Understanding Symbols In Mathematics

Press, Volume CVI, Issue 31226, 25 November 1966, Page 18

Understanding Symbols In Mathematics

“The whole point about a symbol is that the bloke who invented it knows it best. We tend to copy the symbol without always understanding it. We tend to shove these concepts into children too fast,” said Mr J. Dugdale, who is retiring as senior lecturer in mathematics in the secondary department of the Christchurch Teachers’ College. “In everyday life we use symbols only when we are sick of writing something in full—we have used 'it many times to get sick of it and we understand the advantage of the symbol. So it should be in mathematics,” said Mr Dugdale. “Teaching the pupil the symbol before he has anything to symbolise is the cause of a lot of our trouble.”

Mr Dugdale said the average pupil and the below-aver-age pupil therefore needed a lot of attention in mathematics. The extreme shortage of mathematics teachers often led to the unfortunate situation of lower classes being taught by teachers who were not specialists in mathematics. This, in turn, led to some antipathy for mathematics which was hard to live down. “You therefore have first to sell the subject,” said Mr Dugdale. “The interesting new approaches to mathematics have a good chance of overcoming this because the aim to encourage the child to take his part in mathematical discovery." Mr Dugdale said it was important to note the term “new approach” as opposed to new mathematics. Old truths had still to be taught, maybe in a new way. Mathematics was as old as anything else in our culture.

“The sort of mathematical education I would like to see would be heavily slanted towards the history of mathematics and the properties of

number." said Mr Dugdale. “This was the training of ancient philosophers and mathematics formerly was often allied to classics. “There is no real cleavage between the so-called sciences and so-called humanities." said Mr Dugdale. “Any separation is a consequence of modern specialisation which, in some respects, is to be deplored." Mr Dugdale, who will retire in Christchurch, was educated at the Timaru Boys’ High School and took B.A. and B.Sc. degrees at Canterbury University College. He then taught at Te Aute College, Wellington College, the Christchurch Technical College, and the Christchurch Boys’ High School before joining the Teachers’ College staff in 1959.