Module FOUD0367: Mathematical Thinking

Department: Foundation Year (Durham)

FOUD0367: Mathematical Thinking

Prerequisites

• None

Corequisites

• None

Excluded Combination of Modules

• None

Aims

• To provide the opportunity for students to engage in logical reasoning, mathematical modelling, and the formulation of rigorous mathematical derivations.
• To develop students' mathematical problem solving skills through the exploration of open ended problems.

Content

• Problem solving – students will focus on using known techniques in different situations. Explore the problem through examples and try to formulate precise conjectures or solve special cases.
• Mathematical Rigour – Students will learn to present arguments/derivations clearly and precisely, taking care with exceptional cases and defining required notation.
• o Proof – Students will learn basic methods such as contradiction and induction. This will be developed through the use of simple formulaic examples as used in A Level followed by a wider variety of examples e.g. geometric constructions (some examples of tilings) to provide a good conceptual understanding. Students will consider Invariants since finding a suitable invariant can solve many problems, and is also closely related to aspects of proof. E.g. start with parity and generalise to colourings – obvious geometric/tiling examples.

Learning Outcomes

• By the end of the module students will:
• be able to engage in explicit strategies for beginning, working on and reflecting on mathematical problems
• have an awareness of the basic concepts of Problem Solving and mathematical proof

• By the end of the module students will have acquired the skills to be able to:
• apply mathematics to a variety of problems
• formulate and write precise mathematical proofs

• By the end of the module students will be able to:
• demonstrate problem solving skills
• produce clear and precise explanations of results

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Theory, initial concepts and techniques will be introduced during lectures and through discussion in seminars
• Much of the learning, understanding and consolidation will take place through the use of structured worksheets during tutorials and students' own time.
• Ability to recall, select and use knowledge will be tested by a series of five invigilated open book tests and an end of module invigilated exam
• Problem solving techniques will be tested through two coursework problems and within the end of module invigilated exam

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Students will undertake a range of practice tasks and problems as part of the teaching session or in their own time. These will help develop and consolidate skills and provide feedback in preparation for the assessed tasks which will be using similar skills.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University