and South Korea. The approaches employed include: intensive use of technology, including formative and summative assessment practice; lecturer modelling and privileging of technology use; a versatile approach to calculus concepts that encourages epistemic exploration of local properties of functions; and novel orchestration of mathematical thinking through smartphone communication technology. We analyse each of these approaches using the theory of instrumental orchestration and outline some innovative aspects and benefits of them. The student perspective is also considered, with some evidence of the influence on student engagement and attitudes. We conclude by suggesting that in order to teach with digital technology in the manner described here good pedagogical technology knowledge (PTK) is required.

Brazil Delta 2017: the romantic path of mathematics

This thematic collection draws together the six papers finally selected for publication from n23 full-paper submissions for the Brazil Delta Conference, the 11th biennial conference on nthe teaching and learning of undergraduate mathematics and statistics, which took place nin Gramado, Brazil from the 26th November to the 1st December 2017. This marks the nsecond time the group of passionate undergraduate mathematics education professionals nhave met in South America under the Delta symposia umbrella, the first being the sixth nDelta ’07, held in the World Heritage Los Glaciares National Park in Patagonia, Argentina. nThe other nine conferences in the series have been held variously in Australia (1997; 1999; n2005; 2013), New Zealand (2003; 2011) and South Africa (2001; 2009; 2015). This collection nalso marks the sixth time selected papers from the conference have been published as a special issue of the International Journal of Mathematical Education in Science and Technology (iJMEST), and the first time this has been published as an Open Access (OA) Supplement Issue. We acknowledge the continued support of the Editors and publishers at iJMEST and Taylor and Francis for extending the dissemination of our Delta community’s scholarship and research. More about the Delta network, including links to papers from each year’s Proceedings (the papers published separately to the special iJMEST issue), can be found at http://www.deltaconference.org/.