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The World of Illusion Knitting

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PICKING UP THREADS

This was written in
2007
so is now very dated

The school where I was teaching had several Support Teachers and, because I mostly taught groups where the lack of English was a serious problem, I had the same Support Teacher in the classroom with me for at least half the week. He actually had a degree in Classics and that was what he had taught in earlier years but he was brilliant at being able to communicate with these pupils. He was also intrigued by the items that appeared on the classroom wall and he was as likely as I was to spend long periods of time discussing them with groups of pupils. He was captivated by Counting Pane. He would lead groups, or individuals, through ways to express for themselves what these patterns might mean.  Sometimes, to the amazement of pupils, he would fly in through the ever-open door, study the pattern for a minute and disappear just as quickly muttering, “Just passing by … came in to check ….”

Shortly after this we took Counting Pane, and other items, to a Maths Fair that had been organised by a friend. Pupils came in coachloads from various schools and most were free to explore as they wanted. One young girl, aged about 13, wandered in and soon got deep in conversation. We were very impressed by the logic of her thought processes and quite thought that she would be one of the mathematical stars of her school. She told us that she was useless at Maths, was in a low Maths set and hadn’t really wanted to come to the Maths Fair at all. A little later she returned with a friend and proceeded to explain to the friend what she had discovered about Counting Pane. This process was repeated several times during the day and she became more confident with each one. Towards the end of the day she appeared again dragging a man with her. The man turned out to be her Maths teacher and she was not going to let him go home until he had seen it too. He was staggered as she had never shown any enthusiasm for the subject before. We like to think our unconventional approach might have had a long-lasting effect on that young girl.

But Counting Pane also caused trouble in a situation the like of which we were to meet again later. We always referred to those numbers that divide into other numbers as ‘factors’. When we took Counting Pane to the annual Maths conference we displayed it with a brief explanation using the word ‘factors’. Very soon someone, who we would readily accept knew more than we did, said the word was wrong and we were describing ‘divisors’. Fortunately, before we had chance to answer, another, highly-credible mathematician, jumped in to agree with us. It seems that either term is equally acceptable but individuals have a very strong preference for one over the other. It was a situation that we were to meet again. We never got anything seriously wrong but there is always a moment of panic when an academic questions what we have said.

There was also a discrepancy in Counting Pane that we still feel is unresolved. The number 1 does not fit the definition for a prime number because it has only one factor. Should it be coloured blue if it isn’t a prime number? On the other hand, every square has blue in it to show that every number divides by 1. The number 1 divides by 1 so it should be coloured blue and not-blue at the same time. The original version had number 1 coloured in navy blue. Since then we have made two ‘copies’ and both have number 1 in blue. We are not truly happy with either version.

9b. COUNTING PANE continued