Why do we study Matrices?
Because it stretches your thinking skills;
it makes you practise doing arithmetic as a small part of some other task - this is particularly good when negative numbers are included; because nobody else your age will do it;
because it lets you do some things with them that otherwise are well beyond Year 8;
because it lets you see that some things function in a different way to numbers;
and last and least, because DJS invented it when he was your age (but he wasn’t the first inventor).
Principally, we study matrices to make your number work a lot better.
I find it interesting that something we think we have become really quite good at, in this case arrithmetic for Y8 and Y9 pupils, can be moved to a subsidiary position in which the arithmetic equivalent is required to work well so that a related and superior (becasue it fits on top) activity can be followed. When this happens, it is curious how weaknesses in the previous skill are discovered. Many students complained (loud, often) that my teaching was confusing. This is probably true, but the purpose of those techniques was to (try to) cause students to examine how it was they had learned a process and to correct or improve it to the point where these lower level skills became sufficiently robust to be relied upon. Those students who went through this annealing porocess thought my teaching helpful - they became fans. Those who refused to engage, and particlularly those who rejected any suggestion that their thinking might be improved, thought (and probably still think) that I was (am) an idiot. I often said that maths was about thinking and thinking skills. It is often the study of the manipulation of ideas and structures; that requires us to be reliable in the several subprocesses we might wish to use. So I remain convinced that any methods that allow you to test your own results and methods for reliability (so that you might improve upon them) is a good thing.
I found several equivalent situations when playing soldiers. We spent a lot of time learning to be safe in handling a rifle (Skill at Arms was the title). This was tested when the weapon handling was needed to be so thoroughly learned that whatever went on around the cadets would not stop them from being safe with the weapon. For many cadets, this more or less defined ‘fun’, where they meant the huge satisfaction that comes from realising that some things can be learned so well that they can be made into a relaible skill. The Army is very good at this sort of teaching. It is often not so good at the pursuit of understanding, but then much of its clientele is not interested, and one might argue that ‘need to know’ is itself the test for inclusion. At school, this ‘need to know’ can reduce to the perennial ‘is it in the exam’ that to me is so very similar. That is not education but only preparation for a test.
To me proper education encourages a willingness to explore, to find out and to understand. it does not stamp on or stamp out curiosity. Too often the acquisition of skills somehow conflicts with that sense of curiosity. I think there are good reasons for learning as many learning techniques as one can. That includes both those that inspire exploration and self-motivated study and those that cause skills to become so well embedded they are unconscious.
DJS
