Events: Day Break Programme 2004

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The Higher Education Academy

Part of the Day Break programme

Report contributed by Douglas Quinney

	Setting the scene and developing further opportunities
	What teaching can learn from research and what research can learn from teaching: practical case studies
	Interdisciplinary research: links with mathematics
	Linking Teaching and Research in Applied Mathematics
	Undertaking action research into teaching undergraduate mathematics
	Discussion

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This meeting was arranged with a view to covering a range of approaches that may be developed to introduce research topics and techniques into undergraduate mathematics programmes.  In particular, the four-year M.Sci and M.Math programmes usually require a significant project component where specialised research topics may be addressed.  The day was intended to prompt participants into developing and extending their departments’ approaches to integrating research components into courses, based on the expertise and knowledge base available and sharing their experiences with colleagues.

Setting the scene and developing further opportunities – John Blake, University of Birmingham

Professor John Blake, Director of the LTSN Maths, Stats & OR Network, began the day by giving a brief overview and description of the Network, its mission statement and the role of the Learning and Teaching Support Network in general.  He also alluded to the recent EPSRC review with respect to weakness in the area mathematical sciences and the recruitment of students, and possible remedies involving redefining the role of teaching at universities and forging links between research and teaching.  In particular, recent controversies as to whether it was necessary to be strongly research active in order to be a good teacher. 

What teaching can learn from research and what research can learn from teaching: practical case studies – Chris Budd, University of Bath

Professor Budd began by picking up the points raised by John Blake and dispel the myths that researchers are bad teachers and vice versa.  By using a simple example involving Celtic knots he demonstrated how problems could be posed and solved a variety of different levels and that the frontiers of knowledge, where research activities abound, are not that far away from some of the material that is currently taught in undergraduate courses.  This frontier was then highlighted a superb “card trick”, after which Chris illuminated the process by showing that it was an application of a fixed-point theorem.  Professor Budd then went on to give some example of research type problems that had been used in undergraduate courses.

Example 1: Why is the weather in February usually worse than December when the heating from the Sun is at its weakest?

This apparently difficult, and intriguing, problem boils down to modelling the atmosphere by a first order differential equation

,

where is the mean temperature of the atmosphere at a particular position and is a driving force due to the heating of the Sun.  Projects might consider investigating the effect of the parameters and lead to the solution in the form which illustrate the phase lag in the solution inherent in such a model.

Example 2: Fluorescent Tubes.  A model for fluorescent lighting had been developed at a European Study Group with Industry (ESGI) that results in a dynamical system modelled by a difference equation in the form

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and how the solution of such recurrence relations can be used to investigate the cold starting of light tubes.

To end, Chris gave a demonstration of a double pendulum that he uses at all levels to encourage students at all levels and concluded with the suggestion that ESGI is a rich source of mathematical material for mathematical undergraduate research projects. 

Interdisciplinary research: links with mathematics – Neil Challis, Sheffield Hallam University
PDF version of this presentation

Neil Challis illustrated some of the case studies that had been undertaken at SHU.  As a particular example, he looked at a mathematical model related to a number of road traffic accidents that had occurred when lorries carrying rolls of newsprint navigated a round about when the loads became unbalanced even at low speeds.  Neil used this to illustrate how this was used to provide modelling experience for undergraduate mathematicians and argued that this type of research should be just as valuable.

Neil concluded by arguing that projects should be used to help mathematics students to see real examples, and provide real motivational material, for their mathematical studies.

Linking Teaching and Research in Applied Mathematics – John Blake
PDF version of this presentation

After lunch John Blake gave some example of the type of projects undertaken by mathematics students at the University of Birmingham as part of a compulsory project requirement.  The range of projects is extensive and included critiques of research papers and investigations in the history of mathematics.

Undertaking action research into teaching undergraduate mathematics – Chris Sangwin, University of Birmingham
PDF version of this presentation

Chris Sangwin gave examples of the work he was currently undertaking which involve the use technology in undergraduate teaching and the effect this is, and will have, on pedagogy.  He gave a presentation of AiM that is used extensively at Birmingham, and elsewhere, for teaching a variety of courses.  The emphasis of his current research is designing suitable and effective feedback for students using CAL (Computer Assisted Learning) materials.

The day ended with a panel discussion.  In particular Professor Blake reminded the participants of the forthcoming call for proposals to host Centres for Excellence in Teaching and Learning, and the need for the mathematics community to ensure a complete involvement with this activity.