One of the most amazing things I have ever done happened a few months ago. It started a chain of events that leaves me speaking at a meeting to be attended by a number of people in the upper echelons of government. The trouble for me is one of those people is my ultimate boss. If she does not like what I am saying, then I could be looking for work in the near future. If she likes what I am saying, then I doubt my position will change at all. So what did I do? I answered a question.
I had a conversation with a friend in which I was lamenting the lack of real maths understanding my students actually have. His comment was “Why do we even teach maths? The kids hate it, it so why bother?” My first thought was “shock, horror”! Someone questioning the teaching of maths? What kind of treachery was this?
I stumbled out the standard response, “It teaches kids how to take a problem and break it down into its components and develop a solution.” While I was saying that, I realised just how thin that sounded, fatuous tripe actually, it does no such thing. Thinking about it later I developed the question of “Why do we teach Maths?”
Doing a bit of research I discovered that in the Classical model of education a person, man usually very few women, usually wealthy or of “good family” would be considered “educated” if they could sprout, in Latin and Classical Greek, parts of Virgil, Cicero, et al, plus any number of Greek philosophers. They would also know basic arithmetic, and if they were good enough, some advanced maths, Euclid, Ptolemy and science concepts that had not really changed much on the previous 2000 years.
Compulsory schooling started in Northern Europe in the 1740s, and it slowly spread to other countries. The Industrial Revolution began in Britain about 1750 where it was realised that there was a need for a better educated workforce than was required before. To meet that need, the British took the incredibly radical step of introducing a universal and compulsory education program. Unbelievably, it was publicly funded, so at low cost to the families. Amazingly, it was socially egalitarian and even included girls. What they initially taught was English, Latin, Classical Greek, some science and some arithmetic.
Essentially, this new education model was a carbon copy of the Classical Model of education, and spread through the Dominions. The Australian colonies were supposed to set aside land, 200 acres (about 85 hectares), for the upkeep of a teacher in every township but this did not happen. In 1848, the colony of New South Wales introduced compulsory education and the other colonies followed suit.
Changes occurred, schools would teach from what skill base they had and new subjects were introduced, others dropped, but really, it is the same thing now. Latin, Classical Greek were replaced by French, German, (which were replaced with Asian languages here). We have more advanced maths topics, greatly expanded science topics, and more social sciences have been introduced to meet a changing need. But it is largely the same ideas driving an industrial age education model.
To make my point here, there is actually no discernible reason as to why we do teach maths. It is what we have always done, and we seem to be content to always do.
I then looked at the question from another view. “Why do we teach Maths?” I found this was actually quite simple, but I have not found it stated anywhere. I cannot say it is not stated, just I have not found it. My logic was that we, as a society, require our citizenry to have a better understanding of maths than we have ever required before. We use it to handle a range of personal finance details, from mortgages to gifts, home handyman stuff, and a host of other applications. So we teach Maths.
I thought that the question needed a better explanation than that, so I asked “Why do we teach Maths?” I found there is even less justification for teaching Maths, than there was for anything else. What I found was that Plato, yes that Plato, wrote in The Republic, Book VII, something like, if you are good at maths you can be good at everything else. If you are not good at maths, you have a problem, but if you improve in maths, you can get better at everything else. Well, I am afraid that 2,500 years of accumulated evidence does not really support this idea. If you are good in History then you can be good in other things – but really suck in Maths. Entire University programs are built on an aversion to maths.
I would go so far as to say that teaching Maths is more than likely a waste of precious student time. We would be better teaching students Home Economics, where they use weights and measures, lengths for materials and personal money matters. In History they need graphs, statistics, tables, date maths and national and international money matters. Geography requires statistical analysis, charting, and a range of other mathematical skills including time and date math, international economies and other maths understandings. Woodwork, Metalwork, Design of any type, requires linear measurement, area, volume, weights and other measures. Then there is Science. Algebra is the arithmetic of Science. Physics uses so many formula, chemistry, ecology and every other-ology, requires extensive maths skills. Every subject has a large, mostly ignored and undeveloped, maths component in secondary schools. I do recall looking at tabular data in some of my University subjects, but it was assumed that I knew what tables were, and how to use them.
What we teach is Maths, but it has little or no context. As it has no context for students, they cannot always grasp it so readily. It is, more or less, an abstract topic – and that, I suggest, is why so many students find maths so hard. In the Australian Secondary School system, we have students who range in age from 11, starting in Year 7, to 18, ending in Year 12. When they start high school they usually cannot think in abstract ways. Abstract Maths concepts are hard to picture, but we pound it into them. It is worse now – computers have removed the need to remember formula, or calculators no longer require students to do a lot of mental arithmetic. That is why schools are having so many issues with Maths and numeracy in this country. The combination of the abstract and our use of digital technologies have, virtually, wrecked what we used to call numeracy.
Most students do not need much in the way of maths, so why do we insist on force feeding them with it? In one TedEx talk, the speaker, John Bennett, relates the story of his contacts with former students. He found the only people still using the maths he taught were teachers. One school in WA produces a disproportionately high number of pilots. True, they are a specialist school in aviation, but, I suspect their success is enhanced by the placing of maths into an aviation context.
Students who do show an aptitude for maths should be encouraged to continue, but as a specialist subject, not as a compulsory subject. My bet would be that this would prove a far more successful strategy than what we do now.
P.S. As someone said recently when we were discussing this idea of teaching Maths as part of another subject… “Good luck with that one, buddy!” It seems either I am way ahead of my time, or the idea of such a change is so threatening that it will never happen. Oh well, I think I would rather be burnt at the stake as a heretic than placed in stocks as a fool.
End note: I gave that talk, it turned out to be a very interesting meeting. A range of topics were discussed but I got the distinct impression that there was too much emphasis on end results and outcomes, not on the educative process. I put my points across and was politely listened to, but I doubt I was heard at all. So nothing will change.
I taught Math as both a soccer and american football coach. Players might groan from time to time, but they played better at their sport AND did better in class 😉
What kind of Math did you teach, in the context of sport or as a set of abstract concepts?
And this might be of interest:
Maths allow us to model the world, whether its Euler’s Line or quadratics. I was out for a walk with a student. He asked me, What do Maths have to do with anything?” And then he picked up a stone and taking aim into the sky threw it into a pond. I watched the ripples reach the shore and laughed. What does gravity, waves and getting in to college all have in common? They can all be managed through Maths….
Let me put it another way…. the thrust of most of our global development over the past three hundred years has been based on the concept that our universe operates on the basis of certain Natural Laws, that is is essentially a clockwork of incredible complexity. Our science and philosophy have both sought to leverage this understanding, to amazing and sometimes frightening ends. John Bennetts’ friend was a narrow minded fool…… and while I disagree with Plato on, well most anything, he was correct here — when you have mastered tools that provide an abstraction that affords a view at everything, you get better at everything. Yes, there plausible objections to carrying things “too far” (Magister Ludi is a favorite read of mine) but we are nowheres near that level of abstraction. We are dealing with poor pedagogy, poorly trained teachers, and lots of lazy students 😉 although the Piagetians argues that since MOST humans will nver reach the stage of formal operations necessary to manage Algebra we should cease to expect humans to be able to manage same, which in my mind suggests that we really need to put more people back to work hand-farming potatoes. As someone who can do Algebra (and therefore under that analysis has arrived at formal operations), does it bother me little to put the mass of humanity back on the soil tilling it for subsistence (as Plato would arguably recommend?) I guess so, though I would be obliged by the greater access to fresh food 😉
Yes, I wouldn’t disagree with anything you say here, but what you are describing is more or less the complacency that both presaged and accompanied the collapse of the Roman Empire. I think it is obvious the West is in a great deal of trouble, and nothing done so far is changing that. It could be argued that Milton Friedmann and his acolytes have hastened the end result as much as, if not more than, Steve Jobs.
What I am suggesting is that if we require our citizens to have a good understanding of Maths, then it needs be presented in a context that the majority can grasp, not as an abstract concept that students cannot apply because they just do not have the intellectual skills.to make the necessary connections between them.
BTW, I am becoming increasingly convinced that we have misused the main thrusts of Piaget and Vygotsky as justifications for reducing children’s freedom and intellectual development, not improve it.