Introduction: This module gives you the opportunity to engage in mathematical problem solving and to develop problem solving skills through reflecting on a set of heuristics. You will work both individually and in groups on mathematical problems, drawing out the strategies you use and comparing them with other approaches.

General aims: This module will enable you to develop your problem solving skills; use explicit strategies for beginning, working on and reflecting on mathematical problems; draw together mathematical and reasoning techniques to explore open ended problems; use and develop schema of heuristics for problem solving.

This module provides an underpinning for subsequent mathematical modules. It should provide you with the confidence to tackle unfamiliar problems, think through solutions and present rigorous and convincing arguments for your conjectures. While only small amounts of mathematical content will be used in this course which will extend directly into other courses, the skills developed should have wide ranging applicability.

Learning objectives: The intended outcomes are that by the end of the module students should be able to:

• Use an explicit problem solving rubric to organise and facilitate mathematical problem solving
• Explain the role played by different phases of problem solving
• Critically evaluate your own problem solving practice
• Be aware of key literature on mathematical problem solving

Organisation: The module runs in term 2, weeks 1-10. Typically there will be a weekly session for completing the problems counting towards 10% of the module (see below) and a second, longer session discussing the theory a working through problems together. You are expected to attend all timetabled hours.

Assessment Details:

• A flat 10% given for serious attempts at problems during the course. Each week, you will be assigned a problem for the seminar. At then end of the seminar, you should present a rubric of your work on that problem so far. If you submit at least 7 rubrics, deemed to be serious attempts, you will get 10%
• A take home assignment (40%) due in March
• A 2 hour examination in June (50%)