Geometry and Proof

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

This module is intended to give students the opportunity to extend their geometrical ideas and skills, to widen their views about what geometry is, to understand the role of argument and proof within geometry, and to increase their understanding of the significance of the connections between geometry and concepts of proof, including the historical and cultural roots of the subject.  Through tackling problems that are purposeful to them the students will be able to develop confidence in their own ability to do geometry and also to reflect on the nature of the subject.  Through a clearer vision of the nature of geometry students will be able to respond with confidence to ideas and issues raised by this major strand of mathematics and of mathematics in the National Curriculum.

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. explore ideas and problems in geometry using suitable representations;
2. generalise, explain, justify and prove their findings where appropriate;
3. use ICT competently to explore geometry;
4. know the difference between demonstration, conjecture and proof;
5. recognise their strengths, areas for development and preferred learning styles within the area of geometry.

This will include aspects of:

• Euclidean and non-Euclidean geometry;
• transformations;
• vector geometry;
• loci;
• geometric representation of number and algebra;
• alternative dimensions: fractals and 3 and higher dimensional space
• measurement and geometry;
• cultural and historical roots of geometric ideas.
• mathematical thinking within geometry.

Contact Time:

Will include tutor-led teaching sessions, workshops, discussions, tutorials.  This module will draw wherever possible on geometric activities of interest to students.  Problems will be brought to sessions by course tutors but students will also be expected to contribute problems of their own. 

Non-contact Time:

Students will be expected to work on geometric problems in non-contact time and to bring their ideas to sessions.  They will be expected to follow-up references and where appropriate to use computing facilities.  During the non-contact time students will also investigate concept images, definitions, derivations, representations and properties of geometric objects.

Books:

Bennett, D.  (2002)  Exploring Geometry with the Geometer’s Sketchpad; ; Emeryville CA; Key Curriculum Press

Coxeter, H.S.M. (1969)  Introduction to Geometry, London, Wiley

Devlin, K.  (1988)  Mathematics The New Golden Age   London: Penguin 

Jacobs, K.  (1992)  Invitation to Mathematics  Princeton, N.J.: Princeton University Press

Johnston-Wilder, J. & Mason, J. (2005) Developing Thinking in Geometry; London; Paul Chapman Publishing

Kinsey, L.C. & Moore T.E.  (2002)  Symmetry Shape & Space, An Introduction To Mathematics Through Geometry; Emeryville CA; Key College Publishing 

Lauwerier, H.  (1991)  Fractals  London: Penguin

Papert, S.  (1982)   Mindstorms Brighton:  Harvester Press

Schumann, H. & Green, D.  (1994)  Discovering Geometry with a Computer  Bromley: Chartwell-Bratt

Wells, D.  (1991)  The Penguin Dictionary of Curious and Interesting Geometry   London: Penguin

Journals:

Mathematics Teaching; The Journal of the Association of Teachers of Mathematics

Mathematics in Schools; The journal of the Mathematical Association

Other:

School home:

School of Education