# MA3E7 Problem Solving

Lecturer: Mark Cummings

Term(s): Term 2

Status for Mathematics students: List A for 3rd year G100 (and 4th year G101), List B for 3rd year G103 (G105). If numbers permit, fourth years may take this module as an unusual option but confirmation will only be given at the start of Term 2

Commitment: 10 two hour and 10 one hour seminars (including some assessed problem solving)

Assessment: 10% from weekly problem-solving seminars, 40% from take home assignment, 50% two hour examination in June

Formal registration prerequisites: None

Assumed knowledge: None

Useful background: General interest in mathematics outside of university modules (e.g. Numberphile or other maths YouTube channels, Martin Gardner's puzzles).

Synergies: This module is very different from your usual theorem-proof module. It will get you to think about mathematical problem solving in a new way. This module is particularly useful if you are considering a career in teaching.

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%)