Teaching Mathematics and its Applications Advance Access originally published online on May 19, 2009
Teaching Mathematics and its Applications 2009 28(3):150-158; doi:10.1093/teamat/hrp009
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The immortal ant and the expanding balloon
Department of Mathematical Sciences, University of Essex, Colchester, CO4 3SQ, UK
Email: griffm{at}essex.ac.uk
Submitted March 2009; accepted April 2009
In this article we consider, via a specific modelling example, the educational benefits to be gained from running mathematical activities with our sixth-form and undergraduate students that, in modern parlance, might be termed ‘rich tasks’. The idea for this modelling activity arose while the author was reading a popular-science book on cosmology (in particular, on the possible shapes of the universe). Light travelling around the universe was likened to an ant crawling around a balloon. A statement in the book regarding the ant's progress around the balloon did not entirely ring true with the author, and his subsequent investigations led to the activity described here. We explore several scenarios associated with the model in order both to pre-empt possible paths taken by the students and to be able to provide some guidance when necessary. Suggestions are given as to how the activity may be extended, and then, after highlighting the numerous educational benefits, we consider the potential pitfalls and difficulties associated with the delivery of tasks such as these.
Martin Griffiths joined the teaching profession following a career in the British Army. He is now both Head of Mathematics at a grammar school in Colchester and a part-time Lecturer in Mathematics at the University of Essex. His doctorate was in the field of epidemic modelling, although he has a far wider range of mathematical interests. Indeed, over 40 of his articles have been published (or accepted for publication) in journals as diverse as the Mathematical Gazette, the Journal of Mathematical Biology, Mathematical Spectrum and the Fibonacci Quarterly. Many of these articles arose as a consequence of ideas that originated in the classroom or lecture theatre. Martin Griffiths is also the author of a book about the central binomial coefficients, published by the United Kingdom Mathematics Trust and aimed at able 16–20 year-old students and their teachers. He is currently Reviews Editor of the Mathematical Gazette.