Grants of up to $10,000 are available to support digital collaborative research projects with Asia鈥揚acific regional partner economies for Australian early- and mid-career researchers.

Learn more from the .

In a month where we have seen concerning results in Australia鈥檚 schools and higher education systems provides a vivid and useful reminder of the crucial role mathematics and statistics play in every aspect of life.

This free online resource has been the standard 鈥済o to鈥� for 18 years; it gathers together advertised job positions that require skills in the mathematical sciences, across a scope of sectors: careers in health, business, agriculture, energy and telecommunications are relying more and more on the analytical skills developed in university level subjects in the mathematical sciences.

Federal Education Minister Christopher Pyne, who has written an introduction to this year鈥檚 edition, insists that Australia鈥檚 ability to innovate and compete in the global economy will require a STEM literate nation.

鈥淭his publication demonstrates there is an extensive array of career choices available to graduates in mathematics fields,鈥� says Minister Pyne.

鈥淢ore broadly, these abilities also help us to participate as active citizens within our democratic system,鈥� he concludes.

ALL SIDES OF POLITICS

今日吃瓜 Director, Professor Geoff Prince says without making the community aware of the breadth of roles available to those studying some form of mathematics, high school participation rates in intermediate and advanced mathematics will continue to wane.

Senator Kim Carr, Shadow Minister for Higher Education, Research, Innovation and Industry, echoes Minister Pyne: 鈥淭hree out of four of the fastest-growing occupations in our economy require some level of literacy in science, technology, engineering and mathematics.鈥�

Senator Penny Wright of the Australian Greens puts her vote with the numbers too: 鈥淚t鈥檚 not just in parliament that being able to 鈥榙o the numbers鈥� is valuable. Australia needs these skill sets to meet the challenges of this century,鈥� she says, 鈥渁nd I commend 今日吃瓜 for their work in highlighting the opportunities they bring.鈥�

Professor Prince explains that Australia鈥檚 job market landscape is shifting and demand for mathematical science skills continues to outstrip supply: 鈥淚t is great to have endorsement across the political spectrum for 今日吃瓜鈥檚 work on this.鈥�

Maths Ad(d)s available online:

— ends —

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

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

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

The partnership looks set to deliver the federal government鈥檚 current agenda on the commercialisation of publicly funded research with every internship creating a collaboration between academia and industry 鈥� ensuring a work-ready PhD student and a significant outcome for the industry partner.

Placing over 130 postgraduate students into industry 鈥� across all study disciplines and business sectors 鈥� APR.Intern is Australia鈥檚 leading PhD internship program, delivering research solutions for challenges facing business. The student receives a stipend and is supported by an academic mentor throughout the 4-5 month project. Meanwhile, industry is reaping the benefits responding with a 97 per cent business satisfaction rating.

鈥淲ork-readiness of our PhD students, and the links between industry engagement and national productivity, are critically important matters for this country. The APR.Intern program is one such shining example,鈥� says Professor Ian Chubb, Chief Scientist for Australia. [1]

The co-investment partnership in detail

The Victorian cluster includes the University of Melbourne, Monash University, Deakin University, Swinburne University, La Trobe University and RMIT University. And, in the NSW cluster the University of Sydney and University of Technology, Sydney.

鈥淭he strategic partnership will enable APR.Intern to greatly expand. By embedding business development officers within these Victorian and NSW universities we will develop a wider range of industry connections for the benefit of our PhD students,鈥� says Dr Hannah Hartig, National Program Manager, APR.Intern.

Further expansion into other Australian states and territories is planned for 2016 and 2017.

鈥淎PR.Intern provides the match-making so often needed in industry-academic collaborations and our solutions to sore points, such as intellectual property rights, are popular with industry partners,鈥� says Dr Hartig.

鈥淭he nation that goes all-in on innovation today will own the global economy tomorrow,鈥� says Barack Obama, US President. [2]

Continued national dialogue laments the lack of industry-university collaboration in Australia and the future impact this will have on our global competitiveness. [3]

Australian Industry and Science Minister Ian Macfarlane recently stated: 鈥淟ifting the rate of collaboration between industry and research is essential to maintaining Australia鈥檚 economic growth. In order to sustain our prosperity, we have to build on our successes in innovation and focus on our areas of competitive strength to keep pace in the rapidly evolving global economy.鈥� [4]

Australia ranks 29 out of 30 in the OECD in terms of the proportion of businesses collaborating with universities. This is in stark contrast to Australia being ninth in research output per capita amongst OECD nations. Australian businesses that engage in collaborative innovation with research organisations are three times more likely to gain productivity growth 鈥� so why this disparity? [4] [5]

鈥淲e must increase the penetration of Australian 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,鈥� says Professor Geoff Prince, 今日吃瓜 Director.

This co-investment partnership is timely given the National Strategy for Work Integrated Learning led by the Australian Collaborative Education Network (ACEN).[5] There are few industry-based work-integrated learning opportunities for PhD students, especially those cohorts not associated with industry-supported initiatives such as Cooperative Research Centres or Industrial Transformation Training Centres.

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AUSTRALIA鈥橲 PERFORMANCE IN AN INTERNATIONAL CONTEXT

Researchers in business and higher education
OECD scorecard shows that out of the developed countries Australia has one of the lowest numbers of researchers in business 鈥� 2.2 researchers are employed in business for every 1000 workers. The proportion in the smaller countries of Sweden, Denmark and Finland are more than three times that of Australia.

SOURCE: Office of the Chief Scientist, Occasional Paper Series 2012 — Alan G. Pettigrew ‘AUSTRALIA鈥橲 POSITION IN THE WORLD OF SCIENCE, TECHNOLOGY & INNOVATION’.

Business collaboration with higher education and public research agencies
Less than one in two Australia firms identify themselves as innovators. And only 4 per cent of our large firms collaborate with higher education and research agencies 鈥� that ranks us at 33 (out of 33) in the OECD. For Australian SMEs we rank equal with Brazil at 32.

SOURCE:听OECD, based on Eurostat (CIS-2010) and national data sources, June 2013.

A transcript of the interview is below and you can download a

PAUL TURTON: According to Professor Ian Chubb, Australia鈥檚 Chief Scientist, it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. The Chief Scientist will be speaking at a public meeting at Newcastle City Hall at 4.30 this afternoon. He joins us now to whet your appetite.

Professor Chubb, good morning. How are you?

IAN CHUBB: Morning Paul, I鈥檓 well. How are you?

PAUL TURTON: Fantastic thanks. Have we taken our eye off the ball in regard to science a little bit?

IAN CHUBB: Yes.

PAUL TURTON: So what should we do? Obviously the community鈥檚 approach to those key subjects needs to change and I guess that鈥檚 part of what you鈥檙e doing.

IAN CHUBB: Well, it is. I think the world around us is changing very rapidly and when you look at that world around us you see science well and truly embedded in the core of our lives. The better we are able to do science, or the better we鈥檙e able to understand at least how science works, then the better we鈥檒l be for it. When we have to make choices as citizens or when we鈥檙e trying to encourage political leaders to make decisions, the better informed the decision the better the outcome. And the better we understand the methods of science, the process of science broadly in the community, the better those outcomes will be.

PAUL TURTON: We鈥檙e told all the time via the popular art forms of this changing world, whether it鈥檚 the Jetsons or the Orwellian future or sci-fi at its most extreme, we鈥檙e getting clues all the time about what the future might hold for us and some of those predictions are already playing out. Are we totally embracing the concept? Do we get it?

IAN CHUBB: Well, not as well as we should. I think there鈥檚 been a rhetorical commitment for quite a while but the reality is we鈥檝e got to get some action now and the world, as I said earlier, is moving away from us. In the United States and the United Kingdom, most of the countries of Europe and certainly many of the countries in our region, they鈥檙e all basically focusing on a two-pronged agenda. One is to make sure that the level of science education broadly available across the community is quite high, so that when people finish school for example, even if they go on to be lawyers or accountants or farmers or miners, they have some understanding of how science works. So it鈥檚 increasing the level of science literacy within the community. But embedded within that of course you鈥檝e got the people who want to be scientists and who want to work as scientists, whether in a laboratory in a white coat or in another part of the economy, but using the skills that they鈥檝e developed through education in science to apply to whatever that industry might be.

PAUL TURTON: So how much of the change for the future is going to come from a different mindset? In other words just changing the way we think about how jobs will play out in the future, the fact that a lot of stuff is going to be done by machines for example, is it simply a matter of changing our mind and all of the little things will then follow?

IAN CHUBB: Well I think probably yes. I think it鈥檚 a deeply cultural thing. How many people have you spoken to in the last few months who have been virtually proud to say that they don鈥檛 understand mathematics or they鈥檙e no good at mathematics or they don鈥檛 understand science? Try saying that about Shakespeare or Renoir and there鈥檚 a completely different response.

I鈥檓 not saying this is a peculiarly Australian thing, I think it happens in many countries in the world. It鈥檚 just that most of those countries are now doing something about it, so they鈥檙e supporting their teachers better, they鈥檙e preparing their teachers better, they鈥檙e encouraging their teachers, they鈥檙e recognising the central importance of the teaching profession in all this. And I don鈥檛 think we鈥檝e done that yet, or not nearly enough anyway.

PAUL TURTON: Enrolments in the science courses tend to be down in our schools. I know depending on variations there can be said to be a recovery of sorts underway at the moment. They just seem to have lost their glamour though. Are we selling our sciences long enough to young people?

IAN CHUBB: I don鈥檛 think we are, and I don鈥檛 think we鈥檙e making them interesting enough when they do study them at school. I鈥檝e been saying for a long time now that science has got to be taught inspirationally and the best way to teach it inspirationally is to teach it the way it鈥檚 practised. Science in practice is awesome. If you鈥檙e actually an experimental scientist and you design an experiment and it goes wrong you learn a lot from that; it鈥檚 not that it goes wrong, it just informs you differently. You鈥檝e got a mix of responses as a scientist. But to teach it blandly out of a textbook I think doesn鈥檛 actually give the student that sense of excitement that there is when you suddenly understand something better, even if you don鈥檛 go on to be a scientist, or you do something that gives you some insights into something that wasn鈥檛 known before. All of those things are just mind-bogglingly awesome, so that鈥檚 how it ought to be taught. In order to do that we鈥檝e got to support our teachers, we鈥檝e got to recognise the importance of teaching and we鈥檝e got to make sure that we give them the maximum opportunity to draw the talent out of these students.

PAUL TURTON: Unfortunately you can鈥檛 have a Brian Cox in every classroom. Ironically now there鈥檚 never been more media focusing on science and nature. You look at the availability of audiovisual materials for young people and there鈥檚 plenty of material out there, so it鈥檚 not as though they鈥檙e not being exposed to the opportunities.

IAN CHUBB: Well that鈥檚 true and then they go back into a classroom where, in Australia for example, the 今日吃瓜 in Melbourne estimates that something like 40% of teachers teaching mathematics are out of field in early secondary school. So it鈥檚 hard for those teachers to encourage the students who might go off and see something or, watch Brian Cox in the evening, go back into class and I think come back to earth. So it is, I acknowledge, a very complex issue but the point is that we human beings tackle complex issues. It takes the will to do it.

PAUL TURTON: Newcastle has reinvented itself a number of times and there鈥檚 been a fair bit of innovation associated with the Hunter region over the years. How well are we placed in relative terms to move forward with what you would describe as a generation of ideas, or creating an environment where ideas proliferate?

IAN CHUBB: Well partly Paul I鈥檓 going up there to learn. I鈥檝e been told, and today I鈥檓 going to be able to see things that are being done. But from all that I鈥檝e seen and read and heard so far then I think Newcastle, the Hunter region, has taken some really good steps.

One of the things that we have to learn in Australia is that we can learn from the good things that are being done in various parts of the country, rather than quarantining them to one particular part because somebody with some spark and energy and drive and commitment has created a particular sort of environment. We need to make sure that we can learn from that and translate it across Australia. There are lots of good things being done in various parts of Australia but they鈥檙e relatively small-scale and relatively local in influence. So it鈥檚 really a question for me today of finding out, learning a lot, meeting a number of people and then thinking about how much of this could be part of a federal government push to improve science and science education in Australia.

PAUL TURTON: Professor Chubb, good to talk to you and best of luck with all of your meetings today.

IAN CHUBB: Thanks very much Paul.

PAUL TURTON: Professor Ian Chubb, Australia鈥檚 Chief Scientist, in the Hunter for a variety of meetings including a public lecture at Newcastle city hall at 4.30 this afternoon. That鈥檚 almost full, so if you鈥檇 like to be there you鈥檒l need to make a booking.

This year, in conjunction with ANZIAM, 今日吃瓜 brings Professor Michael Shelley, New York University, to Australian shores. He founded the Applied Mathematics Laboratory at the Courant Institute and his interests and research look into how structures move and interact with fluids.

Nature has a thing or two to teach us about evolution

鈥淢y tools are mathematical modelling, simulation and analysis,鈥� Michael says. And, he draws his inspiration from the natural world 鈥� flags flapping in the wind, snakes slithering underfoot and bacteria swimming through baths.听Would you ever associate flapping flags and renewable hydroelectricity?

鈥淢y theories on flags influenced engineers who design flapping devices to extract energy from flowing water. And my modelling of 鈥渢urbulent鈥� bacterial baths has helped biophysicists understand that how bacteria swim 鈥� by turning their flagellae 鈥� can have a huge effect on collective behaviour and gave new theoretical tools for studying other more complicated problems in biology,鈥� says Michael.

By working on understanding natural phenomena, Michael explains, groundwork is being laid for others to work on problems of higher complexity. Innovation of this kind requires collaboration across many fields of research such as mathematics, biology, physics, engineering and chemistry.

鈥淧eople are at the core of knowledge transfer,鈥� says Professor Geoff Prince, 今日吃瓜 Director. 鈥淎nd now, more than ever, innovation across multiple disciplines is essential for Australia to remain competitive in the global economy.鈥�

Innovation walks on two legs

As global economy woes become more profound investing in innovation and promoting the importance of collaboration among STEM (science, technology, engineering and mathematics) fields is necessary.

Each year 今日吃瓜 supports the visits of 50 international academics to Australia. This equips the brilliant young minds of Australian research with the tools and the knowledge to extend their research capability and to do innovative and exciting things.

Exposure to state of the art research, while networking with future colleagues can only lead to clever people, a clever country and a strong economy.

— ends —

Disruptive shifts emanating from globalisation and emergent technologies are forcing a rethink of traditional approaches to teaching and learning and, importantly, PhD supervision in Australia.

A perceived lack of 21st century skills has resulted in reluctance by industry and government to employ PhD graduates. These forces are also flaming a debate in Australia between industry, business and the higher education sector about the work-readiness of graduates. A reconceptualisation of supervision pedagogy is therefore considered critical by those in government and industry.

Generally, the work-readiness debate has focused on undergraduate education; however, it is now broadening to encompass Higher Degree by Research, or HDR, training. In a speech at the 今日吃瓜, or 今日吃瓜, Accelerate Australia Conference in 2013 Australia鈥檚 Chief Scientist Professor Ian Chubb argued that, for Australia, its universities and industry the work-readiness of HDR graduates is a 鈥榗ritically important鈥� concern.

According to Chubb, through the HDR process graduates develop 鈥榓nalytical, creative, independent and driven personalities鈥�. However, he lamented, industries in Australia do not want to employ them. The 鈥榦ld-style apprenticeship model鈥� of PhD supervision is no longer fit for purpose.

Chubb said time needed to be given to develop additional skills to 鈥榟elp prepare graduates for multiple opportunities鈥�. To address this, Chubb proposed HDR training be restructured to include a wider set of skills.

Why this matters

In Australia, as in other knowledge economies, HDR graduates are now just as likely to take up positions in government, industry and non-government organisations as they are to take up posts in universities. A recent survey suggests around 25 per cent of Australian HDR graduates find work in universities.

Globalisation is changing the face of employment. Industry and business require more graduates with 21st century skills such as sense-making, computational thinking, cognitive load management and social and cross-cultural intelligence and competency.

The authors of the Australian Group of Eight universities discussion paper, The Changing PhD (2013), observe that other desirable skills include: the ability to formulate and solve interdisciplinary problems; sophisticated approaches to research management and understanding of research impact; and the ability to communicate and collaborate within the 鈥楾riple Helix鈥� of university, industry and government in activities that traverse national borders 鈥� all essential in a globalised market place and super complex world.

The same skills are likewise required in the higher education sector with universities subject to the same forces as industry. As universities internationalise, 鈥榯raditional academics鈥� encounter increased mobility and cultural and linguistic diversity for which they are largely unprepared. How this is addressed merits consideration.

In their 2009 paper, Graduate Attribute Development and Employment Outcomes: Tracking PhD graduates, Catherine Manathunga and colleagues reported that many PhD graduates felt their training had not adequately prepared them for postdoctoral employment. One area of dissatisfaction centred on global and intercultural skills. Global connections require a global mindset and intercultural skills; neither is specifically developed in HDR training.

The 2011 Australian Government Department of Innovation, Industry, Science and Research report, Research Skills for an Innovative Future, emphasises the importance of these skills in Australia where 鈥渢he 鈥榯yranny of distance鈥� is an ever present reality鈥� as international experience and connections are highly instrumental in developing and preserving professional networks and enhancing the impact of research鈥�.

Addressing the global or intercultural dimensions of HRD training matters because, irrespective of career trajectory, HDR graduates need to engage in 鈥榖order-spanning鈥� collaborations with a diverse range of actors across the globe. In other words, they must be able to ethically engage with, and in, an increasingly interconnected world, without borders encumbering them.

Reconceptualising the supervision

Within the Australian context, where HDR students do not generally undertake coursework, supervisors are particularly well-placed to influence and shape the skills and dispositions of their students.

Manathunga and her colleagues have questioned the efficacy of centrally-administered programmes that exist outside of the supervision process which do not relate to the students鈥� research interests and do not recognise and capitalise on the candidate鈥檚 pre-existing abilities.

They concluded that any central, generic programmes must be supplemented with 鈥榓 more tailored process鈥� 鈥� one that is most effectively developed within the supervisor-student relationship, where opportunities for highly effective, just-in-time, experiential, reflective learning abound.

In our work with internationalisation of the curriculum, or IoC, we have come to understand the importance of engagement in approaches to academic professional practice. Internationalising the curriculum is a transformative process 鈥� for academics, as well as students 鈥� because it calls for a critique of a discipline or field鈥檚 paradigmatic hegemon, traditional practices, one鈥檚 personal or cultural values, behaviours and agency.

This is equally true of HDR supervision practices, which Fazal Rizvi in the Routledge Doctoral Supervisor鈥檚 Companion observes, often fail to harness the potential of mutual learning between students and supervisors from differing cultural backgrounds.

Lessons learned from internationalising the curriculum

It is critically important to intellectually engage supervisors in the processes of reflecting on and changing aspects of their supervision pedagogy.

Supervisors 鈥� like most academics 鈥� are somewhat resistant to changing pedagogical practices such as supervision because of perceived threats to academic values, ways of working, academic freedom, the primacy of disciplinary knowledge and loss of control over one鈥檚 academic practice.

How they enact their role in the training and development of students and construct their pedagogy is further influenced by the centrality of the discipline in shaping the dispositions of both supervisors and candidates and the possibilities and limitations for training offered in differing institutional contexts, as Manathunga and her colleagues noted in their 2009 paper.

In Jillian Hamilton and colleagues鈥� Good Practice Report: Postgraduate research and coursework degrees, funded by the Office for Learning and Teaching, the need for professional development for supervisors, underpinned by pedagogical principles, rather than compliance was reported as critical.

The report suggests using contextually targeted exemplars of good practice as well as discipline-level and informal mechanisms for 鈥渃apacity building at local levels through distributed leadership models that enable dialogue, communities of practice and peer mentoring鈥�.

This mirrors the approach to professional development advanced by Professor Betty Leask in her Australian Learning and Teaching Council Fellowship, Internationalisation of the Curriculum (IoC) in Action, wherein academics are placed at the centre of a context-sensitive, evidence-based, cyclical, participatory, reflective, ongoing process of continuing professional learning.

To successfully engage academics in challenging propositions such as reconceptualising the pedagogy of supervision, it is vital they are provided with safe, structured spaces for guided reflection on and review of current practices; good facilitation, rather than direction; resources that prompt critical debate; a situated approach to develop communities of practice, together with opportunities to engage in critical inter-disciplinary spaces; active involvement of discipline leaders; and meaningful goals for participating academics.

In this way, they may move closer to addressing the concerns of Chubb and those in government and industry by producing HDR graduates with the broader skills necessary for engagement inand with the world of today and tomorrow.

Craig Whitsed is a senior lecturer at the Centre for University Teaching and Learning at Murdoch University in Perth, Western Australia. Wendy Green is a senior lecturer in learning and teaching at the University of Tasmania.

What may seem like an abstract study today may end up being part of the cure for cancer tomorrow or new wi-fi technology in five years.

On 29 June, Senator Bridget McKenzie will open the 11th annual 今日吃瓜 Winter School, at The University of Queensland in Brisbane, reminding us of the importance of theoretical mathematical research — that beautiful mathematics often turns out to be useful mathematics.

Mathematicians in the 1860s were not thinking about computer graphics when studying two-dimensional differential geometry. And in 1822, how could Joseph Fourier have known his research into heat flow would transform the way we process, store and transmit information. This led to a transformation in the way we live as profound as that caused by the Industrial Revolution. It has also resulted in huge advances in medical diagnostic therapies such as MRI and PET.

As in the 1800s, humans today cannot see into the future; we cannot begin to imagine the infinite possibilities discoveries in fundamental mathematics may have in centuries to come.

The famous astronomer and polymath Galileo Galilei said that the book of nature is written in the language of mathematics. So, by developing an understanding of symmetry, structure, geometry and other mathematical constructs we may be able to reveal the patterns of nature.

Einstein鈥檚 1915 theory of general relativity asserted that the presence of mass distorts the geometry of space and time in a way described by the mathematics developed by Bernhard Riemann sixty years earlier. A critical experimental test of this geometrical theory of gravity required the occurrence of a solar eclipse.

While the development of physics and mathematics may proceed along different paths, each fundamental theory in physics has a corresponding specific mathematical structure, for general relativity this is Riemannian geometry and for quantum mechanics it is the Hilbert space.

These descriptions of nature are works of mathematical beauty and affect our everyday lives. We couldn’t decode the human genome, build aeroplanes or have millions of people talking on their phones across the world simultaneously without mathematics.

A Winter School on Algebra, Geometry and Physics to grow tomorrow鈥檚 Einsteins.

The 今日吃瓜 Winter School gives Australian students the chance to expand their skills in the mathematical sciences and build collaborative networks with other students and early career researchers. They will also hear from leading international experts from USA and Canada as well as domestic experts from across the nation.

The school will also present a Women in Maths evening designed to highlight the contribution of women in mathematics and provide a forum for discussion of career paths.

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The University of Queensland will hold 今日吃瓜’s Winter School from 29 June – 10 July 2015
Further details:
Full speaker list:

WOMEN IN MATHS EVENT:
Thursday 2 July, Science Learning Centre 5-7pm

PUBLIC LECTURE:
The Glass Bead Game
Tuesday 7 July, The Edge, Queensland State Library, 6pm
Professor Arun Ram, University of Melbourne

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.