Teaching Mathematics and its Applications - current issue

Preface

Hibberd, S., Demlova, M. — 2008-08-19

On strategies contributing to active learning

Gavalcova, T. — 2008-08-19

Many reasons have been documented about the need for more effective teaching of mathematics in universities. These include changes in the level of mathematical skills of new students; changes in society, particularly technological ones, which have led to a strong preference for visual presentation of information; and new students lacking the independent study skills necessary to succeed in higher education. Several authorities have addressed this problem. In this article, we introduce and discuss ideas and strategies for active learning presented by Krantz and Bressoud. We cite thoughts of Zucker and give a summary of strategies formulated by Zweck.

Increasing engineering students' awareness to environment through innovative teaching of mathematical modelling

Klymchuk, S., Zverkova, T., Gruenwald, N., Sauerbier, G. — 2008-08-19

This article presents the results of two studies on using an innovative pedagogical strategy in teaching mathematical modelling and applications to engineering students. Both studies are dealing with introducing non-traditional contexts for engineering students in teaching/learning of mathematical modelling and applications: environment and ecology. The aims of using these contexts were: to introduce students to some of the techniques, methodologies and principles of mathematical modelling for ecological and environmental systems; to involve the students in solving real-life problems adjusted to their region emphasizing the aspects of both survival (short term) and sustainability (long term); to encourage students to pay attention to environmental issues. On one hand, the contexts are not directly related to engineering. On the other hand, the chances are that many graduates of engineering will deal with mathematical modelling of environmental systems in one way or another in their future work because nearly every engineering activity has an impact on the environment. The first study is a parallel study conducted in New Zealand and Germany simultaneously with first-year students studying engineering mathematics. The second study is a case study of the experimental course Mathematical Modelling of Survival and Sustainability taught to a mixture of year 2–5 engineering students in Germany by a visiting lecturer from New Zealand. The models used with the students from both studies had several special features. Analysis of students’ responses to questionnaires, their comments and attitudes towards the innovative approach in teaching are presented in the article.

Closing the gap between formalism and application--PBL and mathematical skills in engineering

Christensen, O. R. — 2008-08-19

A common problem in learning mathematics concerns the gap between, on the one hand, doing the formalisms and calculations of abstract mathematics and, on the other hand, applying these in a specific contextualized setting for example the engineering world. The skills acquired through problem-based learning (PBL), in the special model used at Aalborg University, Denmark, may give us some idea of how to bridge this gap. Through an investigation of a series of examples of student projects concerning the application of mathematical subjects—such as matrices, differential equations, cluster analysis, graph theory etc.—the skills attained by participating students will be mapped out and discussed.

Promoting student engagement with mathematics support

Symonds, R., Lawson, D., Robinson, C. — 2008-08-19

This article reports the findings of qualitative research undertaken to seek to identify the key reasons why some students are not engaging with mathematics support provided by Loughborough University. The research involved a number of focus groups and ‘on the spot’ interviews with ‘non-users’ from across the campus. Barriers identified include a lack of awareness of the location of support and a fear of embarrassment. Further interviews were conducted with regular users of the support in an attempt to understand how some of these barriers to usage might be overcome. The article will discuss actions that may be taken to improve student engagement with mathematics support and the issue of how student motivation may affect such action.

Which mathematics should we teach engineering students? An empirically grounded case for a broad notion of mathematical thinking

Cardella, M. E. — 2008-08-19

While many engineering educators have proposed changes to the way that mathematics is taught to engineers, the focus has often been on mathematical content knowledge. Work from the mathematics education community suggests that it may be beneficial to consider a broader notion of mathematics: mathematical thinking. Schoenfeld identifies five aspects of mathematical thinking: the mathematics content knowledge we want engineering students to learn as well as problem-solving strategies, use of resources, attitudes and practices. If we further consider the social and material resources available to students and the mathematical practices students engage in, we have a more complete understanding of the breadth of mathematics and mathematical thinking necessary for engineering practice. This article further discusses each of these aspects of mathematical thinking and offers examples of mathematical thinking practices based in the authors' previous empirical studies of engineering students' and practitioners' uses of mathematics. The article also offers insights to inform the teaching of mathematics to engineering students.

Helping engineers learn mathematics: a developmental research approach

Jaworski, B. — 2008-08-19

A mathematics module in the undergraduate programme for first year engineers aims to enable those with low mathematical qualifications to understand and use efficiently calculus and related topics. The teaching approach is designed to develop student's fluency, understanding and responsibility through creating an inquiry community, encouraging students to engage with materials and support opportunities and extending their thinking through investigative problems. Research is exploring the provision and outcomes of the module. Findings so far indicate highly variable patterns of attendance at sessions and scores on class tests. Attitudes to the module, relationships with students attending sessions and appreciation of materials and support are generally good. Achievement of the aims of the module, however, is relatively low.