What will the mathematical science landscape look like in 2040? Who will teach, what will be taught and how it will be taught?

These pertinent questions were raised by one of South Africa’s most respected mathematicians, Professor Loyiso Nongxa (left), the current Chairperson of the National Research Foundation (NRF) and a former Vice-Chancellor and Principal of the University of the Witwatersrand.

As a keynote speaker at the 5^th Annual Diagnostic Mathematics Information for Student Retention and Success (DMISRS) Symposium, held in Cape Town from 5 to 6 September, Professor Nongxa addressed the topic South African Mathematical Sciences in 2040. He advocated for new ways of looking at the world of mathematics: more collaboration across mathematical specialisations and greater engagement across disciplines. 

The need for a fresh look at mathematics was echoed by Associate Professor Kasturi Behari-Leak, Dean of Univeristy of Cape Town’s Centre for Higher Education Development (CHED) who opened the symposium themed What does it take to teach Mathematics for and in higher education? This event, that has drawn 117 participants since 2018, takes place in collaboration with Universities South Africa’s Community of Practice for the Teaching and Learning of Mathematics (TLM CoP).

“The move away from locating the problem in students and refocusing attention on the systemic challenges of the maths curriculum, often invisible, is notable through the DMISRS Project,” Professor Behari-Leak said, adding that the DMISRS Project was also bringing to the fore, interventions being explored to address the challenges in the teaching and learning of mathematics.  

For context: What is the DMISRS Project?

DMISRS is a national collaborative project that is analysing the curricula of first-year mathematics courses in Higher Education to establish how best to address students’ needs through curriculum integrated support initiatives, including blended learning. The Project is an outcome of a task assigned to the Centre for Educational Assessments (CEA), in 2018, to devise solutions to improve first-year mathematics students’ experience across the board.

Professor Behari-Leak said disciplinary and psycho-social demands placed on maths students – who often deem themselves unworthy to study the subject – put them on the back foot in terms of performance and success. But psycho-social mediation did not always get to the source of the problem that is deeply embedded in the way maths is taught and learnt at universities. 

“This gives rise to particular needs where grasp of mathematical concepts is integral with literacy, numeracy, language, social and cultural capital differentials.”

This DMISRS project enables collaborators to dive deeply into the diagnostic data and to create responses to the contextual challenges that students face.

Towards 2040

Professor Nongxa raised a host of broad ranging questions that need to be deliberated on, for South Africa to get ready for the future. Basing his address on a 2013 American report, The Mathematical Sciences in 2025, he said: “When you look at the pipeline of mathematics, the focus is either on pre-university, undergraduate or post-graduate levels. Seldom is what is done in the overlap discussed.”

Referring to the Academic Freedom Act of 1959 that allows academics freedom to choose what they teach, he raised the question of who will teach, what will be taught and how it will be taught. “It is evident that a national strategy is needed – but who will be responsible for drawing this up? We have nothing that shows what the field will look like in 20 years’ time.” 

He said USAf in 2008 issued a booklet on the state of South African science in which there was a chapter on each of the disciplines. “If a discipline is dying, who is keeping an eye on it? Who is responsible for ensuring that it does not die? Who is responsible for the health of disciplines? 

“Is it the NRF’s division of Knowledge Advancement and Support? Is it the Department of Science and Innovation or the Academy of Sciences of South Africa? 

Is it the South African Mathematical Society or the South African Statistical Association or the SA Mathematics Foundation or the Association for the Mathematics of South Africa? None, all, or some of the above?” 

Professor Nongxa said his focus and current interest is on university-conducted mathematics: “We teach those that will teach those who are coming through the mathematical sciences pipeline. We have an obligation to keep abreast of the new developments and adapt our curricula accordingly.”  He found it impressive that much of 21^st century science and engineering will be built on a mathematical science foundation.  “Mathematical science will not only provide the fundamental language for computational simulation and data analysis but is increasingly fundamental to the social sciences and has become integral to many emerging industries.” 

Destructive maths

Referring to a paper by Cathy O’Neill, Weapons of Maths Destruction: How Big Data Increases Inequality and threatens Democracy, Professor Nongxa said mathematics could be destructive “as some algorithms discriminate against quant”. (A quant designs/implements mathematical models for assessing risk, predicting market movements.)

With marketing, he said, people are looking at social networks to support the mathematical sciences ecosystem and a robust educational pipeline.

Future graduates

He asked: “What kind of graduates should we be producing at universities?”

He said it was unfair that someone doing algebraic geometry or group theory – both mathematicians but have nothing in common to talk about.  He urges communication across disciplines where the role of mathematical science can be understood in other areas.

Noting the move that looks to the role of computers to improve mathematical statements, the mathematician wondered what the drivers of change would be after 2025: computing, big data, increasing complexity, qualifying uncertainty and risk?

Specialisation 

Professor Nongxa’s concern is the tendency to look at mathematics as a focus on specialty. “When you look at people who’ve made fundamental contributions, these will be at the intersection of the disciplines, using tools developed in different areas.”

The 2013 report projects the future use of maths in unimagined ways including information science, high dimensionality and large dataset, modelling and imaging.

Graduates, he said, would teach what they have specialised in and that will be no different to the specialities that have emerged in the 1980s and 1990s. “The landscape has remained static – new areas need to be introduced. I’m not against academic freedom that allows lecturers to choose what they teach… But if you feel there are gaps, how do you address that?  I tell the young people I work with they need to find someone who can speak on their behalf when their case is being decided because their papers alone are not enough.” 

The demographics are concerning 

He quoted race and gender statistics that show that 60% of academics consist of African and white men. “No more than six African females have ever got a rating from the NRF in 40 years. And none of their education is completely from a South African university. That tells us about how we teach people,” he said. He added that no more than 40% of early career academics are PhD holders, an entry-level qualification for many universities on the African continent.

Using the local instrument of rating, less than 20% are deemed to have the potential to become established researchers. “Anecdotally, very few mathematically talented students pursue a teaching profession, both at school and university level. A high proportion of rated academics are nearing or past retirement age. But there is an opportunity to transform the national knowledge base landscape and keep older people in the system.”

The problem, he said, was that if there were no qualified students for senior posts, they had to come from “outside” – which raised problems in South Africa. “There are often complaints when foreigners receive awards or grants.”

Teaching capability is worryingly limited 

Professor Nongxa found it disconcerting that those with a bachelors or honours degree were teaching at universities. “I don’t regard an honours degree as a post graduate qualification and without one, you become an apprentice researcher.” That said, he believes mathematics sciences graduate education is non-existent. “The choice of advanced topics is constrained by institutional specialisation with little or no opportunity for broader exposure to important topics. Also, students specialise too early and a topic for an honours project often becomes a lifetime specialty.”

Because of this, areas of contemporary research activity (therefore producing Masters and PhDs) that evolved in the 70s and 80s and have remained static since the 1990s are: mathematical physics, topology, differential equations and combinatorics.

The National Graduate Academy

In 2017, the National Graduate Academy for Mathematical and Statistical Sciences – to which all (but two) universities are members – was formed. The academy pools expertise and resources around the training of the next generation of mathematicians, statisticians and data scientists who will serve the National System of Innovation over the coming decades. Programmes include staff development and research training networks, professional career development, strategic and vulnerable disciplines, new trends and future directions. 

A solution needs to be found

“One intervention designed a programme aimed at young people in the mathematical sciences that helps them realise their potential to become successful academics. The second intervention is to persuade university leaders that it’s crazy to expect people to specialise after four years.”

He said a solution needs to be found to allow for fluid movement of graduates between universities where the constraints highlight the lack of conformity… There are different requirements, for example, with credit transfers, space or issues of accountability.

Professor Nongxa said: “We are partnering with Leibnez, a new institute for doctoral and professional science. We need to reimagine with intention; to create an environment that forces collaboration and the pooling of resources.”

Charmain Naidoo is a contract writer for Universities South Africa