Saturday, May 19, 2007

W W Sawyer - a man before his time?

One book that we own is really special to my husband and it has played a large part in his accepting the unschooling approach. It is Mathematician's Delight, originally published in 1943. The copy we have was printed in 1950 and is worth ten times its weight in gold. It explains mathematical operations in such a way that one can actually understand the logic behind them. For instance, I never realised that multiplication of fractions actually meant a fraction of a fraction - e.g. two fifths times three quarters is the same as two fifths of three quarters.

The author, W W Sawyer was a math teacher in England who realised very early on in his career that ". . . education consists in co-operating with what is already inside a child's mind". He recounted a couple of incidents early in his career, which were eye-openers for him:

I knew I should be doing something different, but I did not know what. The boys said they were interested in aeroplanes. It was only afterwards that I realised what opportunities I had missed, and how, beginning with this general interest. . . I could have led the class into various parts of mathematics.
In a class I was taking there was one boy who was much older than the rest. He clearly had no motive to work. I told him that, if he could produce for me, accurately to scale, drawings of the pieces of wood required to make a desk like the one he was sitting at, I would try to persuade the Headmaster to let him do woodwork during the mathematics hours - in the course of which, no doubt, he would learn something about measurement and numbers. Next day, he turned up with this task completed to perfection. This I have often found with pupils; it is not so much that they cannot do the work, as that they see no purpose in it. (A European Education.)

The book is divided into chapters as follows:

The approach to Mathematics
1. The Dread of Mathematics
2. Geometry - The Science of Furniture and Walls
3. The Nature of Reasoning
4. The Strategy and Tactics of Study


On Certain Parts of Mathematics
5. Arithmetic
6. How to Forget the Multiplication Table
7. Algebra - the Shorthand of Mathematics
8. Ways of Growing
9. Graphs, or Thinking in Pictures
10. Differential Calculus - the Study of Speed
11. From Speed to Curves
12. Other Problems of Calculus
13. Trigonometry, or How to Make Tunnels and Maps
14. On Backgrounds
15. The Square Root of Minus One

One of my favourite passages in the book is this one:

Nearly every subject has a shadow, or imitation. It would, I suppose, be quite possible to teach a deaf and dumb child to play the piano. When it played a wrong note, it would see the frown of its teacher, and try again. But it would obbviously have no idea of what it was doing, or why anyone should devote hours to such an extraordinary exercise. It would have learnt an imitation of music. and it would fear the piano exactly as most students fear what is supposed to be mathematics.

What is true of music is also true of other subjects. One can learn imitation history - kings and dates, but not the slightest idea of the motives behind it all; imitation literature - stacks of notes on Shakespeare's phrases, and a complete destruction of the power to enjoy Shakespeare.
To master anything - from football to relativity - requires effort. But it does not require unpleasant effort, drudgery. The main task of any teacher is to make a subject interesting. If a child left school at ten, knowing nothing of detailed information, but knowing the pleasure that comes from agreeable music, from reading, from making things, from finding things out, it would be better off than a man who left university at twenty-two, full of facts but without any desire to enquire further into such dry domains.


Geeta said...

Dear Scatty,
We too are Sawyer lovers from India. In fact, Sawyer is our "Guru". I was amazed to see that the paragraph you have quoted as your favourite is also a favourite of mine and I have shared it with thousands of teachers for whom I have conducted workshops over last 10 years. We are setting up a Sawyer memorial in Pune. If you are interested to know more about it, I will send you a letter about the same written by the founder of our organization Dr. Vivek Monteiro. Thanks for sharing this.

scatty said...

Dear Geeta,

If you send me the letter, I will publish it on my blog, if I can copy and paste it. This quote from Sawyer says everything about why our children are unschooled. I get a lot of flak from relatives etc, who can't understand why I just encourage my children to do those things that Sawyer describes (my son, in learning guitar in the last while has discovered the pleasure of agreeable music, whereas my daughter spends a lot of time doing scrapbooking and cardmaking and both of them love reading. My two younger ones (now 6 and 8) will sit for hours and play with lego and knex (and gameboys too) rather than practising writing or sums. I see my youngest child developing an interest in maths way beyond what I had at his age (even though I don't "teach" him any of it) and know that if he maintains a love of it, his aptitude could lead him in this direction when he is older. Then again, maybe it won't, but I hope that whatever path he chooses it will be out of passion and enjoyment.

Although my blog is actually about the home education situation in Germany, a lot of the people who come to my blog come here because of this very post.

Sue VanHattum said...

Thanks for posting about this book. I bought it, read and loved it, and blogged about Sawyer's treatment of logarithms. (Here.)

I knew I'd love it, because his book Vision in Elementary Mathematics was also great.

Mark said...

The following website might be of interest!

Best Wishes


Mark Alder said...

I knew WW Sawyer after he had retired to Cambridge and I visited him twice.

My main aim was to put as many of his articles on my website as possible and I have kept this going for many years. Now the people in India have emerged and I very much look forward to what they will achieve.

You can see Sawyer’s articles using the following link.

I hope this is of interest.

Best Wishes

Mark Alder