Its not meant to be a plan, not yet. For now, it’s just a passing thought but I could really enjoy teaching 5 to 10-year olds mathematics. Not arithmetic and multiplication by repetition but proper full on mathematics.
I have looked at the National Curriculum and it has advanced since my day and at least they now teach interesting things like lattice multiplication, but I would love to do something more than go through the syllabus. I would want kids to understand that mathematics isn’t boring and that numbers aren’t boring. Quite the opposite. Our whole world is built on numbers. Nature is full of them. I would want to make numbers fun.
In a plant successive levels of branches are often based on a progression through the Fibonacci series and many flowers have petals that total a number in, or very close those in the Fibonacci series.
The golden ratio has an aesthetic that has appeared in art over thousands of years. whether deliberately we don’t know, but the Parthenon in Athens has golden ration perspectives and Salvador Dalí, explicitly used the golden ratio in his masterpiece The Sacrament of the Last Supper. The dimensions of the canvas are a golden rectangle. We just feel at home and comfortable with the ratio.
If you don’t believe me try this experiment. Cut out of card many rectangles of all different shapes. Start with a square and then make one side longer and longer until it is almost like a piece of string. Then ask a friend which one they would like to see used as a canvas to make the most beautiful picture to hang in a gallery. When you check the results the ratio of the lengths of the sides will be approximately one to 1.61.
My thoughts are based on my own upbringing. When I was a small boy I loved numbers, and knew all about, for example, Fibonacci.
I had some tutoring but that was for the 11+ exams but I also had two inspirational teachers and it is a sorrow that I can’t remember their names. They weren’t interested in just the basic arithmetic of adding, subtraction, etc but we did things that showed me the basic principles.
It turned me into a bit of a numbers geek.
Do you know about Cuisenaire Rods? As a 6-year-old I was using them all the time to play with addition, multiplication, factors and prime numbers. Of course, I didn’t know that was what I was doing. I only learnt that later, but the rods made numbers come to life with shapes and three dimensions.
Those were the days when The Telegraph newspaper published all the county cricket batting and bowling averages. I would spend the summer holidays pouring over the mass of numerical data trying to work out how many a Yorkshire batsman would have to score in his next match to take him to the top of the averages. Often it was Doug Padgett I followed who in the County Championship-winning side of 1959 was the leading batsman with more than 2,000 runs. He usually batted at No 3, though he occasionally opened the innings.
When that had been accomplished I turned to producing a 100×100 multiplication look up. I stuck together many pieces of paper and with 100 rows and 100 columns, filled in each cell with the multiplication product. I worked out very quickly that I only needed to complete everything below the diagonal (think about it!). It had no purpose other than doing it and it was never used for anything.
It was in these early years that I learnt about e, i, ∞and π. I loved the idea that if you head off in a negative direction towards infinity, you end up coming back through positive infinity.
Did you know that if you have a piece of paper with lines across it 50mm apart and if you repeatedly drop a match (less than 50mm long) and count how many times it lands on a line, you can calculate a value off π? I did when I was 9 years old and it was all from a book given to me by my Grandfather.
Maybe you remember learning tables and always getting stuck at the seven times table and never knowing how to multiply such as 3,725 by 11 in your head. (By the way that is very easy. Just add alternate numbers. You can do it in your head. The answer is 40,975. Can you see that?) That never bothered me because I had the principles and patterns in my head as well as the book: The Trachtenberg System of Speed Mathematics.
After the 11+, in the January when I was 10, our ‘maths’ in primary school went off in whacky directions and I learnt, and understood, why sometimes 1+11=100 (alternative bases if you are wondering – binary) and so had a first understanding of computers. We had fun trying to decide on what symbol we would use if we were working on base 12.
What I was taught early or at least learnt early was that numbers are exciting and not the drudgery of learning by rote. I always understood basic principles and I saw numbers as a magic world. When arithmetic finishes and mathematics starts many come a cropper. Moving from numbers to algebra is confusing but not if you understand what is happening behind the scenes. Later you will see that number theory is just another branch of the broad church of mathematics.
I am sure I could make mathematics exciting and show why we slide on ice but not on the road, why we weigh less in space, why we don’t sink when we swim and why we can walk on custard.
I mean, what could be more useful?