Saturday, June 07, 2008

Mathematics

How important is mathematics in the rearing of a child? Speaking personally, mathematics shaped me. The son of poor working class parents, living in a basement apartment in a strange town without relatives at a time when six years of world war had impoverished the nation, I was fortunate in having a father who believed in education. He took a second job to pay the £7 a term for me to go to a small private school at the age of 4. I could already read by the age of 2, though my reading matter was the football results in the News of the World. I cannot remember not being able to read and I was doing simple sums by the age of three.

At this little school I felt out of place because everyone else had nicer manners than I did, but I began to learn the acceptable way to speak, to write, to behave. I liked drawing best of all subjects, but I don't think the teacher appreciated my efforts. however, she did appreciate my arithmetic, and I quickly surpassed the other pupils. We learnt our tables by rote and the magic of numbers appealed to me. By the time I was seven I had finished all the textbooks that the school owned.

My father moved me to a state school then. Here the classes were much larger - as many as 48 in a form. Schools were very different then. Our desks were arranged in rows and silence was expected. Chalk and talk was the rule. To be honest, my favourite lessons were football and physical training, but I enjoyed all of the subjects, especially arithmetic. When I was ten I was given a silver pocket watch by the teacher after getting full marks in a mental arithmetic test for three terms. No-one had previously got as many as 95% in one.

These were the days of the 11+. The elite went to grammar schools and the rest to secondary moderns. If you went to a secondary modern you could look forward to life in a factory, (or digging the roads if you weren't clever enough for that). Girls could expect to work in a shop - the really talented aimed at being hairdressers. Grammar School gave you a start in life. In those days you could get to University if your parents were rich enough or if you won a scholarship by dint of hard academic work, but even some of the clever boys never went to University, because their parents expected an income from them. They aimed for an office job with the local council. Girls hardly ever went to University - perhaps half a dozen a year from our sister school for girls (all grammar schools were single sex). Bright girls were more likely to go to teachers' training college, though one woman in 7 went into nursing. Otherwise they could work in a bank or for an insurance company or perhaps in a library.

At the grammar school I was picked on by the maths master because my work was so untidy. He was nonplussed when I came top of the year for maths despite the untidiness. In the third year we had a choice between woodwork and applied maths. I would have preferred woodwork, but the maths master refused to let me go. 'O' levels consisted of exams in Arithmetic, Algebra and Geometry. I took them a year early. My final mark was 86%, much boosted by 100% in arithmetic and dragged down by my untidy geometry. For applied maths my mark was 92%. I did 'A' level maths a year early as well, but although I passed, I did not do as well as I might have. I was doing Chemistry, Physics and Zoology at the same time and found that the Maths teaching was sketchy. Most boys in the sixth form were sons of engineers (who worked at the nearby Royal Aircraft Establishment). They were taking a combined Physics, pure and applied maths course. Only three of us were taking the biology option and of the three only I was taking maths. The school was not really geared up for combination of subjects that I had chosen.

At Medical School, I might as well have never studied maths at all. I might well have improved my manual dexterity with woodwork.

Yesterday, Simon Jenkins in the Guardian seems to think that learning maths is a waste of time. He says:

I studied advanced maths to 16. I loved wandering in its virtual world of trigonometry and logarithms, primes and surds. I breakfasted on quadratic equations, lunched on differential calculus and strolled, arm in arm, with Ronald Searle's square on the hypotenuse.

It was a waste of time. I dedicated my next two years to Latin and Greek, which proved to be more useful (just). Most teenagers clearly feel the same. They must grapple with difficult techniques and concepts which hardly any of them will ever use, assuming they can understand or remember them.


I actually doubt that he studied advanced maths until he was 16. Only mathematical geniuses start advanced maths so young. Nevertheless, he does have a point that few people use the advanced techniques of mathematics.

A lot of what we study at school is about training the mind to think logically. maths does that, though so, in a different way, do Latin and English grammar. There are aspects of maths that are important for living in the modern world. If we are to be engineers then Calculus is very important, but I can't remember ever having used my Calculus in medicine. On the other hand understanding proportion, weighing up risk, estimating size and knowing about probability are essential.

For example it is very important to buy your lottery tickets on a Saturday rather than a Monday. The reason is you have a greater chance of dying during the week running up to the draw than you have of winning the jackpot. Still if you understood how unlikely a 1 in 14 million chance is, you wouldn't be playing the lottery in the first place.

When I first wrote papers that incorporated survival curves, I calculated the points on the graph using quadratic equations and log tables; nowadays I just load the numbers into the computer and press a button. Because a machine can do it quicker and more accurately, we don't bother with the longhand version. It's the same with children and calculators. Unfortunately, it is easy to throw out the baby with the bathwater and as a result so many people in public life are not only innumerate, but proud of it.

4 comments:

Anonymous said...

The teaching of mathematics in the UK does not now appear to be in very good hands :-

http://tinyurl.com/3srzg8

Richard said...

Not all grammar schools were single sex. I was born in 1941 and went to a grammar school which took boys and girls in about equal numbers. The only time girls and boys were segregated was for gymnastics and for domestic science/woodwork (girls/boys). If you were academically gifted you were expected to try to get a place in university regardless of gender or family background.

Grammar Schools were great institutions for working class children. I was probably one of the poorest in the class. I had to use a small old suitcase for my books as my parents could not afford a leather satchel, as used by the other children. My parents did however realize the value of a good education.

Some of my friends passed the 11 plus but their parents would not allow them to attend grammar school because of the extra cost of uniforms etc. and the delayed entry into the workforce.

I was fortunate to be gifted academically and at that time it was possible to get a State Scholarship. It paid all my university expenses. My old grammar school even gave me a book grant which amounted to about 10% of the State Scholarship.

I am pleased to say that my old school is still alive and doing well:-

http://www.heckgrammar.kirklees.sch.uk/

Barry Lambert said...

Terry, I am three year older than you, although you gained one year because of your academic aptitude. And although my parents considered themselves middle class, that was a matter of attitude and a white collar and not of income (in fact my father, in a low paying white collar job got less than a skilled member of the working class).

Anyone who could get 5 “O levels” and a couple of “A levels” could go to university. Admittedly I did not have to leave home to do so, but a maximum government grant, based on a means test, was adequate to pay my way through. And the grant would have been higher had I had to leave home to go to university.

Mathematics? Well we studied to a level in the 12th form that was not reached until 1st year university in Canada and, I suspect, the US. Three years of engineering maths almost defeated me and, in those days, no civil engineer needed the level we were supposed to learn. For electricals, may be. Anyway I hardly ever used any really advanced maths, and that was long before the days of desk top computers or even programmable calculators. The trusty old slide rule was all I ever needed plus log and trig tables if things really needed to be precise. The general rule was “three significant figures”, and my first boss scoffed at a colleague who had a cylindrical slide rule that was supposed to be more precise.

Ah, those were the days, my friend.

Terry Hamblin said...

My younger son did 'A' level Maths and got a grade A. He went to Oxford Brookes University to study automotive engineering and is now a Formular One race engineer (in Montreal this weekend). He does use ho advanced maths and both at Oxford Brookes and in his firm is the expert on stress mechanics. People on the factory floor still use slide rules, but few others do. Calculators and computers have surpassed them. The fun part of log tables was knowing why they worked.

There certainly were some co-educational grammar schools, though these were a minority. When I was at University there were very few working class girls (perhaps because Bristol was where the posh Oxbridge rejects went).

If you got a University place you were automatically awarded a means-tested County Major Scholarship (maximun £300 a year) and had your fees paid. The brightest could take an extra exam ('S' level) and those with the highest grades got a State Scholarship, which was worth an extra £40 a year.

Anonymous - don't believe everything you read in the Daily Mail, and the University of Plymouth would be a bit like the University of Broken Springs in America.