id: 05671724
dt: j
an: 2010b.00545
au: Griffiths, Martin
ti: The immortal ant and the expanding balloon.
so: Teach. Math. Appl. 28, No. 3, 150-158 (2009).
py: 2009
pu: Oxford University Press, Oxford; Institute of Mathematics and its
Applications (IMA), Southend-on-sea, Essex
la: EN
cc: I54 I55 M14 M15
ut: calculus; mathematical applications; mathematical models; spheres; integral
calculus
ci:
li: doi:10.1093/teamat/hrp009
ab: Summary: 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.
rv: