Home educating the bleak, joyless and utilitarian way
I have noticed that many home educators, as well as those who write books about home education and set up as experts on the subject, view education in a strictly utilitarian fashion; that is to say in terms of what a child will need in day to day life. Mathematics should be about weighing the ingredients for a cake or calculating the change when shopping, history should be about their family tree, geography; the streets around the child’s home. It puts one in mind of the Victorian industrial schools, whose only aim was to provide children with a rudimentary education, sufficient to fit them out for their station in life, which was usually a pretty lowly one.
On one of the larger home education lists, discussion has been taking place which sums up this awful attitude, a frame of mind practically guaranteed to stunt a child’s intellectual development. The subject is ‘higher maths’, by which those contributing to the debate evidently mean anything at all above the most common arithmetic. Here is one of the more influential figures in British home education, expressing his views on the subject:
As to higher maths, yes a handful of people do need this stuff but do we
really need to make so many kids lives a misery forcing them to learn so
much stuff that they have neither the interest or aptitude and which even if
the schools do manage to drill it into them they will instantly forget?
simple geometry, even the stats I've needed for research is easily covered
by the more basic stuff done at GCSE. I've never quite followed why kids are supposed to need the rest of it.
Notice that key word, ‘need’. Why would you teach a child about the wonders of mathematics, the beauty of sonnets and so on unless the kid actually ‘needed’ it. As I say, a utilitarian approach to education which would have delighted Mr Gradgrind from Hard Times! Others go on to speculate that it is all a dodge by the schools, either to ‘stratify’ the children or to keep them occupied at school. The idea that any mathematics beyond basic arithmetic could be exciting for a child is absolutely impossible for these people to appreciate. This means that their children will probably never learn about the Fibonacci Sequence, which shows the arrangement of leaves on a plant stem, the generations of breeding rabbits and many other features of the natural world. They will never wonder at the idea of imaginary numbers; i, the square root of -1. Nor presumably will they be introducing their children to the marvellous realm of calculus. None of this is ’needed’ and so may be dispensed with. They make them learn this boring stuff at school, why should we do it at home?
It is not, as regular readers will know, my habit to be rude about other people, especially home educators, but these people really deserve to be tied to stakes and pelted with stinking offal and old vegetables. Their idiocy is not only blighting their own lives, but also harming those of their children.
Let me tell a couple of anecdotes about my daughter’s education and how mathematics formed an important part of it. When I taught her to calculate the area of a square by multiplying the sides, she asked me how you could work out the area of a circle, since it didn’t have any sides. There were two ways to proceed. If I had adopted the view of those who want the teaching of mathematics to stop at the simple level and to avoid higher mathematics, then I could have given her the formula for the area of a circle and left it at that. Why on earth would I have done that? It would have been meaningless and dry. Instead, I got her to draw a large circle on a sheet of paper and then cut it out. I then told her to cut the circle into long, narrow strips. Kids of eight always like things like this which involve using their mother’s razor sharp kitchen scissors, which were normally a forbidden item.
We then took the narrow strips of the circle, cut them all in half and arranged them in a rectangle. Then we measured the sides of it and multiplied them, to give the area of the original circle. This intrigued her and led to a long discussion in which she correctly suggested that the narrower the strips had been, the more accurate would be the area that we worked out in this way. Oh, look! An eight year-old child has, with a little guidance, come up with the idea of calculus! Other experiments consisted of measuring the volume of a curved vase by filling it with marbles and then filling it with sand. Obviously, if you used infinitely small grains, you could produce an accurate measurement of the volume. All these enjoyable activities laid the grounds for her later learning of calculus. Of course, she didn’t ’need’ to know about calculus at eight, but the experiments had started her interest. I bought her the relevant Murderous Maths book and she soon knew more about the matter than I did myself. At twelve, I bought her a book on calculus and she taught herself the whole thing.
Here is another example. When I explained to her about right angle triangles, she found the topic boring. What possible use was all this stuff? We made a gadget out of a ruler and protractor which enabled us to measure angles of inclination. I then offered to help her measure the height of a tall tree near our home. She was incredulous. We simply measured the length of the shadow by pacing, found the angle from the end of the shadow to the top of the tree, used Pythagoras and Bob’s your uncle. Of course, She has never ’needed’ to do this, but it certainly gave her an insight into mathematics and was also a lot of fun.
There is no doubt that it is possible to make any subject boring for children, whether it is higher mathematics or history. What many home educators seem to say is something along the lines of, ’I was bored at school by this subject and so I shall avoid doing it with my child.’ They might instead say, ’I was bored by this subject at school and so I shall work out new and exciting ways to make it interesting and enjoyable for my own child.’