The Minister in the United Kingdom government responsible for education recently announced that all children should know their multiplication tables by the age of 9. As with any statement by a politician, this is obviously more wishful thinking than a command. However, it did wake up a few ideas in me. What happens to children who cannot learn their tables? How do they feel about not succeeding? What experience does this minister, or others who set educational goals, have of the real world of schools and their pupils? What is so special about the age of nine? What is so special about multiplication tables? I knew my tables when I was nine, but that was over 60 years ago, and I later went on to get a mathematics degree. Has the world changed since then?
When I think back to my three years as an undergraduate, I have memories of sitting for hours in lecture theatres, failing to understand a word of what was going on. That cannot be a true remembrance or the University of Bristol would not have given me a degree, but it has left me with sympathy for school children who fail to grasp basic ideas of mathematics – or anything else. Because progress in mathematics is easy to assess, so is a pupil’s success – and failure. Set a tables test of 20 questions. Well done, those who get 19 or 20 correct, but how do children feel if they score 5 or 6 or 7? There is a saying in the UK: “nothing succeeds like success,” but I have not heard one which says “nothing depresses like failure” – something which is equally true in my opinion.
There are children who have great difficulty in learning things which do not interest them. After several years of 5 out of 20 in tables tests, their toes must curl at the thought of repeating their failure time and time again. No wonder many children hate school, and mathematics in particular. Such children, of course, do not go on to become Ministers of the Crown, nor do they sit on “important” committees.
Although I have retired from teaching, I still work as a volunteer in my local school, helping in mathematics classes for 9, 10 and 11 year olds. The school is very good with an overwhelming proportion of hard-working children. I have helped five teachers, all of whom are as good as you could get for this age range. The internet is “on tap,” and lessons, exercises and games in mathematics can be downloaded and projected on to the whiteboard. Even under these favourable circumstances there are still children who cannot rattle off their tables.
When I first started teaching 50 years ago, I taught “Old Math.” Euclidian Geometry had been around for 2300 years; logarithms (if you’re under 45 you may not know that they were used for doing difficult calculations!) had been around for almost 400 years, and a good facility in arithmetic was necessary because there was no alternative.
Things changed after October 1957 when the Russians were first to put a man in space. The story goes that the content of mathematics in USA schools changed within 2 years to New Math. Whether or not this story is true, schools’ mathematics did change in countries around the world. In the UK, the changes were far reaching, but by the end of the 20th century, the pendulum had swung back some way towards the older content and a balanced curriculum.
However, thanks to the wide use of electronic calculators, logarithms are no longer needed for difficult calculations, and Euclid’s geometry has finally vanished; we are now allowed to acknowledge the existence of symmetry! Algebra, by that I mean arithmetic algebra, remains important.
So, events and inventions – sputniks, calculators, computers – have led to changes in the content of schools’ mathematics, but children are still expected to learn their multiplication tables by the age of 9, just as I did 60 years ago.
If we really do want our children to learn their tables, we must abandon a 9-years-of-age finishing post and motivate them. If you watch a darts match, you will see complicated arithmetic dispatched in the blink of an eye because it is important to the game. What we need is a similar game for youngsters which depends on their ability to multiply.