Tuesday, October 09, 2012

Calculators: Education stuck in pre-calculator age

Archaeological evidence for an abacus goes back to 5th century BC Greece, however, there is indirect evidence of their use in Mesopotamia, Egypt and Persia. It is still widely used in Asia. The humble electronic calculator was the first computer to impact teaching and learning. It quickly replaced mechanical slide rules and mechanical calculators in the 1970s. Calculators now include scientific, algebraic, trigonometric  and graphing functions.
Education is still stuck in pre-calculator age
Everyone’s miserable about maths: employers, politicians, teachers and especially learners, many who fail and hate the subject with a passion. Indeed, governments have become obsessed with the subject, largely on the hysteria surrounding the PISA rankings.
One issue that is receiving intense attention is ‘calculation’, which is kicking up a storm in maths education. The ubiquity of calculators has led some to question the way we teach maths in schools. They claim that the world has changed from analogue to digital and the teaching of maths needs to respond accordingly.
Some argue that calculators have led to a reduction in numeracy and maths skills. They recommend not using calculators in schools until a certain level of competence in mental arithmetic is reached. Others argue that the traditional focus on ‘calculation’ needs to be replaced by a more sophisticated curriculum of solving problems using maths. Why teach long division, when you are unlikely to ever use it in real life? Calculators can also be used to do the necessary calculation spadework on algebra, trigonometry and graphics.
Maths need exaggerated
Some, like Roger Schank, believe that the need to learn maths is grossly exaggerated as only a tiny proportion of adults will use the maths that is taught, beyond basic arithmetic. His point is that most of what is taught, especially algebra, is of no real practical use and does not help people to think logically. He often asks highly educated audiences to tell him the quadratic formula – few ever answer. Sure, some will need maths in their later career, so says Roger, let them learn it later. Roger has traced this obsession with maths back to early 19th century curriculum choices and claims that this is a historical problem, fuelled by the fact that maths is easy to test, especially ‘calculation’
Too much calculation
Conrad Wolfram decries the focus on ‘calculation’ in school maths. We spend most of our time teaching calculations by hand, which any calculator and computer can do better than any human. Practical, mental arithmetic is fine, but what are these numeracy basics? Automation pushes the user towards using the tools in more sophisticated ways. Maths is not calculation and over the last thirty years calculation has been automated by calculators. Education is still stuck in a pre-calculator age.
Far better to understand what you’re trying to achieve. He recommends that programming is a better way to do maths. It makes maths more practical and academic at the same time. He goes further and argues that the obsession with calculation in maths kills off the initiative, intuition and perseverance that maths needs. In other words we’re turned off maths by maths. Students learn to look for and apply formula, which they then proceed to calculate. Text books are full of primitive, dry, exercises that seem like chores. Many now argue that real life problems should stimulate mathematical enquiry through the use of more word based problems.
Calculators and computers
A calculator is pretty standard as a native application on PCs, Macs and mobile devices. Tills automatically calculate the correct change for customers. Calculators are therefore embedded in newer forms of technology making them more readily available. This is one potential use of mobile devices in schools that teachers should consider.
Maths is forced, by law, upon people who see it as lacking relevance and don’t want to learn it, taught by people who, because they’re good at maths, often don’t know how to teach it. Yet the curriculum is aimed, largely at those very few who will use high-level maths professionally.


N Winton said...

I can only agree! When I was a lot younger, I sat an exam in a subject called Arithmetic. Adding, subtracting, multiplying, dividing, percentages... in other words, all the practical 'maths' required to function in the modern world.

The abstract qualities of pure maths are beyond most learners simply because they are taught in the abstract: a+b=c-(x+y) =>WTF!?! As you say, teach them interesting and relevant things like programming... and show them how to find the maths skills they may need to complete their work. Quite apart from anything else, this is much more like real world skills that I use every day.

I love the justification that "learners need to know these things in case their calculators stop working"... one may as well teach them how the internal combustion engine works in case their car runs out of petrol. Pointless.

Thanks for the brain food!

Donald Clark said...

I too sat the old Arithmetic exam, which corresponds to 'useful numeracy'. Time to bring it back methinks. Interestingly, Wolfram also uses your car analogy in his TED talk. It's high time someone 'did the maths' and realised that most of what is taught in maths is not used in the majority of jobs.

N Winton said...

I must now go and listen to the Wolfram talk. Sounds like it is an obvious/self-evident analogy if I can come up with it as well!

Steve Smith said...

I would probably agree with Roger Schank. Simon Jenkins has expressed the same view. Maths is the modern Latin and we are all meant to believe it is vital. (It is more useful than latin, though!)

gutscheine zum ausdrucken said...

very good post

Flora Marriott said...

The most useful bit of maths I learnt, was age 38 when I read about the 'Test of Reasonableness'. It's really obvious, and I'm sure most people expect me already knew about it. But it is the one thing that would have been useful to me all my life, had I been taught it in school.

(The Test of Reasonableness is simply about doing a rough estimate of what something should be. E.g. I'm so hopeless at mental arithmetic that 22 x14 is hard for me. But I can work about 20 x 14, so I know that the answer must be in the region of a bit more than 270).

Donald Clark said...

Good example Flora of what distinguishes real maths and problem solving from obsessive calculation. To be fair 'approximation' is taught at GCSE level.