Academics do the maths on poor results
Six research chairs are devoted to analysing South Africa's maths problem and hope to come up with solutions to raise the level of competency.
Critics call basic education a “crisis” but the government says it is improving. But a research paper from Stellenbosch University in 2012, titled Effective Enrolment, found that, “while 98% of grade six aged children are enrolled in a school, only 71% of grade six aged children are functionally literate and only 59% are functionally numerate.”
The Mail & Guardian asked six research chairs – two for numeracy and four for maths education – what they thought was behind South Africa’s maths woes and what could be done about it.
A teacher, whom I will call Stella Xulu, because she did not want to be named or the village school where she teaches identified, used to teach maths to grade nines at a school near Mthatha in the former Transkei.
“It was difficult,” she says, “because they didn’t have the foundation of grade seven and eight … because there were no teachers [for those years].”
This is unfortunately a common occurrence in many school grades, says Mellony Graven, the FirstRand Foundation (FRF) chair of numeracy education at Rhodes University. Numeracy is a person’s ability to reason and apply numerical concepts.
“The material the learners have from the department is way above their level,” she says.
Two grades behind
She cites the example of grade three pupils in the Eastern Cape. “The vast majority aren’t getting above 40% [in the annual national assessments for numeracy], which means we know they are at least two grade levels below where they’re at. They’re not operating at their grade level.
“Maths is a progressive subject and, until one has developed certain concepts, one cannot leap to abstract and larger numbers. Unless you go back to those early levels of numeracy development, learners don’t have the tools [to go further],” she says.
“The material that’s coming at them is beyond their opportunity to learn … We cannot pretend that these students are [at their grade level] and teach them regardless.”
Xulu says: “I was doing extra classes in the afternoons every day and on Saturday” to help her pupils to catch up. “School finishes at two and I [stayed] until 5.30.”
She did not get paid for the extra work but says that the principal gave her taxi fare to get home. “I don’t need to be paid because it’s about the learners,” she adds forcefully.
The majority of the country’s six research chairs in maths literacy and numeracy, whose job it is to find solutions to the maths education problems and who are each working with 10 schools, say that after-school classes and homework clubs are an important tool in filling the gaps in pupils’ knowledge.
The research and development chairs are an initiative by the FRF in partnership with the Rand Merchant Bank Fund, the department of science and technology and the Anglo American Chairman’s Fund, which is administered by the National Research Foundation under the South African Research Chairs Initiative (SARChI). Unlike the SARChI chairs, which are primarily research based, the maths chairs also have a development component.
Marc Schafer, an FRF chair in mathematics education also at Rhodes, says that this group helps to run a “catch-up” programme for grade 10 pupils. “The rationale is that one of the problems in secondary school, especially grades 10 to 12, is that teachers spend an inordinate amount of time on ‘lost’ concepts and can’t get to the syllabus, because they’re catching up.”
The teachers are required to cover the curriculum, which these academics argue is overly prescriptive.
Hamsa Venkatakrishnan, who holds the South African numeracy chair at the University of Witwatersrand and who was a researcher in mathematics education at King’s College London, says that the curriculum is focused on covering the syllabus. “Week one, you do this, week two, week three [another area of maths]. We can see teachers moving on [to new topics], not because they don’t care but because [they are trying to keep up with] the curriculum.”
Cyril Julie, the FRF chair in mathematics education at the University of the Western Cape (UWC), says that the teachers he works with have asked whether the curriculum could not be resequenced, and whether “they cannot teach what they think would work better”. He says that they are engaging with the Western Cape provincial government, which has representatives on their research and development group.
“We’re finding a culture of very narrow curriculum adherence. Teachers are required to cover the entire curriculum, whether kids understand or not,” says Schafer, who was also head of Rhodes’s education department from 2005 to 2009. “It’s about adhering to the curriculum and there is immense pressure on teachers to cover all the work.”
The M&G asked six research chairs what they thought was behind South Africa’s maths woes and what could be done about it. (Delwyn Verasamy, M&G)
But this practice comes down to more than just pressure to cover the work. “It has a history – the moment you don’t comply with the state or policy, you are seen as anti-policy, anti-state,” he says. “Teachers are not encouraged to approach the curriculum strategically … This requires confidence. Our teachers need to feel empowered [to do this].”
This compliance is also reflected by the pupils, says Graven. “Learners have lost agency – it’s all about teacher compliance.”
She relates a story about setting a group of pupils maths problems during an afternoon extra class and then coming back to check on them 10 minutes later. They had copied the answers from the answer book, neatly filling them into their workbooks.
She says that the pupils did not understand why she was frustrated. “It’s an example of teacher pleasing. The fact that they didn’t learn any mathematics was not problematic. It was neat and they had gotten the answers right.”
There are cultural and historical reasons for the authority-pleasing behaviour found largely in the Eastern Cape, where there were large Bantustans under apartheid, but it is also informed by a lack of teacher knowledge and confidence.
Xulu says that often “teachers teach maths because [there is] no one else to teach mathematics. Then they don’t know and love mathematics … They say, ‘I don’t know about [that section of] mathematics. I’m not going to teach that’.”
Graven says: “Teacher knowledge in mathematics is a stumbling block. We can’t wish it away … but it’s like that in all countries.”
Julie, who has been involved in mathematics education since the early 1970s as a teacher and a developer of resources for school maths, sees teachers and teacher development as linchpins in the system.
“Our approach has been to develop a model from what teachers say they need, and as we perceive as what their needs are, [and to] work with observations in the classroom and gather from that what are the directions to go,” he says. “Working with teachers, we see the horror stories about the content knowledge splashes in the papers [about poor teacher ability] … We believe that teachers are a permanent fixture in this problem we are trying to address. If we work with them to enhance their teaching, we can address the dilemma in school mathematics achievement.”
But teaching maths is not the same as doing maths, says Venkatakrishnan, who also taught maths at comprehensive schools in London. “You can improve your mathematics, but also improve how to communicate it. In improving maths knowledge for teaching, you need to exemplify and explain mathematical ideas rather than just say what they do.
“We treat teachers as professionals and invest time and resources in them. If we don’t pay attention to this, the key resource in the system is going to be degenerated. My central priority is about investing and supporting our teachers, and I think the department of education is moving that way too.”
Jill Adler, the FRF chair of mathematics education at Wits’s School of Education, says that, “in our experience, which is in Gauteng, teachers in the upper levels are quite well qualified mathematically, relatively speaking. Most [schools] left the weakest teachers in grade eight and nine, and that’s where the problem is.”
Starting blocks: First day of school at Louw Geldenhuys in Linden, Johannesburg. (Madelene Cronjé, M&G)
She says her work and research have focused not only on the further education and training level, which is grades 10 to 12, but also on the grade nine to 10 transition. “It’s where there is major leakage … By grade 10, the horse has already bolted.”
But even for teachers who specialise in teaching maths, there is a lack of stability that makes teaching difficult, says Werner Olivier, the FRF chair in mathematics education at Nelson Mandela Metropolitan University (NMMU).
“Every five years, there has been a new curriculum. The first national exams for the latest curriculum are this year and [many] teachers have not been taught the curriculum.”
Graven says that there have been three recent curriculum changes and each time “there is a district meeting and they are expected to have shifted their knowledge. That’s hugely problematic, yet the press reports that come out are that teachers don’t have all this knowledge.”
The NMMU, Wits, the UWC and Rhodes all offer teacher training programmes. But Adler, who also holds a chair of mathematics education at Kings College London, says: “There are teachers in lower grades who are ‘teaching out of subject’ or ‘out of level’ … The mathematics for teaching courses we have developed assume some foundational know-ledge. The impact on teachers without some foundational knowledge is limited.”
Xulu says that the lack of trained maths teachers is the major problem in the system. “That’s why the students aren’t doing well – there aren’t enough teachers … There is a shortage of maths teachers … What result [do you expect] when you don’t know what you’re teaching?”
The department of basic education had not responded to questions about the numbers of teachers, and maths teachers in particular, at the time of going to press.
Xulu says that in rural areas teachers need more resources. “The problem is we don’t have resources to [give to] our learners. In our rural areas, we don’t have materials, resources for mathematics.
‘Content and skills training’
Olivier, who is also the head of NMMU’s maths department, says that his group focuses “on content and skills training to teach the content in an effective way for grades 10, 11 and 12.”
They have digitised programmes and videos for both teacher and pupil training, which can be stored locally on laptops, so that they do not need the internet.
“The curriculum is covered from a package on the laptop of the teachers … We have over 200 teachers, where they receive a package with laptops, funded by the Setas [skills education training authorities].” He says that they have worked with the Eastern Cape department of education, which has “really bought into it, particularly the model of training for teachers”.
Schafer’s group, in collaboration with the University of Applied Sciences Northwestern Switzerland, is “exploiting mobile technologies: we’re developing a database of dozens of silent video clips, three minutes long, using only natural materials – matches, stones, drawings, etcetera – to stimulate mathematical learning”. The programme is called VITALmaths.
But the teacher is still the main point of contact for pupils, and each research chair spoke out about the media blaming teachers.
“It is solidifying the problem; teachers become even more demoralised and learn that they need to hide what they don’t know,” Graven says.
Why are we telling the same story, she asks. “The blame is put on them. Each time we say a teacher can’t do X, it’s actually a story about how province and district haven’t supported the teacher.”
This is why Xulu wants to be evaluated. “Government must come to the school and evaluate teachers. When the department visits, [they] can see that this teacher can teach or cannot.
“We want evaluation – it will help us teach maths. Evaluations is where you can see your progress. Teachers mustn’t be forced to teach mathematics if the teacher doesn’t know mathematics, if they are not interested in learners.”
But this is an academic and political sticking point. The South African Democratic Teachers’ Union has vetoed teacher assessment, calling it demeaning and the academics are also against it.
Graven says: “First, implement a support programme; don’t just go in to assess what we already know.”
She says that it would also not be a fair assessment because the impression of teaching depends on the class and the level of the pupils. “Put me in a classroom with high-level kids, operating at a higher level, and we will have an exploratory discussion. Put me in a township school, where children are three or four levels below their grade level … [and] children are not used to saying what they think ... and they [will wait] for me to tell them what they think.”
Adler asks how we would monitor teacher performance.
“The challenge is relating learners’ performance to particular teachers over time,” she says.
A widely touted partial solution to improved mathematics is after-school classes, in which, Graven says, “learners can learn in a context where they are not constrained by the curriculum. After-school clubs allow for more individualised learning, pulling them along their path [which teachers cannot do when trying to adhere to the curriculum].”
This would also enable pupils to work in an environment that enables learning.
Julie says that pupils from their schools are from low socioeconomic areas. “The environment is not conducive for them to do such work. In Elsie’s River [in Cape Town], for example, matriculants live in council flats with a single parent, and rent out half the house. There’s no space for those students to study. In a township like Mfuleni [about 40km from Cape Town] … there are a lot of children who come from shacks.”
This makes it difficult to study and often parents are unable to help with homework or to train children in fundamental mathematical skills.
Schafer says: “Our focus is geometry. In most of our geometry assessment tasks, learners get these tasks wrong, such as fundamental concepts like parallel and vertical lines. [if you] dig deeper, [you realise] they lack the fundamental skills to deal with geometric concepts. Visually, they often struggle to tell the difference between parallel and vertical lines. the spatial orientation skills have not been sufficiently developed.”
He says his group has developed instruments to assess this backlog, but “it’s not just the mathematical concepts but the deeper, more fundamental skills that kids don’t come to school with. That kind of pre-primary [learning] is done informally in families around the dinner table, at play.”
Xulu asks: “If the parent is not educated, don’t know anything about schooling, what do you expect from that child? In our area, most parents are not educated.”
She tells a story of helping a pupil to prepare for a maths competition by phone: “I am teaching her and then she says to me, ‘Teacher, my candle is finished. I can’t work anymore’ – because she was doing her mathematics with a candle.”
The department of basic education had not responded to repeated requests for comment at the time of going to print.
Are you as smart as a ninth grader? Take our maths quiz at mg.co.za/mathsquiz.
For more on VITALmaths, visit www.ru.ac.za/vitalmaths/.