topics: |  math | puzzle

http://gfoh.blogspot.com/2007/05/w-w-sawyer-man-before-his-time.html:

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.)

CONTENTS

PART 1: 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

PART 2: 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.