Taking maths out of the equation


Furiously factoring, Flickr image by CarnonNYCTop buttons open, tie at an angle, occasional glances to the top desk. Reminds you of a dog off the lead, swift glances to check that his master is still there. Enough of simile — or is it metaphor? Fingers poking at calculators to multiply 7 by 3, to add 15 and 8; pens in mouths or twirled expertly between second and third fingers; glances at wristwatches — how much time left in this lesson?

Tom has no idea what to do, looks around in the hope of inspiration from the bowed heads of his classmates. 'Come up, Tom.' Tom is a big lad, second row of the scrum, too much time with his head stuck up a ... Never mind. Concentrate, you're the teacher.

He reminds you of the lad from Tangmalangaloo — knocks the benches all askew, upending of himself. Is that another simile? 'Sir, what does "solve the equation" mean?'

Oh God. You have been doing this for three weeks and he has never missed a class. But you explain it to him again, the rote set of steps that mysteriously rolls out an answer.

'Is that the answer, sir?' 'Yes, Tom, now you do exactly the same with the next two and come up again when you have done those.' But why are you sitting down anyway? Shouldn't you be moving around, looking over shoulders, pointing at little errors, whispering encouragement, monosyllabic hints?

But then the thought comes: is this any way to spend your life? Will it matter to Tom in ten years time that he cannot solve a quadratic equation? Will it matter to any of them?

Actually, it probably will, because someone has decreed that 15-year olds should be able to do this and if they cannot, they will fail. Well, not fail, that word has gone out of the school vocabulary, but they will be guided into a stream that says hod carrier, professional footballer, backbench MP.

Tom comes up. He has done what you showed him and got the answers. He is smiling. 'I can do this now, sir.' There is no bravado in that, just genuine pleasure. A small triumph, the one that explains why you love this job. Tom may not have many more classroom victories that day, but right now he is happy.

These are earnest kids: keen, wanting to succeed. And society has told them that to succeed they must be able to solve a quadratic equation, draw a parabola, find the vertex, state the axis of symmetry. This city has two million adults. How many of them ever heard of an axis of symmetry?

You used to teach Latin. For a while you taught computer programming: Assembler, BASIC, Pascal, Comal. But no one learns programming any more and that knocked the fun out of computers. So there's your life: Latin, Assembler, quadratic equations. Just as well you were not paid for any output useful to society. What do they call it now? Value adding.

There are calculators that solve quadratic equations but they are not allowed in schools except a few progressive ones in Victoria. They will do calculus for you too — you can't get inside the door of an American university without calculus.

Meanwhile, there are high schools in Australia which don't have a mathematics teacher for their junior classes. But that's all right because they don't call it maths any more. They call it problem solving and get the PE teacher or one of the science staff to teach it.

So here's a suggestion for those struggling with the national curriculum. Forget maths as a universal subject. Offer it as an option in high school to be taken by those with some ability in dealing with abstraction.

Then have it taught by properly qualified teachers, people who actually like mathematics, are inspired by it, regard Euler and Hamilton and Riemann with the same kind of reverence that their colleagues in English regard Shakespeare and Eliot.

We have inherited an assembly line model of schools — everyone of the same age learning the same material at the same time. Never mind that many are bored: they made sense of algebra the first time they met it, and now must wait for their slower classmates.

We are not talking about a few here: up to one third of the students of any unstreamed class are bored. Ah yes, streaming, we can see where you are coming from: you want us to go back to the elite of A, B, C, D, E, F classes. No, I don't. I would like to see a school with only A classes, where the talents a student has can be developed to a standard of useful excellence.

Henry Ford invented the assembly line, and now the CEO of his company is prepared to work for a dollar a year. There must be a metaphor there somewhere. Or is it a simile?

Frank O'SheaFrank O'Shea is a retired teacher. His book Keeping Faith: 40 Years of Marist College Canberra was published in 2008.




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Existing comments

That is a brilliant response. I have struggled with maths but have made a go of a life in the bush.

Nice to see an unfettered mind in action. Well done!
Nev Hunt | 02 February 2009

"Jenny felt sick the other day, but then realised she had double Maths, and insisted on going to school", Mum and Dad told me on parent/teacher night. But the school and principal were so full of intimidation, insidious politics and nasty "capital C" Catholic, not Christian, culture that it was my last teaching stint anywhere. So much for loving your subject!
Frank Bremner | 02 February 2009

When I went to school; grammar school, and no it wasn't a private school, I was in the R stream, below us in order were the A, S, and T classes (3R1, 3R2, 3A1 etc.). The leaving age was 14, and we all learned different things according to what our expectations were when we started secondary school. I have no doubt we all ended up in different places, and not all of us achieved what we thought we would.

Of those who signed up for the old friends network, no-one seems to have bemoaned the fact they chose the wrong strand, certainly no-one had it chosen for them.

Of those in the R strand, I seem to be the failure, I have only three degrees, including a science degree. Which is why I am about to enroll in a science Masters degree, and drop my age from my real 65, to 58 which is how I appear to the world. You see I am not about to give up simply by being stereotyped as being too old.

Whether someone likes math or not, we all come off the school assembly line at roughly the same age, and we all need to be able to check if we have been overcharged when we buy something.

The teachers I had all seemed to have BA as well as MA after their names, and I wonder how many do now.

I have a son who is a teacher. He commented that at one school only he was enthusiastic about teaching, the others seemed only enthusiastic about the end of the fortnight.
GeoffB | 02 February 2009

thanks for your post Frank.

I feel that ANYTHING could be taught using games. (I noticed a Wii game reviewed in the computer pages 2 weeks ago - it allows you to wield a scalpel in a virtual operation.)

I admire your efforts in teaching in school. I had a go at it last year, at the age of 64. The senior maths classes were great fun. The junior maths and junior science was much more difficult - there was a mini riot in the class sometimes - like something out of Lord of the Flies.
richard | 02 February 2009

At school,I didn't understand algebra at all. In the 50 years since leaving school, I have worked as a priest, a trade commissioner, and a social worker. I have never been aware, at any point in those 50 years, that my inability at mathematics was hampering my effectiveness. So why did I have to beat my head against a wall for five years trying to master algebra?
Peter Downie | 02 February 2009

Learning maths the traditional way, like learning Latin, can only appeal to a minority. But perhaps the others are secretly being "dumbed down" by our increasingly bureaucratised system. The following looks so innocuous, until you see the horrible way it is being used - to churn out students who do exactly what they are told and nothing else:

A rubric is a scoring tool for subjective assessments. It is a set of criteria and standards linked to learning objectives that is used to assess a student's performance on papers, projects, essays, and other assignments. Rubrics allow for standardised evaluation according to specified criteria, making grading simpler and more transparent.

The rubric is an attempt to delineate consistent assessment criteria. It allows teachers and students alike to assess criteria which are complex and subjective and also provide ground for self-evaluation, reflection and peer review. It is aimed at accurate and fair assessment, fostering understanding and indicating the way to proceed with subsequent learning/teaching. This integration of performance and feedback is called "ongoing assessment."

richard | 02 February 2009

New Scientist recently featured an article about dyscalculia.

There is a difference between mathematics and arithmetic.
Mathematics is a world of abstract construction, and arithmetic is the basic counting skill on which mathematics depends.

Arithmetic is also the basic counting skill on which accountancy, economics, geography, social research, depend.
People who do not realise this distinction oft enjoin others to "do the math".

Perhaps arithmetic and mathematics should be taught as two separate courses, to which entry may be completed after assessment for dyscalculia should precede any demand.
David Arthur | 02 February 2009

The argument in favour of maths education has always been that it teaches students problem solving skills that they can apply in the outside world. Why not instead teach them problem solving skills, applied to outside world situations? E.g. What's involved in building a house? How do you go about constructing a household budget?

Then again, I enjoyed maths even though I can't remember much at all about matrices and differentiation.
Joseph Vine | 02 February 2009

The title says it all! Maths is so divided against itself that it is almost a metaphor for the present fragmentation of society.

Having taught maths for over 30 years in a large provincial high school, I recall the year when the first cohort came arrived who didn’t know what a fraction was, followed not long after by those who couldn’t divide.

For me, it’s not about quadratics or axes of symmetry – it is far more basic. After a decade of reflection and looking closely at the historical issues, it’s actually a spiritual problem. Can you understand God without understanding maths?

The moment you become aware that the Greek word ‘logos’ and that curious Hebrew symbol of truth, alef-taw (untranslated in Genesis 1: 1) both refer to an indivisible (pun intended!) unity of words and numbers, that’s no longer a simple question. Logos refers to a specific mathematical idea – last celebrated exactly 500 years ago in a masterwork illustrated by Leonardo da Vinci: DE DIVINA PROPORTIONE. You need division to approximate it and a quadratic to solve it exactly. It goes without saying that there’s a fractional approximation of it in the Greek text of John 1:1.
Anne Hamilton | 07 February 2009

Has noone heard of the new uni student, often female, who enrols eagerly in psychology, only to find to their horror - 'It's all statistics and maths!' I've heard that canny psych lecturers book the biggest lecture hall they can find for the first few months, and thereafter take a nice cosy one in the certain knowledge that at least half the students will have dropped out by then, scared off by the dreaded stats...

The New Scientist article linked to above evokes a similar story, a young woman wanting to study (sorry, 'read'!) political science but deterred by the maths entry requirement. How many of the social sciences now have a similar requirement?

It does a prospective student little good protesting that they won't be pursuing the 'maths bits' of the discipline.
Jason Covell | 05 June 2009

Frank, it was precisely Mathematics which lit the flame of curiosity about God, science, the universe and the eventual conversion in many people. I know one.

Mathematics, Music and Science actually lead you to God.
Annette | 23 March 2010


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