The Fibonacci Sequence

This week's article by Marcus Du Sautoy in his Sexy Maths column for the Times was all about the Fibonacci sequence, which inspired me to write a little about my Fibonacci Master Class which deals with Leonardo Pisano's famous sequence.

By the way Marcus Du Sautoy is my favourite living mathematician. I never imagined I would have a favourite living mathematician, but I guess he doesn't have much competition as I probably couldn't name another one! Having said that he is a pretty cool guy. If you are not aware of him he is the current Simonyi Professor for the Public Understanding of Science, you might have seen him with Alan Davies on Horizon recently, or have followed his Story Of Maths last year on BBC4 or have seen him a couple of years ago on the Royal Institution Christmas lectures. He tell the stories behind huge mathematical ideas in an engaging and lively way; sort of a modern day Johnny Ball for grown ups (with real Oxbridge kudos and academic publications behind him!)

Du Sautoy's awe and wonder approach is what I try to achieve with my Maths Master Classes; a series of lessons I designed for a school in Bradford, which I'm now using in schools as part of my work. They focus on the lives of famous mathematicians and artists trying to get more able upper KS2 children to be inspired by maths and to investigate and explore the discoveries of these characters in an open ended way. These classes generally work best when delivered as a sequence of lessons, and contain 4 to 6 hours of material; with resources including PowerPoint presentations, worksheets, images and videos. I usually deliver the sessions with staff from the schools observing and quite often participating. In fact one of the really pleasing aspects for me is the number of times teachers and other adults get out their pencils and ask for a copy of the worksheets so they can investigate the ideas themselves! I also get huge pleasure from the way children in all settings respond with enthusiasm as they try to make the discoveries of Durer or Gauss or Pascal etc themselves. A colleague at a school in Halifax recently said she felt quite emotional when she watched one of her pupils explain how he had found a way produce a magic square using a strategy of his own.

This particular Master Class follows on from a Master Class on the French Mathematician Blaise Pascal. It is introduced by referring back to "Pascal's Triangle", the children are encouraged to explore a set of diagonals on the triangle which produce the Fibonacci sequence as their totals. They are asked to explain what they have noticed in the sequence before being introduced to Leonardo Pisano, or 'Fibonacci', himself. As an aside we look at his home town of Pisa and I usually set the children the task of researching whether Fibonacci could have seen the famous 'Leaning Tower' - I'll let you do the same, if you want - answer below.*

The sessions continue with the children recording in their own ways the results of 'Rabbit Problem', posed by Pisano in his book Liber Abaci. They are encouraged to present their findings in a diagrammatic fashion so that they can present them back to the group. I encourage the children to refine their ideas so as to be as efficient and clear as possible.

Finally the pupils are shown how to create a Nautilus spiral using a series of Squares with the dimensions of the Fibonacci sequence.

Watch the video below which shows the slides from the supporting PowerPoint presentation, clearly it is only an indication of the content. If you are interested in this or any other Master Classes please get in touch via the blog or email me through my profile.



My whole approach to the Master Classes could perhaps be summarised by Blaise Pascal himself when he said
"We are generally better persuaded by the reasons we discover ourselves than by those given to us by others."

*ANSWER: He was alive whilst the first part of the tower was built, it then began to lean before being completed approximately 120 years after his death.
http://en.wikipedia.org/wiki/Leaning_Tower_of_Pisa