Mathematics – are we on the right track?Posted: February 23, 2014
David Pavett writes
There was an interesting piece in the Guardian by Simon Jenkins a few days ago (For Britain’s pupils, maths is even more pointless than Latin). I don’t agree with all his conclusions but the issues he raised deserve discussion. What should be taught in mathematics classes? It is rare for this subject to be raised. In fact in general too little of the time we spend debating education is devoted to the question of its content.
It is not that I want to avoid discussion of the organisation of our school system with that most evasive of slogans “standards not structures” (as if the two could be separated) even in its distilled form according to which it is teacher quality that makes or breaks the quality of education independently of the framework within which teachers ply their trade. All that is specious nonsense which we must continue to challenge.
But that still leaves the vast question of content to be debated.
I taught maths or maths related subjects (e.g. physics) for more than 30 years. During all that time I had the feeling that there was something wrong with what I was doing but I could never quite work out what it was. Over the last few years of retirement I have helped several adults and teenagers trying to come to terms with basic maths. In each case there was clearly an enormous psychological barrier to the subject. When faced with a simple mathematical task tears would sometimes well up. For millions the result of ten years of school mathematics is maths phobia. There has to be something wrong with a system with such an outcome.
Everyone agrees that we need basic arithmetic (although we might disagree about what that entails). That many leave school without even attaining this is clearly a problem. This failure provides a clue to broader issues of maths education. Why do so many people forget nearly everything they encountered in school maths? Learning without understanding, cramming for tests, leads to short-term memory. Things are forgotten as quickly as they are learned. For many (most?) this the story of maths education. The fact is though that taking an interest in the social and political events around is strongly aided by knowledge of maths. For example, we are bombarded with data by politicians which we need to know how to evaluate.
We encounter numbers and mathematical relationships everyday of our lives but most people have learned to switch off when that happens. After a while they don’t even realise that they are doing it. We deal with risk assessments, rates of change, compound interest, ratios, fractions, percentages and much else besides. Simon Jenkins says that all we need is basic arithmetic. Those who agree might reflect how many things they decide not to read/follow just because it involves a little algebra or more than a one-line calculation. How many pathways of knowledge are thereby closed down?
Maths in general education should:
1. be about developing a sufficient feel for the subject to be able to tackle the mathematical issues that can arise in the course of life and in the course of taking an intelligent general interest in the social affairs and the technology that one is likely to interact with (why is a kilobyte = 1024 bytes?). That’s a big ask but in my view a reasonable one. The emphasis here is on “being able to tackle” i.e. being able to work things out on some basic principles rather than simply applying given formulas received as a piece of magic. (Why does the breaking distance of a car double when its speed is increased from 25 mph to 35 mph?)
2. produce an understanding of mathematics as a creative field of human endeavour and not just a vast block of knowledge of which one learns the easy bits without having any awareness of the challenges faced by the subject in the past and the challenges faced today. For example, should pupils not be aware that calculators and computers do not merely do calculations faster than we can but that they are the only sensible way to tackle some problems. Even some very simple equations cannot be solved analytically but are easy to solve with an iterative solution using a calculator (e.g. x = cos x with x in radians). The behaviour of some equations is truly weird. This links with problems of weather prediction. Maths has mystery. This is excluded from syllabuses which seek only to inculcate simple calculating ability.
A perennial problem in education is that the desire to make things as simple as possible can result in educational material that is, frankly, unchallenging (i.e. boring). This natural problem is exacerbated a 100-fold by an education system in thrall to testing mania and competition by league tables. These encourage teaching to the test and syllabuses that can be reduced to mechanical check lists.
Simon Jenkins suggests that politicians are obsessed with maths and science and our national standing in these areas as reflected by PISA tests. He says that part of the reason is that maths is easily testable (things are right or wrong) unlike the rather more “slippery” humanities. I think that he is right about the obsessions but wrong about the nature of mathematics. If maths were taught as a creative, open-ended subject it would become less dogmatic and would, as it should, be an exercise in understanding and imagination. The flip side is that assessing it would become more “slippery” but that is a price to be paid for making its content reflect the true nature of the subject. We all need maths but it should be real maths and not a desiccated selection from it taught as dogma. The time for a fundamental rethink about mathematics education is long overdue.