My fruit and vegetable shop assistant left school many years ago and
calculates all bills quite efficiently by using addition only. She
reads from the balance the price of whatever mass is there, sometimes
adding two figures to get the total for the item, and then adds one
at a time all the items bought. So the paper on which she writes has
things like:
| 3,50 +2,75 = 6.25 +4,20 = 10,45 + 18,36 = 28,81 +¼, |
I then realised why we have to teach and learn Mathematics! Of course, 365 ×2 = 2 ×365 would have helped her a lot (365 +365) as would the process of multiplication itself. We take these (and other) ideas for granted if we know them. Without them life is certainly harder than the effort needed to learn them.
A five year old girl was showing off her mastery of simple subtraction by answering questions like, ``There are 10 socks in my drawer. I take out 3. How many are left?" The answers came back fast and her mother tried 20 socks in the drawer and taking away numbers both smaller and larger than 10. Again the answers came rapidly. Her mother was getting a bit bored and decided to finish the game: ``I have 10 socks in the drawer and I take out 11. How many are left?" This time there was a pause, and then, ``Zero one". This was not the ``Impossible!!" answer that the mother hoped would end the game, so she asked, ``How come ?". ``Well, you see, when you go back 11 from 10 on the number line you come to zero and then you still have to go another one where there is nothing. So I called that zero one". This five year old had grasped the idea of a negative number without being taught anything more than the numberline.
Perhaps if we played more such games with the young and we listen to their answers carefully we could help them to make such discoveries, so that there are fewer and fewer adults in the unfortunate position of the shop assistant.
I am glad to be a Maths teacher!
Richard Knottenbelt teaches at Victoria High, Masvingo