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# 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.

Hi Kevin,

I found a video clip of Franco Vivaldi talking a little about writing, thinking logically and mathematics on a Queen Mary website of some sort or another. I’m really keen to know more about it because I want to study mathematics at university but I find that the A level pedagogy sort of spoils it for me. It’s exactly how you’ve described it (using your mechanics analogy).

I’ve got some second hand A level maths books and an A level syllabus but I’m finding hard to get critically engaged with the material. Are there any strategies that I can use to develop my rudimentary understanding?

Cheers

Ivor

Dear Ivor,

That’s a tough one to answer as I don’t know how you study (which could be the problem). If you are studying by yourself, then you may like to try to focus on one part of the syllabus. Learn one part well rather than all parts poorly. Don’t try to learn the whole, become an expert in some part of it. Become the person that can differentiate and integrate anything at any time, any place and knows why all the rules work or the person who can answer the tough questions in mechanics. That approach can kick start your interest in the syllabus and lead you to learn the rest. It’s a good ploy as approaching a large task can be dispiriting but learning a small part – well anyone can do that. It’s only small, right?

Dear Kevin,

thanks for the advice! That makes it a lot easier to tackle. As to your point about how I study, well, to be honest I don’t really know how. I haven’t been at school for a long time and even then, I was only ever average academically, just working enough to stay out of trouble. Then a friend lent me A Mathematician’s Lament by Paul Lockhart and I immediately understood what I’d been missing. So I got some A level maths books from a local second hand book shop and a syllabus. I’ve never really studied so what sort of skills do I need? Are there any that are particularly important to mathematics?

Ivor

The main skill is perseverance. You need to work at it regularly and that requires perseverance. If you are studying by yourself, then you don’t have a teacher hounding you for homework and that is one of the best services a teacher provides.

If you are interested in study skills, then see http://calnewport.com/blog/. For mathematical skills, see my booklet http://www.kevinhouston.net/pdf/10ways.pdf

I was interested in your mechanic analogy for maths teaching. It occurred to me that if a customer comes in saying ‘My car doesn’t accelerate properly’ then of course this could be anything making the car’s running less efficient, i.e. not only the fuel pump but misfiring spark plugs (these I think could result in a ‘funny noise’ too), clutch slipping, problem with the air intake (I had this problem with an A-reg. Fiat Panda in the late 1980s) to mention probably just a few. I think you’re absolutely right – pupils and students need to have ‘USE INITIATIVE’ drummed into them from an early age & not just with mathematics. I recently gave myself a maths initiative test of which more anon.

In my more paranoid moments though I wonder if there’s some grand plan to have the education system turn out droves of obedient, unquestioning little worker bees for the Government’s rich corporate friends. I don’t know if you ever take ‘Private Eye’ but hardly an issue goes by without their reporting some instance of unhealthy relationships between Govt and ‘MegaCorp’. The current issue, showing on the front cover ‘Call Me’ Dave of The Buller chumming cosily along with Rebekah Wade I feel sums the whole thing up.

I noted with appreciation your advice to the other poster Ivor on self-study – thanks from me, too, food for thought there definitely. I’m sure you’re right on my own experience, perseverance pays. I hate giving up and looking up.

Best of luck with getting your students to wake up – hope you don’t have too many experiences like that of the history teacher and sulky A-level set in the Lindsey Anderson film ‘If…’ (1968) where the teacher eventually says in desperation, ‘Well if you will insist on sitting there like a row of Christmas puddings you can at least write!’ before setting an instant essay on George III.