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Mathematics education lessons from SA and Ireland

- Wits Communications

The Marang Centre for Mathematics and Science Education is advancing specialized knowledge in the field locally and through collaboration with the global north.

Specialist knowledge in mathematics is the current focus of the global mathematics education fraternity. The Marang Centre is poised to contribute research in the field that is both uniquely South African and globally competitive.

“Colleagues in Marang are working on specialist knowledge for teaching in mathematics and in science, because this knowledge is critical for quality teaching in mathematics and science and ultimately for supporting progress in learning” says Dr Craig Pournara, Director of the Marang Centre.

The Wits School of Education hosts two SARChI Chairs that focus on mathematics education and numeracy respectively, both of which are engaged in research and development. Professor Jill Adler, a twice National Research Foundation A-rated researcher (i.e., recognised by her peers globally as an expert) holds the chair in secondary mathematics education. She is also President of the International Commission on Mathematical Instruction (ICMI). Adler says the focus on specialised knowledge for teaching is not peculiar to South Africa.

African-Irish specialized mathematics education knowledge

“There’s been a lot of work on specialized knowledge. There is specialized knowledge you need for the different professions – mathematics for biology, mathematics for engineering, etc. For a teacher, they need to know where the mathematics is coming from and where it’s going to in terms of the school curriculum. It’s a focus just about everywhere,” says Adler in her capacity as President of ICMI.  

Merrilyn Goos is Professor of STEM [science, technology, engineering, mathematics] Education and Director of EPI-STEM, the National Centre for STEM Education, at the University of Limerick, Ireland. Goos, who visited the Marang Centre in January 2018 is an Australian native who spent 25 years at the University of Queensland before relocating to Ireland. This experience and her current vice-presidency of ICMI enable perspective on mathematics education from the global north.

“People may be surprised to think there is a connection between Ireland and South Africa – surely they’re different educational contexts? – but we seem to be interested in many of the same things,” says Goos.

EPI-STEM and Marang have similar goals and interests and these three researchers have a long-standing relationship.

“I’m interested in the commonalities and challenges that face us all over the world, in every country, and to see if there might be some common research interests and some joint research that would advance knowledge in our field,” says Goos.

Prof. Jill Adler (L), Dr Craig Pournara and Prof. Merrilyn Goos are advancing mathematics education in SA and Ireland

Out-of-field teachers in South Africa

One such commonality is the interest in understanding what kind of special mathematical knowledge teachers need in order to teach mathematics well. The global interest in specialist knowledge is driven by curriculum reforms, which in turn have been influenced by international assessments – mathematical literacy, science and reading appraisals such as PISA (Programme for International Student Assessment – in which South Africa does not participate), and TIMMS (Trends in International Mathematics and Science Study).

“All children learn mathematics from the first grade. In many countries in the world, primary school teachers are not specialist mathematics teachers; they’re generalists, so they don’t get trained as mathematics teachers. The school curriculum has changed in many ways, making primary mathematics teaching more demanding, so the focus on maths knowledge needed for primary teachers has taken root in many countries,” says Adler.

But at the secondary level, the situation differs slightly, and it happens in the UK, Ireland, Australia and – more extremely – in South Africa:  

“We don’t have enough teachers for the secondary school and so you have your qualified teachers teaching in the upper levels of the secondary school, and you often have teachers who are out-of-subject teaching in Grades 8 and 9. They might be science teachers or other teachers, and they end up teaching a mathematics class, or they’ve come up from primary school, and so you get what we would call ‘out-of-field’ teachers, who then need some specialist training,” says Adler.

So how do you do it?

Preparing teachers to teach mathematics

In response to the challenge of out-of-field teaching, the Wits Math Connect Secondary Project (WMCS) developed an intervention to upskill teachers with specialist mathematics knowledge. This year-long short course is delivered in face-to-face mode over 16 contact days, with teachers required to submit assignments for each two-day unit. It equips grades 8, 9 and 10 teachers to teach mathematics and thus improves learner outcomes.

The course focuses on specialist mathematical knowledge for teaching and on the core elements of teaching practice, such as selecting good tasks and example sets and providing mathematical explanations that are accessible to learners yet retain the integrity of the maths – something that’s often an enormous challenge. 

The project operates in low-fee and no-fee schools in Gauteng which are considered to have potential but are under-performing.

Out-of-field in Ireland

Educators teaching out-of-field is not unique to South Africa. Goos says a national survey in Ireland to establish the extent of the issue there found that 48 percent of people who were teaching junior secondary mathematics were actually qualified to teach in a different area.

“I think the wrong approach is to demonise and criticize these teachers and say they shouldn’t be teaching subjects for which they aren’t qualified – because the simple fact is that they are. We need to find ways of supporting these teachers and help them to do their job in a way that helps children learn mathematics,” says Goos.

The University of Limerick leads a consortium that delivers a national Professional Diploma in Mathematics for Teaching in Ireland. Diplomates continue to teach full-time and study part-time over two years. The programme is offered in blended learning mode including video, online, and face-to-face tutorials. The programme comprises 75% undergraduate mathematics subjects and 25% mathematics pedagogy subjects.

“What’s missing from our diploma programme is the specialized content knowledge that ‘unpacks’ secondary school mathematics – the kind of professional knowledge that only mathematics teachers need. This is what Jill and Craig are working on in their programme. That’s not there, I don’t think, to the extent that it should be in our diploma in Ireland, mainly because we’re constrained by external accreditation requirements. It would be nice to look at ways of improving our diploma programme based on what we can learn from the work at Wits,” says Goos.  

African-Irish impact collaboration

Despite the notorious difficulty of tracing the impact of a teacher education programme on learner attainment, Pournara and a team of colleagues is attempting to do this through a National Research Foundation-funded study. This study builds on a smaller study completed in 2013 which showed that learners taught by teachers who had completed the WMCS course made more gains than their peers taught by teachers who had not attended the course. This type of study holds the possibility of a Wits and EPI-STEM research collaboration.  

“This is a programme of research that hasn’t been done in Ireland that I’d really like to set up, and it is perhaps where we [Marang and EPI-STEM] can collaborate. For a start, I would like my research team to go out into schools and find out what teachers who’ve graduated with the diploma are doing in their classrooms now, and how their practice compares with that of teachers that have not done the diploma,” says Goos. “What has changed? And what impact is this having on students’ learning of mathematics?”

A global research agenda

In 2005 when Goos was five years out of her PhD, she submitted a paper for the ICMI-15 Study Conference on Mathematics Teacher Education – a field she had just entered. Goos subsequently submitted a chapter for the conference book, entitled The Professional Education and Development of Teachers of Mathematics, which served two important purposes:

“Firstly, it documented the state of the art in the most up to date way at that point in time in the field, and secondly, it set up a research agenda for the next five to ten years,” says Goos.

Pournara and Adler attended the same conference.  “I realized then that we had lots to tell the rest of the world about what was going on at this University two years into our brand new undergraduate maths teacher education programme. We had thought deeply about the design of that programme because our context forced us to do so. But it wasn’t just speaking to Wits or to South Africa – it was relevant to the global community,” says Pournara.

Now, 13 years later, the conference book remains a relevant literature benchmark of mathematics education.

ICMI continues to launch and then support international studies in key areas of mathematics education, where an invited set of scholars across the globe develop the agenda for a focused study conference, following which a study volume is produced. The study volume for Study 23 entitled Building the Foundation: Whole Numbers in the Primary Grades will be published later this month, a study in which Professor Hamsa Venkat, the Wits SARChI Numeracy Chair, has had a key role.

Study 24 on curriculum reform in school mathematics is underway and researchers will convene in Japan at the end of 2018 for its study conference. Factors driving curricula reform include international comparative assessments, technology, globalization, and economics.  

“As the study unfolds”, says Adler, “we are going to see different forms, but there will be similarities given what’s driving mathematics curricula reform across the world. So the fact that we have changed our mathematics curricula here [in South Africa] is part of a global picture.”