The Carol Vorderman review of mathematics

Today Carol Vorderman’s review of maths for the Conservative Party is unveiled and I was invited to talk about it on BBC Radio Leeds (I’ll give a link when one appears, UPDATE: For one week from today see here from 1:18:15). The report is hard to find on the web so I was only going on the rumoured recommendations. [Update: it’s here. The report was actually mainly written by Roger Porkess rather than Carol Vorderman.]

The main points are
1. Maths should be compulsory until the age of 18.
2. There should be a two types of GCSE.

The first of these is not going to help the standing of maths with the general public, is it? Maths is not the most popular of subjects and forcing people to do this until 18 is not going to help. However, that is a rather small point. The real killer of this proposal can be summed up in the question “Where are we going to find the teachers?”. The country has an acute shortage of maths teachers already; enacting this proposal will only make it worse. It will force teachers to be spread more thinly leading to poorer learning. So I can’t see it going ahead, at least for a number of years. The secretary of state for education, Michael Gove, has said he would like the majority of students to be doing maths up to the age of 18. This may turn out to be like Tony Blair’s 50% of young people going to university, i.e., end up being “more of an aspiration”. [UPDATE: See section 9.3 of the report. This problem is not really dealt with in my opinion.]

The second proposal, two types of GCSE, is something we have got already with the intermediate and higher versions. What is proposed here is that there will be a different curriculum, probably arithmetic, rather than an easier exam in which the best you can do is get a C as with the intermediate GCSE. So it is a bit like the difference between English Language and English Literature. Again we have the problem of where are we going to find the extra teachers? In this case of course we won’t need as many as the pupils are already being taught maths. So this is more likely to happen.

What would I have recommended? Well, I’ve said at different times that students should do more problem solving. Currently, we teach our students the methods of solution of very specific mathematical problems. I can perhaps explain our current system of maths education by an analogy with training car mechanics. Imagine we had a system where we teach our trainee mechanics by saying if the fuel pump is broken, then this is how you replace the fuel pump; if the timing belt needs adjusting, then this is how you adjust it. We then set an exam where we say, here’s a car with a broken fuel pump, now fix it, etc. We could produce mechanics who were brilliant at passing exams but are completely useless at fixing cars. Why? Because when someone comes with a car, they say “It’s making funny noises”, “It doesn’t accelerate properly”. The mechanic would be at a loss unless someone came in and said, “My fuel pump’s broken”. Yet this is exactly what we have done with maths teaching. Students can give answers to well-defined specific problems. But give them a problem that involves thinking or more than a step or two and they are at a loss.

Another suggestion would be to teach grammar as it helps students learn that words have meanings and it helps logical thinking. This idea is explained more in a talk by Franco Vivaldi which will be available soon on a DVD I am finishing. More information in a few weeks.

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