I have been thinking about this since the reports that Australia is apparently not training enough mathematicians.
The reports came along with the inevitable "Mathematics and science need to be fun" type remarks. They came with the usual claims that students are losing interest because these subjects are not seen as "exciting", rather they are seen as irrelevant.
It seems that school has to be constantly "exciting". If it is not then the student's interest will not be engaged. The child will not learn. School should not actually be about work. You are there to be entertained and enjoy yourself.
Now, that may be the problem. Work is often repetitious and - let's face it - boring. There may be parts which are exciting but, for the vast majority of the population, work is something you do in order to get paid. If you are lucky payment gets you the other necessities of life and a bit over for a bit of fun. There may be parts you enjoy but there will be other parts you will do because they have to be done.
It is my considered opinion that school should be viewed as the childhood form of work. There should be no expectation that it be constantly exciting or that it should be seen as a form of entertainment. That is not to say that the working environment of a school should be unpleasant, far from it. There are, after all, certain occupational health and safety considerations as well psychological health and safety considerations. Even in the workplace there is room for some entertainment andenjoyment.
But, there is also the need for some hard slog, boring repetition, rote learning. I believe this is possibly one reason we could be failing to encourage a multiplication of mathematicians. Too many students simply do not have the 'number facts' at their finger tips. There is no point in understanding set theory if you cannot add, take, multiply and divide with confidence and without the use of a calculator. Learning number facts is only done with hard slog, boring repetition and by rote learning - however we might try to dress it up with 'games'. If you cannot add 2+5 with confidence then it will come between you and an understanding of a more complex procedure.
Much the same can be said about spelling, punctuation, grammar and vocabulary development. It also may be why we fail to teach well languages other than English. It may be why students have only a superficial and, all too often, inaccurate understanding of so many other issues.
If we want to train a multiplication of mathematicians then we will need to work at the basic number facts - and the basics of everything else.