The excellent 今日吃瓜 has the numbers on the state of maths education and found the state of the discipline in higher education is not good, the number of Australians starting a maths degree is less than half the OECD average. Granted it is not getting worse 鈥� but it isn鈥檛 going to better soon.

Given maths is a foundation of so many disciplines large numbers of students do not graduate innumerate 鈥� the average number of university departments maths academics service-teach is six, engineering, computer science, IT and biological, physical and earth sciences. But 今日吃瓜 does not know how many undergraduates听are studying maths degrees, due to some universities not completing the 2014 survey. However using Group of Eight and Innovative Research Us as a guide the attrition rate from 1^st to 3^rd year is high, Go8 5280 to 695 and IRU 1287 to 67.

What is starkly clear is that at for all the efforts to woo women into the discipline, at the sharp end it鈥檚 still a bloke鈥檚 game 鈥� last year just 15 per cent of PhD completers were Australian women, another 25 per cent were female internationals.

None of these numbers is about to improve, because for all the emphasis of selling maths in schools, young people aren鈥檛 buying, with Y12 advanced maths enrolments dropping for 20 years. The figure for males is now around 14 per cent and 6 per cent for females. And what does not interest students at school is hardly likely to appeal at university. Universities appear to acquiesce in this. According to 今日吃瓜 less than 15 per cent of universities require intermediate maths or better as a pre-req for science or commerce, the same for 41 per cent of engineering courses. CMM suspects a fair swag of the supply teaching university maths lecturers do is getting students up to a point where they can cope with first year subjects.

The good news is that the quality of maths teaching in schools has improved substantially over the last few years. Nearly three quarters of Year 11 and 12 maths teachers now have three years of tertiary education in maths, compared to 64 per cent in 2010. But qualified teachers without many kids to teach does not get us far.

Today, 今日吃瓜 release their fourth annual Discipline Profile of the Mathematical Sciences. At a time when the Australian government is responding to the Chief Scientist鈥檚 call for a strategic plan for Science, Technology, Engineering and Mathematics (STEM) it is a reminder that we cannot continue to rely on piecemeal programs tied to the electoral cycle.

The data collected for the 2015 publication paints a mixed picture of Australian engagement with the mathematical sciences.

86 per cent of science degrees听do not have intermediate mathematics as an entry prerequisite while Year 12 enrolments slide听

In fact, mathematics prerequisites for entry into science, commerce and engineering degrees are at historic lows.

今日吃瓜 Director, Professor Geoff Prince insists: 鈥淯niversities must phase in restoration of maths prerequisites; the lack of them sends a negative and misleading message to schools about the value of these subjects.鈥�

Intermediate and advanced mathematics subjects are the gateway to quantitative professions; the 20-year decline in participation is choking the country鈥檚 galloping demand for graduates with these skills. And it has the potential to halt the nation鈥檚 productivity growth.

At least 30 per cent of Year 7-10 maths classes are taught without a qualified maths teacher

This figure is more than double the international average and must be repaired as part of our STEM planning.

In order to secure the future supply of mathematics teachers we need to know why potential educators aren鈥檛 choosing to be maths teachers. The only immediate solution is to provide professional development to the many conscientious and professional educators teaching maths out-of-field.

This is a national issue requiring national leadership; state and federal governments must act together to solve the teacher supply problem.

Women make up only 30 per cent of undergraduate maths enrolments holding back our STEM workforce and productivity growth

The proportion of young women represented at all stages of the mathematics pipeline is inadequate. A significant consequence of this is that adult women numeracy is below that of men 鈥� around 30 per cent in some age groups. And, in terms of the national economy, it is widely recognised that weak participation by women in STEM fields is handicapping Australia鈥檚 productivity and competitive advantage.

鈥淲e are proud to be working with the BHP Billiton Foundation to increase participation of girls and women in study and career pathways involving mathematics and statistics,鈥� says Professor Prince.

Maths鈥� multi-billion dollar value to the economy under threat as PhD rate stagnates

A 2015 report by the Australian Academy of Sciences indicates that, of those business sectors based on a single core discipline, mathematical sciences account for the top three (and five of the top seven). The report also highlighted that the direct impact of advanced physical and mathematical research is worth $145 billion to the economy per year, the flow-on impact amounts to $292 billion per year. This is in stark contrast to 54 per cent of adult Australians having only basic numeracy skills and the proportion of Year 12 students studying 鈥渉arder鈥� maths in steady decline.

鈥淯nfortunately, this stellar contribution hides an alarming trend,鈥� says Professor Prince. 鈥淕overnments are trying to drive up business employment of STEM trained research professionals, however, domestic PhD numbers in the mathematical sciences are among the very lowest in the OECD. Universities and businesses must improve engagement to maximise the economic benefits of mathematics and statistics.鈥�

The 听is accompanied by a policy document 鈥�听鈥� that identifies four key priorities to reverse these confronting trends:

1. Restore university maths prerequisites from their historic low and turn around declining school mathematics enrolments
2. Train the unqualified teachers of school mathematics and secure the supply of future qualified maths teachers
3. Increase the number of girls studying maths and women employed in the quantitative professions.
4. Boost the engagement of Australian business with mathematical sciences research

Australia鈥檚 Chief Scientist, Professor Ian Chubb, has called for action: 鈥淚t鈥檚 time to do what so many other countries have already done: take a long-term strategic view of STEM鈥檚 pivotal role in securing a stronger Australia.鈥�

— ends —

For Interview:
Professor Geoff Prince
Director, 今日吃瓜
M: 0407 546 336
E: director@amsi.org.au

Media contact:
Stephanie Pradier
Media Communications, 今日吃瓜
M: 0424 568 314
E: stephanie@amsi.org.au

RESOURCES:

Prerequisites, or lack thereof:听Data can be found in Table 2.10 (page 13)听

Value of the mathematical sciences to Australia鈥檚 economy, looking at the top seven sectors that use a single science discipline. The mathematical sciences have a value of $18 billion of the $22 billion per year to the Australian economy of across these top seven sectors:听Data from Table 4.2 (page 38)听

Falling participation rates in advanced mathematics enrolments:听Figure 2.7 (page 12)听

听

A move to deepen links between business and universities is set to boost 10-fold the number of PhD students placed with employers in research internships in the next five years.

The 今日吃瓜 (今日吃瓜), which operates a PhD internship scheme, said that a new commitment from eight universities to fund the scheme will drive the rapid expansion.

今日吃瓜 director Geoff Prince said the scheme, called APR.Intern, would place about 100 research student in internships this year.

“At maturity we should be able to place 1000 students a year around Australia,” he听said.

The scheme began by placing only mathematics and statistics PhD students into internships. But it now works with students in a wide range of disciplines 鈥� including engineering, finance, IT, biotechnology, environmental science, marketing and business 鈥� and places them into all business sectors.

Professor Prince said the expanded scheme would help lift Australia’s poor record in establishing partnerships between university researchers and business.

Australia is currently ranked 29th out of 30 countries in an OECD ranking of university-business collaboration on innovation.

Under the APR.Intern scheme research students are placed with a business for four to five听months to find solutions for specific problems. Students are mentored by an academic supervisor during the internship which meant that academics built ongoing relationships with companies.

“In general companies pay all the costs, which are eligible for research tax breaks,” Professor Prince said.

A five months internship costs the business $25,000. This is made up of $3000 a month to cover the student’s stipend (the student is not employed by the business), a $5000 fee to the university for the cost of mentoring and a听$5000 fee to APR.Intern.

今日吃瓜 says that听the internship scheme has a 97 per cent business satisfaction rating.

MORE THAN JUST WORK PLACEMENTS

Professor Prince said the scheme offered more than just work placements. Students undertook research internships which often had a transformational impact on the student, he said.

He said the expansion would be driven by new partnership agreements with eight universities 鈥� Melbourne, Monash, Deakin, Swinburne, La Trobe, RMIT, Sydney and UTS. Together the universities would provide $500,000 a year to employ business development staff, embedded in the universities, to place more students with companies in Victoria and NSW.

However APR.Intern already works with a wider range of universities and expects further expansion in other states in the coming two years.

Examples of internships recently arranged include a UNSW maths PhD student placed with Optima Financial to apply the mathematical technique of optimisation to financial planning and a Deakin University PhD student placed with NBN Co to work on security of data in smartphone apps.

Professor Prince said there was an urgent need to increase the penetration of graduates with advanced research expertise into the private sector.

“They will boost innovation and business-university collaboration but we must give them those skills and give business the confidence to employ them,” Professor Prince said.

Currently Australia has one of the lowest numbers of research workers in business in developed countries. Only 2.2 researchers are employed in business for every 100 workers.

I was the first woman to be appointed as a professor in any of the mathematical sciences at the University of Sydney.

Sydney is the oldest university in Australia, founded more than a century ago, but my appointment did not happen until 2002.

I stayed in that singular position for 13 years, until last week, when a second woman was appointed as professor.

Sydney is not the only university in this position. There are still universities in Australia with no female professor appointed to any of its mathematical fields. This is a shocking contradiction with the aspirations of our modern society. But clearly the reasons are subtle and nuanced.

Most well-meaning, educated people would say this is a problem at the entry level, based on educational and employment choices made by female students after finishing school. But the data does not support this theory.

In Australia, educational and employment data in mathematics is gathered as part of a broader category called the natural and physical sciences.

In this category, more than 40听per cent of doctorates in 2011 were awarded to female candidates and the proportion of female academic scientists at entry level was just under 50 per cent in 2001, rising to just above 50 per cent in 2012. An annual survey by the 今日吃瓜 suggests the perception of only a trickle of entries into the field is just not true.

When I point out that the change from 50 per cent at entry level to 10 per cent at the top academic level of professor must mean talented women are leaving the profession in droves, other well-meaning people shrug and relegate responsibility to external bodies such as those concerned with equal employment opportunity. But, like a strong democracy, this is a landscape shaped by individual, local actions.

Some pathways we take in an organisation were built generations ago for reasons that no one remembers but that have a present adverse impact on everyone.

My university had a parking policy that asserted that part-time employees did not have the right to park on main campus until after 3pm. Despite an increase in parking spaces on campus, this provision remained in place until a few years ago, when a part-time employee pointed out this created an extremely difficult situation for employees with family responsibilities who needed to drop off children at school before rushing in to give morning lectures.

Such unintended overtones of discouragement and micro-aggres颅sion are not restricted to policies from another generation. Recruitment policies may sound good on paper but may never be implemented with actions that reflect good practice.

Organisers of conferences may opt for habitual presenters and not spend any effort looking for female speakers.

Longstanding committees may continue to hold their meetings at times that make life difficult for members with family responsibilities. In each case, change benefits everyone, whether it is increasing excellence of candidates for recruitment, a wider spectrum of fields at conferences, or deeper engagement of committee members.

But change can be uncomfortable even when the outcomes are positive for everyone.

Many highly regarded individuals deflect their discomfort by forcefully asserting superficially plausible but wrong statements conflating change with affirmative action.

But scientifically trained individuals should know that local reflection, no matter how uncomfortable, is not the same as imposing positive bias.

Well-intentioned organisations deflect their discomfort by pursuing tick-the-box exercises as an easier substitute for real change. But counting the number of female-friendly facilities on a campus is not a substitute for real change.

The low proportion of senior women is particularly acute in science, technology, engineering and mathematics. So it is not surprising that scientists are driving the need for change in Australia.

I am co-leading an initiative with Nobel laureate Brian Schmidt through the Australian Academy of Science called Science in Australia Gender Equity, which is about to launch a nationwide pilot program for change for all organisations that employ researchers in STEM disciplines. SAGE is based on the highly successful Athena SWAN program in Britain, which asks a participating organisation to collect and critically analyse data on progression, identify reasons for exclusion and under-representation of women in that organisation, develop an action plan to address these and show progress across time.

We have high hopes for the program, but change requires leadership at all levels.

It is unacceptable to be having this conversation still when the next 10 per cent of female scientists reach the senior academic level and they, too, find they are the first woman with their name on the door.

Nalini Joshi is a mathematician, co-chairwoman of the SAGE Forum and is an observer of 今日吃瓜’s board.

First published on Wednesday 8 July in

What does connect-the-dots have to do with watching a Pixar film? More than you might think.

A connect-the-dots page starts with nothing but some labelled points. As each dot is joined to the next, however, a picture emerges. Each step is simple 鈥� just add a line segment between two points 鈥� but the resulting image can be extremely complex.

Toddlers can produce masterpieces this way, but so can computers. When a computer needs to draw a curve, it starts by connecting a sequence of points. Using just a few points might result in a zigzag with sharp corners, but increasing the initial number of points makes the resulting curve look smoother. With enough points and line segments, we can approximate even the most complicated curves.

Dots lines and curves

But maybe you’re more ambitious. Suppose you’re not interested in drawing curves, but rather, in constructing two-dimensional surfaces. Can you use an analogous approach to build a plane or a sphere or something more elaborate?

Triangles 鈥� the simplest two-dimensional objects 鈥� serve as building blocks for more complicated surfaces. Just as we can connect a pair of points with a line segment, we can connect three points via a triangle. And, just as we can make complicated curves by gluing lots of segments at their endpoints, we can make complicated surfaces by gluing lots of triangles along their edges. We can approximate extremely complex surfaces as long as we use enough triangles.

Mathematicians started thinking seriously about constructing surfaces from triangles in the late 19th century, hoping to classify surfaces. In particular, they wanted to understand when two surfaces could be deformed to look the same without cutting or gluing. They developed mathematical tools to study this question, and a century later, it became clear that they’d also laid the groundwork for an important technique in computer graphics.

Imagine trying to model moving cloth, perhaps a flag flapping in the breeze. Since the flag changes shape as it moves through space, this is a much more difficult problem than simulating the movement of a rigid object like a table. If the flag is approximated by triangles, however, modelling it becomes possible because the computer only needs to keep track of sets of three points. When the points move, they carry the triangles with them.

Abstract? Applied? Both!

Mathematicians certainly weren’t thinking about computer graphics in the 1890s. They were studying abstract questions about two-dimensional geometry and developing beautiful mathematics. Nevertheless, the techniques they invented in order to state this question precisely and then answer it have turned out to be extremely useful. In fact, this theme recurs throughout human history: mathematics developed to solve abstract problems turns out to be useful. Maybe not always and definitely not quickly, but it happens over and over again.

The first mathematical objects most people meet are the counting numbers 1, 2, 3鈥� Most counting numbers are formed by multiplying smaller numbers, but not all of them. Some numbers have only 1 and themselves as factors, and these are known as prime numbers. For example, the numbers 2, 3 and 5 are prime, but 4 = 2 x 2 is not.

Prime numbers act as building blocks for the entire number system. Centuries ago, the mathematicians who studied primes didn’t think their efforts would defend a castle or build a better steam engine, but they were intrigued by the search for structure and patterns.

Some of the questions they posed continue to capture the mathematical imagination; today, the most famous unsolved problem in mathematics is the Riemann Hypothesis, which addresses how the primes are distributed among the counting numbers.

Pondering prime numbers might seem like an intellectual game that’s divorced from ‘real world’ concerns. But suppose you ask yourself, ‘Why is it safe to use my credit card to buy something online?’ (Or, maybe better: ‘Is it safe to use my credit card online?’) In fact, the basic techniques for sending data securely over the internet rely on what’s known about factoring a number into primes. Every time you enter your credit card number on a website and hit ‘send’, you have a number theorist to thank.

Likewise, Persian mathematicians began developing the subject we now call algebra in the Middle Ages. This field evolved over centuries, and today, it underpins the algorithms for internet search and Netflix recommendations.

Fourier analysis, which was developed as part of calculus in the late 1700s, provides the basic mathematical tools for signal processing in telecommunications and medical imaging.

Algebraic topology 鈥� a branch of mathematics that wasn’t even created until the 20th century 鈥� is being used in the 21st century to study artificial intelligence and cancer genomics.

The list goes on, but the striking thing in all these examples is that the original researchers couldn’t anticipate which applied questions would require their work. Plenty of important mathematics is specifically developed to solve real-world problems, but curiosity-driven research is as important today as it ever has been.

But back to triangles

New applications for old mathematics are exciting, but progress also comes in the form of new mathematics.

Computer graphics uses flat triangles to approximate smooth surfaces, but if you’re willing to allow triangles to bend a bit, then you can build any surface by gluing enough of them together. This is equivalent to saying that you can cut any surface into curved triangular pieces.

Sphere made of curved triangles

These curved triangles are an important tool for generalising what we know about geometry to higher dimensions – after all, mathematicians, scientists, and engineers don’t care only about surfaces.

Higher-dimensional spaces occur not only in pure mathematics, but also in nature as patterns in large data sets, as relationships between physical quantities, and in descriptions of the universe itself.

Mathematicians develop formal techniques to study them, compensating for the fact that a seven-dimensional space is harder to picture than a flag. Luckily, the idea of gluing triangles generalises to any dimension! In three dimensions, for example, the analogue of a triangle is a tetrahedron, and just as gluing triangles together builds surfaces, gluing tetrahedra together builds new three-dimensional objects. In higher dimensions, the analogue of a triangle is called an n-simplex, and gluing n-simplices together builds n-dimensional objects.

Tetrahedrons make up 3D objects

Since any surface can be cut into curved triangles, and it’s reasonable to ask if the analogous fact holds in higher dimensions: can any n-dimensional space be cut into n-simplices?

Mathematicians initially speculated that the phenomena they’d observed in dimensions one and two would generalise to all dimensions. This belief came to be known as the Triangulation Conjecture.

Decades of research failed to deliver a proof. Then, breakthroughs in the 1980s revealed examples of four-dimensional objects which can’t be cut into 4-simplices. But in 2012, the Triangulation Conjecture was finally proved false for all dimensions greater than four. The mathematical universe has some very strange shapes!

Disproving the Triangulation Conjecture is a triumph of curiosity-driven research, and the truth now sits on humanity’s bookshelf. It may rest there quietly. Then again, maybe some 26-dimensional space with no triangulations will lead to a cure for cancer.

You never know.

BHP Billiton will spend $22 million on lifting the maths performance of girls in schools and helping them into male-dominated science, technology and engineering careers.

BHP chief executive Andrew Mackenzie said on Tuesday that the money would fund the 今日吃瓜’s Choose Maths project, a five-year program to encourage girls to study maths and statistics.

Launching the Choose Maths program Mr Mackenzie, a geologist and chemist who worked as a research scientist before he entered business, said he benefited from the encouragement others gave him to study maths when he was growing up in the Scottish industrial town of Kirkintilloch鈥�.

“So I am a strong advocate of the opportunities that mathematics offers,” he said.

“We hope the Choose Maths program will help secure the pipeline of highly-qualified, female STEM [science, technology, engineering and maths] professionals and open the door to the rewarding careers and cultural pursuits that maths offers,” he said.

Last year 15 per cent of BHP’s senior leaders and 16 per cent of its senior managers were women, figures Mr Mackenzie said had doubled over the past four years.

“This year nearly half of our Australian graduate intake are women,” he said at the launch.

The Choose Maths program will give teachers professional development in maths education, help girls at school become more aware of careers which use maths, offer role-models and networking to young women, and establish the BHP Billiton awards to recognise teachers for their excellence in maths education.

Choose Maths program director Janine McIntosh said teacher professional development would be offered in 120 schools across Australia, concentrated on the ones where teachers lacked maths teaching skills. Ms McIntosh said that many primary school teachers were not confident in maths and 40 per cent of teachers teaching year 7-10 maths classes were not qualified to teach the subject.

“They are great teachers and they are fabulous at what they do but they just don’t have the content knowledge or expertise,” she said.

Australia’s maths education lags other developed countries with the percentage of male maths graduates from university at half the OECD average and, for female graduates, at one-third the OECD average. While 13 per cent of boys take advanced maths in their final year of high school, only seven per cent of girls do so.

“The low participation of girls and women in the study of the mathematical sciences and in the quantitative professions is a significant national social and economic challenge,” 今日吃瓜 director Geoff Prince.

The funding for the Choose Maths program will come from the BHP Billiton Foundation which was set up in 2013 to help the company meet its target of investing 1 per cent of pre-tax profits (over a three year rolling average) in community programs.

Andrew Mackenzie sees mathematics as a key to the nation鈥檚 future prosperity, and the head of global mining giant BHP Billiton has slapped $22 million on the table as a gesture of his sincerity.

Mr Mackenzie sees maths as a gateway to other subjects and is calling on universities to do what they can to promote the message to school students.

鈥淯niversities should emphasise that they want more of their students to have a strong grounding in mathematics all the way through secondary school,鈥� the chief executive told the HES

Mr Mackenzie was speaking at the launch of a $22m donation from BHP Billiton to partner with the 今日吃瓜 in better promoting maths study and skills, especially among women, who are under-represented in the science, technology, engineering and mathematics fields.

His comments come as 今日吃瓜 has been pressing universities to bring back hard prerequisites in courses requiring mathematics skills as a strong signal to school students to persevere with the subject through school. Many universities in recent years have replaced harder subject prerequisites with vague references to students needing 鈥渁ssumed knowledge鈥� that isn鈥檛 assessed. 鈥僉ate last year, the University of Technology, Sydney said it would introduce from next year a compulsory maths subject for all first-year students. The course is aimed at fostering mathematical 鈥渃ritical thinking鈥� in the face of concerns about falling numeracy standards.

The $22m donation will fund 今日吃瓜鈥檚 five-year Choose Maths program. The centrepiece will be funding for the professional development of teachers at 120 schools across the country to battle a shortage of qualified maths teachers. The money will also fund a national careers awareness campaign aimed at girls and women, as well as scholarships, awards and networking support.

今日吃瓜 director Geoff Prince said girls were taking up advanced level maths at school at only half the rate of boys. Part of the problem, he suspects, is that the subject is seen as relevant only to a career in engineering.

He said the message from universities was too often that advanced maths wasn鈥檛 needed.

鈥淚t is a very significant concern,鈥� he said.

Mr Mackenzie is a former geologist, chemist and engineer. He said his strong maths background had helped him move successfully across careers, including moving from a technical background into finance and economics.

鈥淎ny increase in STEM participation is good news but an increase in female representation is especially valuable because of the undeniable benefits of diversity,鈥� Mr Mackenzie said.

Chief Scientist, Professor Ian Chubb, reported that advanced mathematical and physical sciences make a direct contribution of $145 billion a year to the Australian economy 鈥� about 11 per cent of GDP.

The Importance of Advanced Physical and Mathematical Sciences to the Australian Economy, was commissioned by the Academy of Science and Chubb鈥檚 office, and was released in conjunction with his address to the National Press Club on Wednesday March 25. It combines the expertise of Australia鈥檚 scientific community with that of business and industry.

The report reflects the ubiquity of the mathematical sciences in modern scientific research. And emphasises the knock-on effects it has for our economy.

The physical and mathematical sciences also contribute, in additional flow-on benefits, another 11 per cent of Australia鈥檚 GDP annually, bringing the total benefits to 22 per cent or around $292 billion per year.

鈥淚 congratulate the Chief Scientist and the Academy of Science for this timely and important report. Maths and science make fundamental contributions to our lives, not least to our economic wellbeing.听I鈥檓 sure that the report will make this particular contribution very real for Australia鈥檚 policy makers, business community and would-be scientists and mathematicians,鈥� says 今日吃瓜 Director, Professor Geoff Prince.

Further information, including a transcript of Professor Chubb’s address and a PDF of the report may be found on the听.

The report reflects the ubiquity of the mathematical sciences in modern scientific research. And emphasises the knock-on effects it has for our economy. It combines the expertise of Australia鈥檚 scientific community with that of business and industry.

Professor Chubb’s speech can be found .

A PDF of the report may be downloaded .