'Meaningless' maths gives way to compulsory multilingualism

Maths equation'I assure you that in real life there is no such thing as algebra.'

The quote is attributed to American humourist Fran Lebowitz, part of an address to a graduating class in her former school. It draws an uncomfortable laugh because we realise it is true. If there ever was a need for the average citizen to be familiar with algebra in order to be a productive member of society, that need has been well and truly superseded by advances in modern technology.

I spent a working life teaching mathematics and I love the subject, its logical neatness, its way of reducing nature to equations, of predicting what will happen not because God or Newton or Einstein said so, but because the algebra says so.

The highlight of my tertiary career was the day a lecturer derived Maxwell's equations for our small class. The highlights of my teaching career were the occasions when I helped my senior students derive Euler's equation:

algebra 1

I explained to them that what Mozart and Michelangelo and Shakespeare did to show the meaning of the word sublime, Euler did with that simple equation. I think they connected with my enthusiasm.

I do not make those points to big-note myself, though I claim that they give me membership of an elite group. I wonder how many productive, law-abiding adults — politicians, say, or judges — have ever heard of either Maxwell or Euler. Let us put 10 per cent as a working hypothesis.

That might well be a suitable figure also for those who can still us solve a quadratic equation, but is surely an order of magnitude higher than those who have ever needed to do so.

Now visit any year 9 or year 10 mathematics class in any school in the country and even allowing for the absence of national curriculum, it is a safe bet that those children have struggled with quadratic equations at some time or are about to do so.

Let us not attempt to put a financial figure on this waste of effort, though surely it would frighten us. Instead, let us consider the poor kids who struggle with the work. Here is one way of solving quadratic equations: you 'plug in' appropriate values into the expression:

algebra 2


and the answer pops out. I guarantee you, dear reader, that the whole process means about as much to the average year 9 or 10 student as it means to you. Yet, counting revision and homework, your sons or daughters will spend anything from two to six weeks of their lives doing just that: meaningless, routine work that a calculator does more quickly and without ever making a mistake.

This is only one example. I haven't told you about index laws and similar triangles and trigonometry and ships on the horizon and angles of elevation and compound interest. I admit that our students need to understand compound interest: sit them down at one of our Prime Minister's new computers with one of a dozen programs which they can find on Google more quickly than we can; let them enter the amount borrowed, the time of the loan and the interest rate and let them play with it. Did I say play? Oops, sorry.

Remember, mathematics is a core subject. There was a time when girls could get out of doing it, but equality got rid of that idea. It takes up approximately one-sixth of the time and effort of a school day. Go ahead, Mr Tanner, work out what that costs and then what returns the country should expect for such expenditure.

The simple truth is that the country does not need people who can solve quadratic equations. Today's engineers, scientists, architects and designers have computer programs to do their work for them.

What this country does need, and badly, is people who can speak Mandarin, Korean or Thai. We need people who can work in Indonesia, Vietnam or the Philippines without being taken for fools by the locals.

The OR in those sentences is intended as what mathematicians call the exclusive OR: any second language would do. Citizens of a European country would use the inclusive OR for their children's polyglot education — how often in our European travels, we have felt ashamed of our monolingualism.

Mathematics is a difficult subject. It blights the school lives of many children. Instead of the rarely questioned assumption that it must be a compulsory subject, let us make it optional after year 6. That simple act would free up our second-level school curriculum for work that would be more beneficial for the students and the country.

Give a child some competence in a language that would enable them to travel in Thailand or Korea, and we are giving them a skill for life. And that is not to note the research that suggests competence in a second language can make study of a third or fourth language easier.

People of my vintage studied Latin at school. It was a core subject, at least for boys. I never regretted the effort I put in to learning the declensions and conjugations. But I do not regard myself as better educated than today's generation who never learned Latin. It would make good economic and educational sense if mathematics went the way of Latin.

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


Flickr image by Robert Scarth



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Existing comments

Frank O'Shea's article presupposes that the time in the curriculum created by deleting mathematics would be given to the difficult task of learning a foreign language. As an experienced teacher I would have to say that this is highly unlikely. Mathematics may well be one of the only subjects a student does that requires strict adherence to logic. And the ability to apply logic may not be a bad thing in life generally. Students who have trouble with basic mathematics are not likely to be the ones taking heartily to the study of often difficult to learn foreign languages. As for the classical languages, students who study these are not uncommonly also quite capable in mathematics. An academically able student is likely to be able in a number of subjects. It's not politically correct but the less academically able students may be better off either out of school learning skills in a workplace or enrolled in vocational training.
Peter Ofner | 24 April 2008

If only I could have read this 50 years ago!

I always felt a failure because I could not get my head around Algebra, and of course have never had to use it in my professional life.

Our young people MUST learn at least one other language to be citizens of the world.
Christine Slattery | 24 April 2008

The more mathematical power calculators and computers have, the more mathematical skill users need to understand what they've calculated. You understand what it means for a computer to solve a quintic equation (and what use that might be) because you've done quadratics by hand. The computer revolution has produced a flood of data, and it's mathematics that can extract knowledge from it - and high-level mathematics at that. If students are shut out of mathematics training, they'll never be able to fill the growing number of jobs in bank risk, climate modelling, data analysis and so on that are at the centre of the modern knowledge economy.
James Franklin | 24 April 2008

The next generation will not be able to read, write or do mathematics if they are not educated properly. There will be no computers for them to use if we do not teach mathematics, computers do not magically appear, they are understood and developed over and over again each generation. Mathematical knowledge is used by everyone every day, not directly solving the quadratic equation, but by solving algebraic equations in their head. Very well for Frank to have benefited from Latin and Mathematics, why take that away from the next generation? I speak four languages and work with mathematics for a living, I am not particularly bright, but I was taught well and given the opportunity and challenged to learn. Let us stop the dumbing down of education, our children are capable of learning!
Mark Boland | 24 April 2008

As an engineer I strongly agree with the comment from James Franklin. In my work I use a lot of sophisticated software in engineering design but I often find myself going back to first principles in maths and physics to ensure that the software is producing reasonable/realistic results. I wish I had paid more attention during my maths lessons at school. It certainly would have made life easier for me further down the track.

Chris Halliday | 24 April 2008

I wholeheartedly agree Frank! Kids all over the world are in desperate need of a proper education that helps them in tomorrow's world. Why should maths be sacrosanct? The mental agility that this subject should impart can be easily done with a language. Kids aren't dumb or fools and too many of them are voting with their feet and leaving school.
Bill Donovan | 24 April 2008

Mathematics and Science subjects have much to impart about logical thought which is of general application. They are also an important part of our culture. The O'Shea thesis is consistent with my own observation as a parent, going back some years, of a rather undemanding Catholic educational environment conducive to soft options that may leave some children achieving less than their true potential. This of course is entirely impressionistic and anecdotal and can no doubt be refuted by appropriate statistics. But can it?
Robert French | 24 April 2008

Thanks Frank. I'll stop feeling guilty about having forgotten how to do differential calculus and various statistical calculations manually. I'm not sure though how I might understand the meaning of regression and correlation analysis if I'd never struggled with such things.
Sandie Cornish | 24 April 2008

But it might be useful in the logic driven world of computers to understand logic. Kids are not as good with this as we and they think they are. I would have loved: game theory which explains much of the human thinking, straight and crooked thinking, whether the symbolic language that is used by the practitioners is useful in "real life" is doubtful, but baby with the bath water?? y = mx+c
Richard Pickup | 24 April 2008

I think the point has been missed by some. Frank has not said we shouldn't have mathematics, but rather it should be optional. Those students who need maths for their future careers would still be able to do it. I agree wholeheartedly that languages are a major Australian downfall. I am currently doing a PhD in linguistics, and completed my undergraduate degree in Indonesia - in Indonesian. The language abilities of Australians that i met on my travels was varied, some better than others, but there was a general feeling overseas that Australians are very bad at learning other languages (a bit like the Americans). This doesn't have to be the case. Language learning is vitally important as it teaches us about other cultures as well. For a country striving to be an inclusive multicultural society this is definitely a positive step forward.
Katrina Langford | 24 April 2008

Is O'Shea advocating the abolition of mathematics from the school curriculum or is he urging that it not be compulsory for all? James Franklin is surely correct in his statement but we should take note also of Christine Slattery's comment. I hope no one is suggesting that we should wait till high school to begin teaching foreign languages. But we also have to acquire and retain teachers able to implement the serious study of language. In many schools there are spasmodic language courses that students are unable to complete because language teachers move on taking their expertise with them.
Denis Matthews | 24 April 2008

One of the troubles with education is that there is not a consensus with respect to its definition.

I see the role of education as helping us to see more the "what is" not the "why is". Ultimately we never know the "why" but we can make more effort to identify the "what", the good,the bad, the indifferent

Mathematics is essentially another language. It is grounded in the stuff of life. Mathematics cannot ultimately prove anything, it can only help report what is. So too with any language.

The theologian Bernard Lonergan, who also happened to be a good mathematician, reminds us that science started to make progress when it focused more on the "what is" rather than "why is". This is the principle which guided his theology.

Can we use this as a model for good education?

I see good education grounded on solid empirical data. Students should be taught how to gather and report such data, "the what", and identify relationships between such data. Mathematics can help in this endeavor so also being multilingual.

Good education should provide students with sufficient tools to mine the historical data of one and another's culture, and then to pull it all together in a logical and meaningful manner.

Being good at mathematics, languages and indeed the many other subjects taught in school can help with this task.
Rich | 24 April 2008

At least one reason why we now find ourselves in a cultural and spiritual wasteland is that we have lionised,
as peerless leaders, those whose understanding of the world coincides with their fetish for the spreadsheet
package and the "data" used as its dubious input.

The only way to counter the morally corrosive spreadsheet approach to society and its problems is to expose its shallowness. The only way for any of us to understand how shallow it is, is to have some mathematical knowledge.

Rather than downplay mathematics as
irrelevant, let us teach it in a way that engages students in its dynamic and restores to them, as citizens, some power for critical numerical reasoning. Not that it is easy to teach; but it does matter that it be taught.

Art, language, and mathematics are of one piece. If Frank O'Shea sees the beauty of Maxwell and Euler's work, he will not begrudge lesser students the chance to feel the same (perhaps more modest but still real) elation on solving their first quadratic equation.
Fred Green | 24 April 2008

Surely it is about time that English was taught at school.
Peter Skinner | 24 April 2008

But people learn maths in Thailand and Korea. If we are to learn maths, why not learn it in Thai and Korean? This would kill two birds with one stone.
richard | 24 April 2008

A cursory search of www.newscientist.com turns up a number of reports in which it is found that lannguage is most efficiently acquired between ages 1 and 7. Perhaps we should have more multi-lingual primary school teachers, and the language spoken at home by children of various ethnic identities exploited in lesson planning.

Ages 7 to onset of adolescence are when children learn about the physical world; perhaps this is when a focus on on natural science (and the maths that is the natural language in which it is described) could be most efficiently taught.

After start of adolescence, all bets are off: relationships with peers, the need to establish pairs to produce the next generation of humans, is all-consuming, is the major driver for the next decade.

Out of this drive comes much of the art, creativity, growth, change, unsettlement that progresses human societies; peacocks, on the other hand, grow beautiful blue feathers.
David Arthur | 24 April 2008

Once again the old mistake is made - one size fits all. The mathematically gifted will do mathematics and the underpinnings of the tech world will be okay. It's those who find languages easy who advocate the very good idea or necessity of learning another! How about teaching "relevant" mathematics to the mathematically challenged, and a cleverly taught second language early. Much more approriate attention to each child's natural ability and feeding that of course requires expensive discernment. Montessori knew all about it years ago. Perhaps some of her admitted "hunches" could be tested and put to good use - early! I wasn't bad at maths but no one taught me how to use it or apply it. I could do with a refresher on how to calculate the height of a tree. It matters now. It didn't matter to me 50 years ago. My efforts with Italian took off once I had to do the family shopping in the language.
Ann Long | 24 April 2008

"The simple truth is that the country does not need people who can solve quadratic equations. Today's engineers, scientists, architects and designers have computer programs to do their work for them."

We could (in the year 2050) have a computer system which acted as an intelligent tutor, chatting to us about quadratic equations, and "doing our work for us". But we would still be learning about quadratic equations (or whatever was fashionable to learn in 2050) even if the computer system did the work for us.
richard mullins | 25 April 2008

I agree Frank that we could do things a lot differently. (Do we need schools at all today?). But it is not a case or either learning maths or learning Korean - we could do both - we could learn Korean and talk about equations in Korean.

People who studied quadratic equations (such as Descartes) were no doubt hoping to discover the secrets of the universe.

While you can solve quadratic equations by algebra, and also cubic and quartic equations (Cardono found the solutuon for cubic, and Descartes the solution for quartic), there is no solution for the quintic or higher powers. Galois proved this, and his theory is used today for error correcting computer codes used in data transmission.

No doubt one day much more will be discovered about the secrets of the universe.
richard mullins | 25 April 2008

By all means, abandon the current teaching structures.

For many years, education departments for high school maths have been urging teachers to promote discussion, art, and other approaches to looking at maths. In general, they urge that students be able to develop their own approaches to a topic.
richard mullins | 25 April 2008

So instead of maths we should learn another language? I've never felt that I've missed a trick by not knowing Korean, or Thai or Mandarin, but where would I be without Maths. I'm a Creative Director and I use maths directly and its effect on my logic ability every day for marketing, operations, coding, budgets, purchasing etc.

Visiting Thailand, India, Egypt or any other country I love mixing with the locals even given my/their language barriers but I still have the constant haggling requiring quick mental currency conversions. Maths is not language dependent.

As a child i learnt French and Indonesian for several years – I've rarely used it and forgotten most of it.

So Frank knows stuff mathematically that he never uses to any great purpose, I know that if you put blow dynamite on top of a flaming oil geyser the flame will go out. My head's full of useless crap like that (until that oil worker application gets accepted). It's also full of useful stuff like maths.
ben Parer | 27 April 2008

There is no doubt that learning a second language can be a deeply enriching experience with undeniable direct practical benefit. Certainly that was my experience from language study at high school.

But there is another principle that ought give us pause before we rid the crowded secondary curriculum of mathematics; that education is also about teaching/learning to think, and to think critically at that.

There are particular unique ways that mathematics, as well as the sciences, can nurture such thinking and reasoning. Working through a mathematic problem or establishing a 'proof' is not as far removed from the discipline of developing a clear line of reasoning and thus a good argument, in an essay or similar piece of writing.

I have always maintained that my mathematics study helped me write better essays at school and university. Equally, I felt indebted to this same mathematics when successfully calculating, in the course of my biochemistry degree, the correct dilution factors to determine the enzyme activity per gram of liver!

Even now, as I pursue further study in theology, I realise how my years of maths and science study have sharpened my analytical and reasoning faculties. Long live the mental discipline of mathematics!
Ruth Dunnicliff-Hagan | 28 April 2008

I no longer memorise phone numbers because of cell phone usage. It's not problematic until my phone is dead and I need to contact someone. Since spell-check, my general spelling abilities have decreased. I become concerned when I have to write something manually and do not want to seem illiterate. Sadly, I am an educator.

If math becomes optional, what interconnected skills will inevitably diminish? Will people have an ability to think when the technology fails? Will people recognise input errors? (Currently, I have many students who argue that an incorrect answer is correct because the ”calculator says so".)

What social class will really opt out of math? Is this another good intention that will result in additional educational and economic gaps? Will our employment systems change after math becomes optional? In what departments will the "math-opt-outs" work?

I think the notion is great to encourage foreign language studies. Many English words are foreign to my students and they are American born. If we promote foreign language studies, we must mandate funding for foreign exchange programs. Many of my students do not travel outside of their borough in NYC. Maybe our pilot program can be an inter-borough exchange.
Baindu | 28 April 2008

Socrates, in Plato's perhaps apocryphal account, taught a slave that the diagonal of a square had the length square root of 2, by question and answer (Socratic dialogue). I thought it was interesting that Socrates said that cooking could not be taught by his method of Socratic dialogue. Today we would not accept this - but we might accept that some artistic skills, e.g. pronunciation of a foreign language, cannot be taught by Socratic dialogue. The Socratic dialogue might give you an approximation only, but not the real thing.

Isn't it true that we could find quadratic equations in a host of areas (such as cooking) if we looked hard enough. Isn't this simply an engineering task, to find some quadratic equations in cooking? If this task was funded appropriately (e.g. by allowing teachers and students time to think), then answers would be found.

Chebyshev functions were discovered in order to account for the movement of the linkages between a railway engine and the wheels.

It is quite possibly the case that quadratic equations were originally invented in order to solve some practical problem that is now forgotten.
richard mullins | 02 May 2008

Bags not let it be my children who grow up and enter the Big World without the complete package of mathematical logic in their back pockets.

Who WOULD like to volunteer their children as the guinea pigs?

I am however, happy for them to leave for Indonesia with a Lonely Planet Guide and a translating dictionary in their back pocket as next month they will probably be in Bhutan, or Thailand, or Italy or Morroco or ......

Oh! And I see it that school education is for the "What" and University should be for the "Why is".
Alexandra Tiffin | 02 May 2008

Thanks for your article, Frank O'Shea.
What I am wondering is whether all of our learning can be digested into pieces that are as EASY to understand, as, say, quadratic equations.

Currently, this is not the way we are taught. Instead, courses are made more and more difficult (at least to the casual observer) as one progresses, so that at Ph.D level only a few such as Stephen Hawking can follow what is going on.

But need it be so? Is this all a hoax to support our current power structures and current revenue streams? I suspect that it is.

Since the 1960s many people have blown the whistle on philosophy and literary criticism - it is only a matter of time before people realise that there is a huge industry of bogus construction of special knowledge, and that the hierarchies that are presented to us in maths, computing, management, could be greatly simplified.
richard | 03 May 2008

Surely not a case of either/or. I realise that both/and cannot be extended indefinitely, but are we linking education and vocational training too tightly? It is so sad to see someone struggling to get his/her head around a simple everyday challenge because of an inability to conceptualise the relationship between things. The studies of both mathematics and languages (and other disciplines, of course) are training pathways for the mind; different, complementary, one sometimes more needed than the other. But as we physically exercise all parts of our body for maximum benefit, so let us stimulate our imaginations in as many ways as we can.
Vaughan Bryers | 07 May 2008

i dont know maths can you please teach me
ujjwal sapkota | 22 June 2008

Thank God nobody taught me Korean or Japanese when I was at school. This would have been completely useless in Tanzania where I lived for two years teaching mathematics. I needed to learn Swahili and the students in my class felt very fortunate to be learning mathematics.

I question the manner in which students learned algebra and compare it to how I try to teach it today. It may not be useful to have the quadratic formula branded on your brain, but students have fun and feel empowered when they learn that leaping frogs require a perfectly predictable and quadratic number of jumps to pass each other. I do everything I can not to teach the way I was taught. I like to think that my students feel empowered by having understandings of the world around them that can be valuable. Maths students feel most powerful when they learn that they are able to solve real problems. Mathematics is a way of making seen that which is not seen - if you learn it the right way.
Damian Howison | 28 August 2008

the article was very informative,and amusing. and i am sure most ladies were happy when excused

however all i want to find out is the answer to the following
£500000 invested at 2.5%, how much a month can be withdrawn over fifteen years
tony bryant | 07 February 2010

tony bryant07 Feb 2010

the article was very informative,and amusing.

however all i want to find out is the answer to the following
£500000 invested at 2.5%, how much a month can be withdrawn over fifteen years

the answer is now available in the maths curriculum in high school. Or you can google to find formulas.

Please note that these formulas have only been taught in recent years, now that computers are available.
The calculations are easy now but once would been a specialist's life's work to master.

richard mullins | 29 October 2011

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