By Diana Bagnall
reprinted from The Bulletin
October 2002

Mathematics is out of favour with the young and experts in the field are worried. But in what some see as a golden age for maths, Diana Bagnall reports Australia is in danger of missing the boat.

There's panic in the maths department. All around the country, the same story's being told. Something's snapped in the culture. Maths education is being eaten away from the inside. Quick fixes are the order of the day. The academy has shrunk several dress sizes. In short, maths is losing its grip just when it counts most to hold on to the currency and language of science and technology.

"Maybe we've been too self-indulgent or more interested in doing maths than in interacting with the society around us," says Peter Taylor, who runs the Australian Mathematics Trust. It's an unusually frank admission. Mathematicians are not known for their humility. To the priests of the partial differential equation and their brethren, the purpose of their discipline is self-evident. Everyone should learn algebra and geometry, not because it is necessary for managing a warehouse or calculating percentages at sale time, but because maths teaches a way of thinking. It's the purest expression of reason and logic.

It's also fundamental to the developed world that we Australians take for granted. New technologies can go only where maths has been before. Take engineering, for example. Australian-born maths prodigy Terry Tao did so in an email to me: "The engineering of today usually relies on the mathematics developed 30 to 50 years ago, but the mathematics being created today will power the engineering 30 to 50 years in the future. For example, the mathematics for understanding protein folding is only just being developed, but is going to be crucial for the development of future biotech industry."

That maths should have to explain itself, to justify its existence, is bad enough. Yet two years ago the Australian Mathematical Society's executive officer, Jan Thomas, wrote a detailed paper stating in categorical terms where the structural problems in maths were most acute and what needed to be done to rectify them. She identified falling maths achievement in schools, a shortage of maths teachers and a brain drain of maths academics as needing immediate attention. Mathematicians, she said, believed in a high-tech, high-wage society but couldn't conceive of that without a strong maths culture. How else would people acquire the quantitative skills that underpin all sorts of fields, from actuarial work to information technology to molecular biology to environmental science to cryptography to supply chain management to computer graphics. You get the picture. Elementary, dear Watson.

In May, she produced a terse update. It began, "... little has changed. If anything the situation has worsened, particularly in the universities".

To be ignored is galling enough. But that this should be the case when countries across Europe, North America and Asia are all investing heavily in mathematical sciences begs the question of how Australia can survive as a competitive trading nation with a high standard of living, and enjoying real security in an increasingly dangerous world, says Peter Hall, who chairs the Australian Academy of Science's National Committee for Mathematics.

Take the vexed issue of a maths research institute. Over the past decade, successive federal governments have knocked back the proposal, which has been endorsed by the Australian Research Council and the National Committee for Mathematics. In July, the United States government announced the creation of three new maths research institutes, doubling its total to six. Canada, New Zealand, South Africa and Singapore, to name immediate competitors, have all established such institutes. It is only this month, with seed funding of $1m over three years from the Victorian government, that Australia has begun building its first maths research institute. (The Canadians, in comparison, fund their institutes to the tune of about $3m a year, says Thomas.) "We're the odd country out, not the clever country," Hall says.

His own field, statistics, offers one of the most striking examples of the shrinking academy. A decade ago, Australia had eight university statistics departments. Now there are three. Yet there is huge unmet demand for statisticians in Australia. At a high-level meeting called by Australia's chief statistician Dennis Trewin in July to discuss the problem his organisation has in finding the people it needs to analyse government data, a pharmaceutical company representative reported that his company's US office was considering shelving plans for growth in Australia because it couldn't recruit the senior statisticians that it needed to run clinical trials. That sort of news has mathematicians tearing their hair out. It's so cheap to train statisticians, says Hall. You need a computer and a desk. So what's going wrong?

The first symptom appears in maths enrolments at upper secondary level. On the surface, maths looks in healthy enough shape. Enrolments in Years 11 and 12 maths have stayed relatively stable over the past decade (about 88% of students take maths, according to the Australian Council of Educational Research). But when those enrolments are broken down into degree of difficulty, a different picture emerges.

Over the past decade, there's been a steady decline in the numbers of students taking advanced- level maths courses and a corresponding increase in enrolments in "easy" maths. It's a nationwide trend, says John Malone, a professor in maths education at Curtin University of Technology in Western Australia, who has been keeping data on upper secondary maths enrolments since 1972. In NSW, for example, the number of students doing the most difficult Higher School Certificate maths courses (3 and 4 unit maths) fell from 15,273 in 1991 to 9547 in 2000 (the last year of the old HSC). Conversely, the numbers choosing "maths for dummies" (Maths in Society) rose from 18,422 in 1991 to 27,614 in 2000.

It's not as if Australian students suddenly can't do maths. International competition results disprove that, as do comparative international studies. In the most recent of the latter, conducted by the OECD in 2000, Australian 15-year-olds achieved above the OECD average, with only students in Japan having significantly higher levels of mathematical literacy. And there will always be those whose talent will flourish wherever it appears. Two contemporary Australian novels, Sue Woolfe's Leaning Towards Infinity and Tom Petsinis' The French Mathematician, buy into the romance of mathematical genius persisting under adverse conditions, as does Hollywood's version of the life of Nobel prize winner John Nash, A Beautiful Mind. But that isn't what's at issue here. What University of NSW maths professor Garth Gaudry and others mean when they speculate morosely about the "extinction" of maths is the gradual erosion of mathematical training across the board, and the consequences of that further down the track for the nation.

At the heart of any discussion about maths education lies a great paradox, explained American mathematician Roger Howe in Mathematics Education Dialogues, an erstwhile publication of the National Council of Teachers of Mathematics. "Although our society is utterly dependent on mathematics for many of our daily needs, and even for the very shape of our civilisation, for the most part we do not need personally to be able to master very much of the mathematics that serves us." In other words, there is a huge gap between the maths most of us need to cope with everyday life and the maths that some of us have to know so that the rest of us can enjoy its fruits in relative ignorance.

There is an argument, and it has definite intellectual appeal, that maths should not be promoted for its usefulness or as a hurdle to be cleared in order to get a good job. American maths professor Dudley Underwood, writing in the journal of the Mathematics Association of America, put it succinctly: "One of the tasks of schools is to do their best to teach students to think, and of all subjects none is better suited. In no other subject is it so clear that reasoning can get results that are right, verifiably right. Mathematics increases the ability to reason, and shows its power, all at the same time."

Paddy McCrudden, 29, who has a PhD in the purest of pure maths fields, known as category theory, bailed out of academia a year ago. He's still thinking logically and laterally, but he's much better paid. He works for a global investment bank as a portfolio manager and strategist. "You don't necessarily use the sophisticated maths tools I used as an academic to solve the problems in this industry. But you need a clear head."

Andrew Hassall, 34, has stuck with the academy. He won a gold medal for Australia at the IMO in 1985. He did post-doctoral work for four years in the US, at the Massachusetts Institute of Technology and at Stanford University, before taking up an Australian Research Council fellowship at the Australian National University in 1996. When he teaches his honours students proofs, he's teaching them to construct a logical argument, he says. "It's not so very different to teaching logic in philosophy. It's abstract logic which makes it harder, but if you can think abstractly, the chances are you can apply it to concrete situations."

Kids are not stupid. But in the main they are very pragmatic. Their focus, and the focus of many of their teachers, is on getting over the line. The hearing they'll give the above argument is next to zilch when it comes to the push and shove of maximising a UAI score. "Most people say they don't take maths beyond where they have to, and we ought to face up to that," says Barry Kissane, a senior lecturer in maths education at Murdoch University in Western Australia. "People are opting to do other things when they can. A lot of kids who were captured [in maths courses] by the constraints of the education system now have more freedom and aren't as enticed by the maths curriculum."

Others attribute maths' diminished appeal to the pervasive influence of its pumped-up offspring, technology, in the minds and lives of the young. It's not unusual for a high school student to be doing an assignment on a computer on which instant messages are coming and going, while they listen to MP3 music files on a mobile phone which is also receiving calls and text messages. It's questionable how much intellectual effort is being put into the assignment, certainly. But the attention span required to manage all these different sources of information is of a different order to that needed to solve a complex maths problem. "The most important thing about maths is the ability to concentrate and think about one thing for a period of time," says Hassall. "I don't know how many people are able to do that any more."

Teachers such as Peter Hobson, of Dickson College in Canberra, have responded to what he believes is a profound generational shift by changing the way he teaches maths. He's aware that the use of technology (calculators, computers) is the most controversial issue in maths teaching. But he's unrepentant. He uses animated graphics software as a major teaching tool. "I get their interest better by having them work on the computer," he says. "These kids are second- and third-generation television watchers and first- and second-generation computer users. Their whole life is a push-button approach. They're used to concentrating for hours at a time in front of a computer game, which is not to say that they could concentrate for that long in front of a spreadsheet or graphics program, but my finding is that in general the kids love putting in the time."

There's another factor in maths achievement that people talk about less. Class. University of Melbourne education researcher Richard Teese, in his book Academic Success and Social Power (Melbourne University Press, 2000) argues strongly for social level being a powerful indicator of maths achievement. In 1994, he writes, as many as half of all boys in working-class north-eastern Melbourne attending high schools failed final-year maths exams, more than double the rate of their counterparts in the educated inner east of the city.

Why? Maths may be potentially the most universal and accessible of disciplines, but it is difficult to teach widely. The maths curriculum acts as social translator. The attitudes and behaviours that students need to master maths concepts are much more likely to be cultivated in families who understand academic pressures and whose lifestyles reinforce school values and interests – through early reading, intellectual stimulation, structured leisure time, supervised homework and friendships, and choice of school. Wealthier independent schools have more clout in the labour market and it is not uncommon for their maths departments to be headed by PhDs. Less privileged schools are slamming people with phys ed backgrounds into classes at upper secondary level to teach maths, says John Malone, professor of maths education at Curtin University. "They are as terrified of the subject as the kids are."

At a time when many experienced, well-qualified teachers are retiring, there's a been a steep decline in people signing up for maths education courses. The fall from grace of teaching as a career is now a cliché' but maths teaching seems to be doing it particularly tough. Contrary to popular perception, a good maths degree goes a long way in the job market, both in the public and private sectors, which are soaking up mathematicians faster than the universities can produce them.

A discussion paper prepared for the current federal review into teaching and teacher education notes that between 1992 and 2000, the number of teaching students specialising in maths in their first year fell by 46% (only physics has fared worse, with a 62% drop). Estimates from government and from the Australian Mathematical Society suggest that 40% of junior secondary students are being taught maths by teachers with little or no maths background and no studies in maths teaching, and that 30% of those teaching maths to Year 12 do not have a maths degree. The Australian Association of Mathematics Teachers began warning education authorities of this situation five years ago, but it's only recently that the penny seems to have dropped. Last year, for example, the NSW education department began offering an intensive six-month course run by the University of Newcastle to retrain primary and secondary teachers with little or no maths background to teach secondary maths up to Year 12, and an 18-month course run by Macquarie University to retrain other professionals with maths qualifications to teach.

What this drought of maths teachers means is that fewer and fewer kids are encountering teachers who know their stuff and in maths, probably more so than any other discipline, the killer application is a fired-up teacher who can make sense of the textbook. "We are dependent on the school system getting the kids here," says Gaudry. "We can't perform if the school system collapses." Implicit in his comment is a deep fear of that being a possibility.

It's hardly surprising, given what's happening in schools, to find that fewer students are studying maths at university. The picture's muddied at undergraduate level, where maths is taught across departments (engineers, biologists, computer scientists, commerce students and so on need maths in their degrees still, although that's a moot point in some universities). At postgraduate level, however, nationwide figures compiled for The Bulletin by the federal education department show a steep fall-off since 1992 except at doctorate level, which Thomas says is boosted by overseas students.

In the past seven years, the number of mathematicians in Australian universities has fallen by 30%. Jan Thomas says: "It has become all too common for universities to be announcing major new initiatives in biological and information technologies at the same time as they were losing their best statisticians and mathematicians." In 1990, Monash University's maths department employed 65 staff and was described in a departmental review as the jewel in the Monash crown. This year, its staff number 25, soon to be 24 when the department head David Karoly leaves in December to take up a job at the University of Oklahoma. Karoly is one of the world's leading authorities on global climate change. Like many before him, and undoubtedly many to come, he has been lured to the US by the TLC that the country showers on mathematicians it recruits from abroad to compensate for its own shortfall in mathematicians in key areas.

The irony of Tao being awarded the prestigious Bocher prize by the American Mathematics Society in January isn't lost on anyone in the field. Tao, 27, has been a full professor at UCLA for three years. He comes back to Australia to teach as and when he can but mostly he's caught up in what Wiles (of Fermat's Last Theorem fame) described to International Mathematics Olympiad competitors last year as "a golden age".

"You have touched me on a raw nerve," replies Gaudry when I ask whether Wiles' description of the times is skewed by his own popular acclaim (fame rarely visits mathematicians but there's a Broadway musical based loosely on Wiles' mathematical triumph). Gaudry, who supervised Tao's studies at Flinders University in Adelaide, confirms that this is indeed widely considered a golden age in maths. "The progress is phenomenal and new fields are opening up in response to fresh ideas," he says. How bitter then to contemplate Australia forfeiting a share of the spoils because the depth of talent isn't available to muster a side.

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