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I developed a fascination for mathematics long before I got hooked on ringing – encouraged by my mother and under the guidance of good teachers. I didn’t take it up professionally but retained an interest in recreational maths, and of course ringing is rich with mathematical concepts. I find it hard to imagine going through life without maths as a mental tool to enjoy and make sense of the world, but I know many people do. I also care passionately about telling people how exciting ringing is. So when I was invited to talk about ringing to a group of bright maths pupils, it was an opportunity not to be missed – something I have wanted to do for several years.
I have given many short ‘assembly talks’ in primary schools, but I realised that secondary schools would need something more substantial, and also that with teaching time under pressure, any extra activity would need a good justification. It seemed sensible to link ringing to subjects in the National Curriculum, and such is the richness of ringing as a topic, that it was easy to relate it to many subjects. Music, maths, ICT (computing), physics and technology are the obvious ones, and without too much stretch I included social history, PHSE (Personal, Health & Social Education) and Citizenship. The descriptions of what could be offered went on the schools page of our tower website. All I needed now was an interested school.
I tried the Church’s local schools co-ordinator without success. I consulted some teachers, one of whom advised me to find a school that did diplomas instead of A-levels, and a pupil who wanted to use ringing as the subject of the ‘Extended Project', but I failed to find either. I even discussed it with a curriculum planner whom I met while on a walking holiday.
Then I came across a basic article about ringing on the website of NCETM (National Centre for Excellence in Teaching Mathematics). I contacted the co-ordinator, expressing my interest, offered to help if appropriate, and pointed her to our website. She then put an article in a later issue inviting maths teachers to look at the schools page of our website, and contact me if they were interested. As a result, I was approached by Carol Gainlall, who was running a mentoring scheme for G&T (Gifted & Talented) mathematicians at Park House School in Newbury.
By coincidence, I had just put together a 2 hour presentation for the Maths Group of my local U3A, so I used the material in that to give her an overview of the sort of ideas that I could use. We agreed a broad outline of about 2 hours, with exercises and practical sessions for the pupils interleaved with the lecture material. The group of 12 pupils spanned years 7 to 12 (1st form to lower 6th form). As well as thinking about how to put the ideas over to teenagers, I had to check what mathematical concepts they were unlikely to have met, and which I would need to explain. Interestingly I was told that they were more likely to be familiar with the Fibbonaci series than with factorials – the reverse of the order I came across these concepts 50 years ago.
I began by explaining how bells work, and how the physical constraints impose mathematical order on bell music, and then explored the more mathematical aspects. These included the relationships between rows and changes, the blue-line and structural similarities of methods at different stages, the use of coursing orders, the significance of groups and Q-sets, and a few other things like internal falseness and row parity. I told the story of how it took 300 years to find whether a bobs-only peal of Stedman Triples was possible, and I showed them how ringing has been represented by complex geometrical shapes, including the wire models that I built over 40 years ago.
Exercises and demonstrations included exploring the number of rows and changes on different numbers of bells, exploring the effect of repeated application of the Queens transform on different numbers, trying some composition (with the aid of a spreadsheet to work out the coursing orders automatically), listening to the different types of music in hunting on 12, and ‘walking’ a plain hunt on 8. In fact they were so keen on this that they did it again after we had finished, without being asked.
Feedback from the pupils afterwards was positive. They had no idea that bell ringing was so mathematical and were intrigued by the links between the two subjects. One student wished that parents could have come, because her father have loved it, and another is thinking about learning to ring. Carol (the teacher) is planning to base a patchwork on plain hunt, with each bell as a fabric of a different colour. I left them with a list of references and websites to look at, so they have things to follow up if they wish. I understand that the next edition of the school’s impressive magazine will include a feature on maths and ringing.
One thing I realised was the importance of understanding the additional layer of abstraction when a string of numbers represents a transform (where the figures refer to positions in a row), rather than a row (where the figures refer to bells). That is a fundamental concept (in maths and computing as well as in ringing) but once you understand it it becomes so intuitive that you can forget its importance, and that it is not ‘obvious’. Maybe that is why so many ringers have difficulty understanding the difference between a row and a change.
There is an overview of the talk at: http://jaharrison.me.uk/Ringing/Maths.html
Information about ringing and other curriculum subjects is at: http://allsaintswokinghambells.org.uk/ASRinging/Community/Schools.html
This is the text of the article published in The Ringing World on 27 May 2011.
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