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
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.