Saturday, October 27, 2012

Do the maths: 7 reasons why the obsession with maths doesn’t add up

I'd much rather employ this smart, innovative, humorous and creative person than someone who actually knows how to apply Pythagoras's Theorem. Maths has never been the sole touchstone for being 'smart' or 'employable'. So I'm annoyed that maths has become a weapon of mass distraction in education, a topic full of bluster and exaggeration. Maths is hard to learn, hard to teach and easy to test, in other words the ideal recipe for mass failure. Everyone seems to agree that we have a huge problem in maths. The problem, it seems to me, is a lack of a basic understanding of maths by politicians, employers, even experts in education. So here’s some FAILS, or failures to do the simple maths.

FAIL 1 Numeracy not maths
There is persistent exaggeration in the size of the so-called maths problem. This is caused by people shooting arrows, drawing a chalk circle around the arrow and calling it a bullseye. Typical is the recently formed National Numeracy charity, which claims we have 17 million (nearly half the working population) with poor numeracy. They do this by relying on one ‘survey’ and conflating numeracy with maths, as their definitions are based on GCSE achievement.
This exaggeration is endemic and a simple failure in statistics. The actual needs in the real world match what we call ‘functional maths’: basic numeracy, use of a calculator, some understanding of statistics etc. This is not congruent with what is actually taught in GCSE maths. If they were represented as sets there would be a small overlap. When employers talk about poor maths, they are largely talking about poor numeracy. These are two different things. In fact, almost invariably people conflate and confuse maths with numeracy (or functional maths). A simple Venn diagram is all that’s needed to make this clear.
FAIL 2 Most maths quantifiably irrelevant
What’s the quadratic equation? What’s a surd? When was the last time you divided two fractions? When did you last use algebra? The recent report into the teaching of maths confirmed, yet again, that the curriculum is largely irrelevant to most students, as they are unlikely to use much of it in later life. They rightly recommend a new qualification in functional maths. If GCSE maths were a pie chart, most of it will not be used by the vast majority of people in later life. In any case, if we do need the more complex stuff, we can learn it later. Do the maths. It doesn’t add up.
FAIL 3 Maths is easy to test
Rather than test what really matters in problem solving and real life, we’ve stuck to a lazy and often irrelevant method of testing that puts maths at the top of the tree. Why because it’s easy to test. Maths problems have single solutions and are therefore easy to test. Nevertheless, problems, largely of calculation, are perceived as being a good test of one’s ability in a general sense. This is nonsense. Maths problems are rarely realistic. Nobody goes around using maths to share marbles, split up pizzas, share out cakes at parties or dilute orange juice. There is a critical failure to ‘bridge’ between the real world and its representation in mathematical language. But in an age of perpetual testing, maths is an easy option.
Fail 4 Maths a transferable skill
If knowing maths teaches you to think clearly, how come the world has been plunged into a financial crisis by people who are good at maths but couldn’t see the problems they were causing. The answer to this problem was identified by Thorndike over a century ago. ‘Transfer’, the degree to which learning transfers to actual performance in the real world is still a largely misunderstood or ignored issue in education. Learning is largely (not always) a means to an end, namely the application of that knowledge or skills, yet few educators know or care much about transfer. They assume it exists where it doesn’t (for example in maths and Latin) and make little effort to make sure it happens. Thorndike showed that transfer depends on the similarity of the situations or domains. This principle of ‘identical elements’ led him to recommend problem solving and practice in real-world contexts, so that the learning tasks and context matched the real world. Has this lesson been leant in the teaching of maths, or Latin? No.
FAIL 5 Calculators calculate
Almost everyone has a calculator in their pocket, as it’s a native app on almost every mobile phone and computer. Yet we insist on teaching people how to ‘calculate’ as opposed to useful, functional numeracy. Experts, like Wolfram and others, have pointed to the crude culture of ‘calculation’ in school maths, at the expense of real, functional and conceptual maths. Richard Norris has shown that maths in the workplace is intimately tied up with computers, spreadsheets and others forms of software. Yet maths and ICT are treated as two separate subjects. Isolating ‘maths’ in this way presents it as a purely abstract and often irrelevant subject.
FAIL 6 Miscalculation on teachers
Statistically, your child was, is or will be, almost certainly taught by someone whose knowledge of maths is rather poor. We know, with mathematical certainty, that primary school teachers have poor maths skills. The recommendation of the recent Government report into Maths teaching is a minimum B pass in GCSE before you’re allowed to teach the subject. This sounds like a bad joke until you realise that our children are being taught by largely primary school teachers with an absurdly low competence in maths. It claims that, “Almost all of those on primary PGCE courses gave up studying mathematics at age 16. So, by the time they taught their first classes, they had not studied mathematics to any meaningful level for at least six years.” Only about 2% of primary school teachers have a degree in science or any STEM subject. Another shocker is the fact that in secondary schools, “24% of all children in secondary schools are not taught by specialist mathematics teachers”. Read that again. Most maths is not taught by maths teachers or even by teachers with a solid grasp of the subject.
FAIL 7 PISA ‘standards’
The PISA results show plummeting performance in maths by our young people. The Chinese have screamed to the top. We’ll be an economy the equivalent of Bangladesh in a few years if we don’t get our maths scores up.  This is all baloney. A more detailed analysis of why PISA is wrong.
This is a common mathematical problem among politicians, employers, even so called experts in education. Our performance has remained stable. There is no ‘drop’ in standards. If you construct a league table, you can, mathematically, rise and fall in that table while remaining the same in terms of competence. That’s the problem with league tables – they create the illusion of winners and losers.
Gove is an English graduate with scant knowledge of maths and science. I know because I challenged him on a shared platform at the Tory Party Conference in Blackpool when he claimed that all schoolchildren should know that the orbit of an electron relies on the same force as the orbit of the planets around the sun! There were guffaws from the audience, so I suggested he needed a new example as the forces at work here couldn’t be more different (true story). He went apeshit but he was still hopelessly wrong. His EBacc has all the hallmarks of a PISA-led curriculum, far too academic, and exclusive. His greatest crime is to have moved the goalposts after goals have been scored. If you change the goalposts so dramatically and quickly, you simply condemn 85% of students as failures (only 15% currently meet the Ebacc standard). What’s worse, Gove is applying the measure retrospectively. This is like moving the goalposts at the end of the game and disallowing goals scored. It’s madness. Do the maths. You can have schools with high achievement in Maths and English plummet down the new league tables from near the top to near the bottom, as they haven’t focused on humanities or languages. One weird consequence is that a student who does Latin and Ancient History will be judged above those who do Business Studies, Engineering, psychology, a third science and lots of other subjects. It’s worse than bad, it’s perverse.
We don’t actually live in a more mathematical world. We live in a world where most maths is done by calculators, computers and machines, or a relatively small number of experts. The vast majority of us need little actual maths, other than ‘functional maths’. To funnel all young people into a path that demands a mostly irrelevant, maths curriculum is to turn them off school and learning. This obsession with maths may, mathematically, be the very things that lowers our general educational attainment.


Ihor Charischak said...

Make that 3 of us. I'm with you 100%. I'm writing a book about it. Let's stay in touch.


Ihor Charischak said...

Make that 3 of us. I'm with you 100%. I'm writing a book about it. Let's stay in touch.


Jose Vilson said...

But, but, but ... if you don't know what the calculator is telling you, then you're failing both at numeracy and the maths.

Donald Clark said...

Jose - I'm arguing for 'functional maths' which includes basic numeracy.

Churchill said...

I have exactly the same feeling about Maths and Science. There is just too much emphasis on these two subjects. Here is my post on this topic

manolis said...

Interesting (though I think that people who were good at maths would see the problems they were causing and the problem is not the lack of transferability but more complex factors including bad modelling techniques, lack of communication, shared understanding, greed etc.).

Two questions: Which Richard Norris you mean? And what is the book you refer to at the beginning?

Mike - National Numeracy said...

Agree with a lot of what you say about numeracy requirements for life rather than maths exams - as you will see if you have a look around our website - BUT if you are to use our name in vain then please get your stats right.

the 17m that we quote has nothing to do with GCSE achievement - it is based upon a survey of 7,000 adults carried out on the government's behalf last year. The questions in the survey relate to 'functional maths', which somewhat pulls the rug out from your first point I feel...

You will find the numeracy / maths venn diagram on our website.

Re. the rest of your points, I think that the bit you are missing is 'mathematical thinking' - i.e. adding a quantitative element to otherwise purely qualitative decision-making in life and employment - this is vital 'for everyone, for life' along with your narrower definition of numeracy.

Happy to speak on 'phone or meet for a coffee since we are nearby!

Donald Clark said...

Much to applaud in terms of the attempt to distinguish numeracy from literacy on your site Mike and I applaud your attack on Gove's manic approach to teaching maths in primary schools.
However, my argument is against the general hysteria around 'numeracy and maths', which your charity, I think, almost inadvertently promotes.
On a practivcal note, the 'survey' you use covers everything to level 2 and above (Level 1 is GCSE (D-G) and Level 2 (GCSE A*-C) and in fact shows not much change since 2003.
The survey admits that it doesn't compare ICT skills between 2003 and 2011. However, I'd bet my house on the fact that these have improved vastly. This is significant, as I and many others, have argued that people do not need to do detailed calculations as they did in the past. We have calculators, tills, computers and mobiles that do this for us.
My main concern is the 17 million figure, which is already being bandied about as if it were a natural disaster, and leading to a hardening of attitudes among Conservatives about the Ebacc (your chair is a Tory peer which is a bit worrying).
Happy to meet for a coffee.

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