August 28th, 2006
Teaching Theory of Knowledge you teach a lot of students who actively dislike mathematics and don’t want to engage in any mathematical thought. The idea that mathematics could be a beautiful thing, or that beauty may have a mathematical aspect is often surprising.
This activity was one I concocted for my students and it has worked well on numerous occassions. Having downloaded and printed in colour the Mathematics and Beauty Cards PDF you can give a set to a group of four to six students with the straightforward instruction that they order the cards from most beautiful to least beautiful without any equivocation. This will likely take them twenty minutes. If you have an interactive whiteboard you may then also find useful the Mathematics and Beauty Flash Application which offers a very simple mechanism for reviewing the decisions students make.
With all such activities there is no obviously right and wrong answer, but you are likely to find that students consider incorrect answers such as 1-9=2 to be ugly in a way that correct answers, such as 1+3=4 are not.
Obviously geometrical diagrams may be considered less beautiful than images that area highly geometrical like Da Vinci’s Last Supper or the fossil. That offers opportunity to discuss issues such as perspective, the golden ratio and the fibonacci sequence.
You are also likely to find that many highly ranked elemenys are considered beautiful by authority; a student once told me that the Mona Lisa must be top because “it’s the Mona Lisa”. The group agreed that, on reflection, this did not constitute a good argument.
My favourite part of this activity however is to use it as an excuse to introduce to them the Mandelbrot Set, which they are unlikely to have seen before, but which is extremely interesting. I will publish more details of what I do with the Mandelbrot Set on another date.
I have found that as a hook for thinking about aspects of mathematics that go beyond the mathematics classroom it is a highly valuable activity. It allows me, as a mathematics specialist, to break off along a variety off different avenues and discuss with them a host of concepts that they are unlikely to see in other places. After running this activity, I often find that two or three lessons worth of material is generated from the questions that the students pose. I hope you enjoy it.