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Module Description

Title / Historical and Cultural Perspectives on Mathematics
Module code / SKM41
Aims / All societies have developed some mathematics in order to help them understand the world in which they live. The mathematics we study today is a culmination of what has gone before and reflects the age and society in which it was developed. Mathematics continues to change due to the curiosity of its practitioners, advances in technology and the changing needs of business and industry.
The influence of different ages and cultures can be seen in all aspects of the subject. This module provides opportunities for students to study these influences and, through examining them to deepen their own understanding within the subject.
Learning outcomes / By the end of the module students should be able to:
1. recognise mathematical activity in possibly unfamiliar contexts;
2. interpret original writings of mathematicians of the past and appreciate their efforts to communicate new ideas;
3. appreciate and understand that mathematics develops in response to a changing social environments;
4. explore links between areas of mathematics.
Content / Some specific topics will be covered such as the development of number systems and views on infinity.
Students will consider the development of mathematical ideas not only across time but also across differing areas of the globe. Students will be encouraged to compare educational texts from different countries of the world.
Learning and teaching strategies / Contact Time:
Each session will include a mixture of lecture and mathematical activity undertaken by students through small group work and discussion and reflection on the processes involved in mathematics. Reflection on the nature of the activities whilst working at them will be a key aspect of the course.
Non-contact Time:
Students will be expected to read extracts from original writings, to work on mathematical problems and techniques from other cultures and to bring their ideas to sessions.
Learning support / Books:
Ascher, M. Mathematics Elsewhere: an exploration of ideas across cultures; (2002) Princeton NJ: Princeton University Press
Berggren, J. L. (2003) Episodes in the mathematics of medieval Islam; New York: Springer
Davis P.J. & Hersh, R. (1981) The Mathematical Experience Boston MA: Birkhauser
Dunham, W. (1990) Journey Through Genius New York: Wiley
Dunham, W. (1997) The mathematical universe: an alphabetical journey through the great proofs, problems, and personalities New York: Wiley
Eves, H. (1981) Great Moments in Mathematics before 1650 New York: MAA
Eves H. (1981) Great Moments in Mathematics after 1650 New York: MAA
Fauvel, J. & Gray J. (1987) The History of Mathematics London: Macmillan
Hersh R. (1997) What is Mathematics, Really? London: Penguin
Hofstadter, D. (1984) Godel, Escher & Bach London: Penguin
Joseph, G.G. (2010) The Crest Of The Peacock: non-European roots of mathematics Princeton NJ: Princeton University Press
Kline, M. (1972) Mathematical Thought From Ancient to Modern Times London: OUP
Kline, M. (1953) Mathematics in Western Culture London: OUP
Selin, H. & D’Ambrosio, U. (2001) Mathematics across cultures: the history of non-western mathematics New York: Springer
Stewart, I. (1987) The Problems of Mathematics Oxford: OUP
Smith D.E. (1959) A Source Book in Mathematics Vols 1 & 2 New York: Dover
Struik, D.J. (1969) A Source Book in Mathematics 1200 – 1800 (1969) Harvard: Harvard University Press; London: Oxford University Press
Journals:
Mathematics in Schools; a Journal of the Mathematical Association.
MT: Mathematics Teaching; The Journal of the Assoc of Teachers of Mathematics
Electronic Sources: (accessed February 2015)
African Mathematical Union: http://archives.math.utk.edu/topics/history.html
Clark University Pages: http://aleph0.clarku.edu/~djoyce/mathhist/
History of Mathematics archive: http://www-history.mcs.st-and.ac.uk/
The MacTutor British Society for the History of Mathematics: http://www.dcs.warwick.ac.uk/bshm/index.html
University of Tennessee: http://archives.math.utk.edu/topics/history.html
Other:
BBC Podcasts (Du Sautoy): http://www.bbc.co.uk/podcasts/series/maths
Assessment task / Students will be required to complete the following task:
Task (Weighting: 100%)
Each student will prepare a sequence of poster style display boards (3 to 6 in number) which sequentially describe the development and application of a mathematical topic or technique. The boards may be submitted in A4 or A3 format or as an electronic file but should be capable of being used as a set of posters. The boards will consist of a mixture of text, diagrams and samples of work. They will contain examples of original mathematical texts and mathematical techniques not considered standard in Europe today.
(1000 words equivalent)
The task will be marked on a Pass / Fail basis.
Referral task: Reworking of original task
Assessment criteria / ·  creative and innovative explanations of mathematical activity in unfamiliar contexts (LO1);
·  interpretation or illumination of original writings of mathematicians of the past (LO2);
·  demonstrating how mathematics has developed in response to a changing social environment (LO3);
·  identifying connections between areas of mathematics (LO4).
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