This special issue incorporates a selection from the proceedings of the Calafate Delta’07, the Sixth Southern Hemisphere Conference on Undergraduate Mathematics and Statistics Teaching and Learning, held at the World Heritage Los Glaciares National Park in Patagonia, Argentina, in November 2007.
Delta is a community of academics committed to improving mathematics and statistics teaching and learning at university level. The first conference was held in Brisbane, Australia, in 1997, and subsequent conferences have since been held every two years, attracting participants from all continents, but predominantly from the Southern Hemisphere. The concept of continuous change in university mathematics teaching and learning inspired the name, Delta, and this is reflected in the evolution of the conference themes throughout the years. The Delta community has also evolved and grown in response to the changing needs of the participants.
The theme for the first Delta, “What can we do to improve learning?”, embodied the basic objective of this group, encouraging all points of view. At the Delta’99 conference, which was held near the Great Barrier Reef, the theme was “The challenge of diversity”, and this inspired many papers to consider the diverse backgrounds of our students, students' diverse thinking and learning styles and the kinds of courses and teaching appropriate for them. Delta’01 was held in the Kruger National Park under the theme “Gearing for flexibility” where many papers addressed flexibility, which was frequently made possible by the use of technology. Delta’03, held in Queenstown, New Zealand, was the largest gathering in the Delta history; its theme “From all angles” encouraged the discussion of a very wide range of topics treated in a variety of ways. It also included Statistics in the title of the conference for the first time. Delta’05 returned to its birthplace, Queensland, this time on Fraser Island and had the theme “Blending beyond the boundaries”. This conference commenced with the practice of publishing a selection of papers in this journal, to share with its readership some of the work that formed the basis of the discussions and collaboration between participants.
Continuing with the Delta concept, the theme of Delta’07 is “Vision and Change for a new century”. The papers published in this special issue reflect some of the current challenges faced by teaching academics and include contributions from several countries. On the surface, these challenges may not look new, but the solutions and various approaches evolved in new directions adapting to the changed students’ expectations, the changed higher education landscape, and the changed needs of the graduates who will operate in this new century.
Adequate preparation for mathematics studies at university level is an important aspect contributing to a positive student university experience and to their engagement with mathematics. This special issue begins with two papers on this matter. The first paper, by Britton, Daners and Stewart, presents a self-assessment approach to be used by commencing students at the University of Sydney to decide whether to enrol in the higher-level first-year subject, and analyses its effectiveness as a predictor for successful performance. The second paper, by Parnell and Statham, describes a pre-university certificate programme introduced at the University of Auckland to prepare students for university studies, and discusses their findings on the effectiveness of its mathematics component.
Two papers follow on the theme of offering to first-year students the best programmes to ensure their success with their university studies, particularly in mathematics. Steyn and Du Plessis discuss the effectiveness of developmental support programmes for South African engineering mathematics students who are at risk of failing, and compares their success in improving their mathematics competence in the first year and completion rates with those of the main stream students. On the other hand, Miller-Reilly focuses on the importance of the teachers’ role in acknowledging students’ backgrounds in relation to mathematics knowledge and their attitudes towards mathematics, and presents the findings of a large-scale study in New Zealand which included the collection and analysis of quantitative and qualitative data.
Current students are presented with an enormous range of choices of courses and career pathways. In this competitive environment, the biggest challenge for mathematics departments around the world is to attract students to mathematics. The most effective way is to expose students to good teaching that inspires them with the nature and beauty of mathematics and its relevance in the further advancement of human kind. Seven papers in this special issue present examples of how this could be done. Four of these papers are about teaching techniques. Wood, Joyce, Petocz and Rodd discuss the importance of the use of multiple representations in lectures to ensure that all students benefit from them. The work of Cavallaro, Anaya, García Argiz, and Aurucis, on how engineering students in Argentina learn to make estimations and probabilistic judgement, informs the teaching of probability and statistics. Stewart and Thomas apply Tall's three worlds of mathematics—embodied, symbolic and formal—to the learning of linear algebra concepts and investigate the effectiveness of this approach. In another paper, Wood and Harding address the general question of what constitutes good lecturing, particularly in the context of mathematics. The paper by McLeod and Huinker present techniques used in the University of Winsconsin-Milwaukee teacher training programmes to prepare teachers for their important role of educating and enthusing students. Finally, the two papers by Harding and Engelbrecht present an insight into visualizing complex roots and propose the use of the historical development of this concept, coupled with their visualization, to enrich the student learning experience.
These selected papers are only a small sample of the breadth of the discussions held in Patagonia in November 2007, but we hope that this sample is large enough to give you an insight into the work of the Delta community and its commitment to the future of mathematics and mathematics teaching.
VICTOR MARTINEZ-LUACES
University of the Republic of Uruguay, Uruguay
CRISTINA VARSAVSKY
Monash University, Australia