International study at the University of Brighton

Profound Understanding of Fundamental Mathematics

Level: 5
Credit rating: 10
Module type: Taught
Semester offered: 2
Pre-requisites: None
Aims:

The aims for this module are set into the context of the QAA National Qualifications Framework and they relate to the SEEC descriptors for level 5 study.

This module presents mathematics as a 'way of thinking' rather than a 'body of knowledge'. Its purpose is to analyse what is meant by 'mathematical thinking' and to develop the processes involved so that students are properly equipped to cope with the demands made in terms of mathematical thinking in both concurrent and future modules.  The aim is to make the students aware that their ability as mathematicians will depend as much upon their ability to think mathematically as their knowledge of content.  Students are required to keep a journal of their experiences.
Learning outcomes:

In relation to the QAA Framework for Higher Education Qualifications and the SEEC level descriptors for level 5 study, by the end of the module students should be able to:

  1. pose and extend problems and generate their own lines of enquiry;
  2. understand and use strategies such as specialising, generalising, conjecturing, making and testing hypotheses, convincing, justifying and proving;
  3. demonstrate effective use of algebra;
  4. demonstrate depth of analysis and personal reflections when exploring a ‘good’ problem.
Content:

Likely to include:

  • the identification of mathematical processes such as:
    • problem posing;
    • specialising;
    • generalising;
    • conjecturing;
    • hypothesising;
    • convincing;
    • justifying;
    • proving.
  • starting points selected to include aspects of number and geometry
  • expressing generalities using algebra
  • an examination of the 'rules' of algebraic manipulation.
Learning and teaching strategies:

Contact time:

  • working in groups in a 'conjecturing atmosphere' on investigations;
  • sharing experiences, including drawing on journal entries;
  • tutor-run 'clinics' to support students in overcoming particular difficulties and extending skills

Non-contact time:

  • working on open ended problems;
  • reflecting critically on processes;
  • keeping a journal of experiences.
Learning support:

Books:

Brown, S. & Walter, M.  (1991)  The Art of Problem Posing   New Jersey: Lawrence Erlbaum

Brown, S. & Walter, M. (1993)  Problem Posing: Reflections and Applications  New Jersey: Lawrence Erlbaum

Burton, L.  (1995)  Thinking Things Through  London: Blackwell

Mason, J.  (1992)  Learning and Doing Mathematics  Buckingham: Open University

Polya, G.  (1990)  How to Solve it  London: Penguin

Watson, A., Houssart, J., and Roaf, C.  (2005)  Supporting Mathematical Thinking London: David Fulton

School home:

School of Education