I can do mathematics of the most exquisite kind. I can run up stairs. Now that is applied maths of the highest order, especially when the stairs are, as they usually are, too close together for one step at a time to be comfortable, and yet too far apart to maintain a constant two at a time gait. My brain can calculate things very well in some ways but it is less good at processing sums using words.
Is it right to put mathematically gifted people in charge of teaching mathematics to those for whom it does not come naturally? I suspect this is the surest possible way to ensure the deepening divide between the mathematically capable and those who scorn the subject out of frustration. I cannot do mathematics well but I admire those that can and I envy them, too many people who have talents in other areas but cannot handle mathematics with ease tend to despise and put down those with mathematical ability. If I can't do it then it isn't worth doing, seems to be the attitude. That attitude may be excusable when considering things like touching your nose with your tongue or blowing cigarette smoke out of your ears but it is very unhelpful for something as important as numeracy.
Teaching Mathematics: a natural approach?
I have many images in my head of unhelpful hectoring teachers telling me that this stuff was easy so I should not be making such a meal out of it. Would it have been a better idea to train teachers who had difficulty in mathematics themselves to become mathematics teachers? It is a strange idea, but think about it, imagine trying to teach somebody how to take a dump or how to walk.
I can teach people how to use a computer quite easily because it was something that I had to pick up in stages and I can remember going through many of those stages. In contrast I would find it rather difficult and frustrating to teach somebody how not to wet the bed because it is something I can do with little effort and I have forgotten how I mastered the skill myself.
Just think about it for a few moments. Who is going to make a better swimming teacher for beginners: Amanda, who learned to swim before she could walk and was in training for the Olympics at the age of nine, or Brian, who is a qualified teacher, who learned how to swim three years ago at the age of twenty five and has since worked on his strokes to the point where he can nearly catch Amanda, if she gives him a three second head start?
If you do it naturally you cannot empathize with those that do not have that natural ability. There is no shortage of intelligent people with natural ability to teach but who have difficulty with numbers. Put them on intensive courses and make them into mathematics teachers who can help the enormous number of people who find mathematics difficult. This is in complete contrast to the current situation, which is totally bizarre, which involves taking naturally gifted mathematicians and making them happy to teach (for relatively low pay) morons they have no empathy with how to do something that they find to be as natural as breathing. Is it any wonder that so many mathematics teachers hate their job and their pupils hate their lessons and their teachers?