Module Description s1

s Module Description

Title Geometry and Proof

Module code SKM44

Aims The 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.

Learning outcomes 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.

Content 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. Learning and teaching Contact Time: strategies 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 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.

Learning support 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: Computer Packages such as: Geometer’s Sketchpad and Logo

Assessment task Students will be required to complete the following task:

Selected extracts, with commentary, from a log of work completed during the module (1000 words or equivalent)

The task will be marked on a Pass / Fail basis.

Referral task: Reworking of original task Assessment criteria The assessment criteria are:

 the ability to generate questions, conjectures and directions for exploration (LO1 & 4);  the quality of explorations, demonstrations, conjectures and proofs; (LO1 & 4);  the ability to generalise and justify findings (LO2 & 4);  demonstrating competence in use of ICT (LO3);  the quality of the reflective commentary (LO5).

All learning outcomes must be achieved in order to pass the module Examination board Combined Area Examination Board (SKE Mathematics) Module co-ordinator SKE Maths Team Date of first approval February 2015 Date of last revision NA Date of approval February 2015 Version number 1 Course 20 week SKE Mathematics School home School of Education External examiner(s) Marcus Hill, Liverpool John Moores University