Hi everyone my name is Garrod Musto, and I am head of mathematics at
Kingswood school in Bath. I wanted to talk to you today about a project I
developed at school and have enjoyed delivering for the past 4 years.
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works in addition to providing them a way in which they could learn to
communicate ideas and instructions mathematically to describe particular
crop circle constructions. It also gave our less able but more creative students
a chance to shine in a mathematical context, which they enjoyed immensely.
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I hope therefore to spend a little time providing some background to Euclid;
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designs found not too far away from the University here at Reading.
I hope there will be opportunities for me to show you some of the multimedia
resources I used from sources such as YouTube, and give you an opportunity
to try out some of the compass construction skills using the tools of a circle
maker.
Once you have had a go at one of the tasks we set the students, I then want
to detail the development of the project in school, this includes looking at
some of the crop designs that were created here in this part of England,
Online resources which I have detailed at the back of this set of session
notes, and the use of dynamic software Cabri Geometry, all of which I have
included in the session resources.
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Euclid organized the teachings of Pythagoras, his disciples and other Greek
thinkers, into his great work, The Elements. In fact, this book is a synthesis of
past teachings. Euclid, thought to be a student of Plato's disciples, organized
the epic, Elements, from centuries of Greek geometry, and refined lots of it.
The Elements is one of the most widely read books ever, and his approach
has dominated mathematics for the last two millenniums.
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Elements with particular reference to proposition 4 and 5, which detail how
you find the centre of the circumcircle and inscribed circle respectively.
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Stop 9;19 minutes into the video.
As you can see the clip tried to look at a variety of possible reasons which
might describe the phenomenon. However I was very struck by the human
interest story of David Hughes on Galtee More Farm, and thought this might
be a good way to explore circle designs, but do so in a meaningful way which
aims to inform the students about the negative effect of crop circles on the
farmers of the area.
Therefore lets now look at the next design found on Galtee More farm.
This is the audience participation bit of the session.
In retrospect this also provided an excellent opportunity to consolidate
aspects of symmetry and properties of polygons. To begin the overall project I
wanted to get the students to think like crop designers, hence I wanted them
to begin to work with their tools, which are rope and a plank.
My classroom version consisted of a piece of string and a board marker to act
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Break
Leave this up and break for about 10 minutes while delegates have a go
The mathematician Bert Janssen shows here that this pattern can be
made using geometrical instruments,
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field? Probably, but what about the next two slides?
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Having tried to make the design using a set of compasses on paper and also
using string and a marker pen on a whiteboard, I wanted to show the class
how to create the design using the Cabri Geometry package we have at
school. Students very quickly developed a feel for the software and were able
to recreate it very easily.
A homework assignment was set, design and draw your own circle design
providing enough instructions to enable another student to recreate it.
I then decided on the best ones and distributed a crossection of the designs
to groups of pupils, deliberately ensuring that no student was allowed to be a
part of drawing their own design.
I purchased a tub of thick chalks, and the pupils went out in to the school yard
during a lesson and tried to create some crop circles before the other pupils at
school came out for lunch.
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Many of the students commented on how important it had been to provide
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enough detail. Here is an example of one such design;
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Generally this use of crop circles in schools has proven a very positive
experience. Students consolidated their understanding in a number of topics,
in addition to developing their appreciation of the need for mathematical
communication and showing their working.
I just wanted to finish with a few other designs created summer 2007, and
2008 which I enjoyed sharing with the students as it provided opportunities to
bring other curriculum areas into the project, in addition to showcasing
transcendental numbers and highlighting further examples which illustrate the
structure of these beautiful creations.
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I hope you have enjoyed the session today. I have included the ppt notes, and
all the video clips and images in the delegate resources and I would love to
hear from you should you wish to try to do something similar in your schools.