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Guarding Art Galleries: Design and evaluation of an undergraduate research based group project in mathematics

Annual Learning and Teaching Conference 2010, Nottingham Trent University (29/03/2010).

"Problem Solving" is a second year BSc (Hons) Mathematics module aimed at developing mathematical and transferable skills and not based around a particular topic.

Some literature was reviewed in relation to transferable skills and what group projects and self-motivated learning can achieve in skills development. This review was used to inform the design of a group project task based around independent student research.

The project task involved students working in groups to research a mathematical topic and using these findings to solve a series of set problems. Students were given skills development sessions on finding and using references, giving presentations and writing reports. An indicative initial reading list was given as a starting point but, apart from the skills development sessions, there was no formal teaching material. Students were required to research the topic independently to answer a set of problems, then to explore the topic more broadly in a direction of their choosing to propose an extension of the original problem. Their findings were presented in a fully referenced report and in a presentation to peers.

The topic chosen was Art Gallery Problems, problems of determining the number of guards needed to keep every point in a room under surveillance. These are pure mathematics problems using a real world context for inspiration but not intended to be applicable. This means the simplifying assumptions allow plenty of room for students to explore the limitations and possible extensions of the theory.

Undergraduate mathematicians are logical problem solvers but can tend towards more formal teaching scenarios and can lack skills around communication and group working. This task was intended to address module learning outcomes around working in groups, using reference information and communication using reports and presentations. In addition the task was designed to encourage critical evaluation of a mathematical model and communication of mathematical ideas to audiences of differing mathematical abilities. The model of independent student reseach - unusual in mathematics teaching - fitted very well with these module learning outcomes.

This talk will outline the literature findings and the design of the group project task and associated assessment. Results from a student evalutation are used to provide an evaluation of the teaching.