Solving the problem of maths
Our expensive testing and research still do not tell us enough about how children learn the subject, writes Elizabeth Henning.
The recent spate of test results has reminded us again of the national lack of success in mathematics learning. First there were the annual national assessments (ANAs), then the Trends in International Maths and Science Study (Timss), and this month the big one – the matric results.
The media paint a gloomy picture. The department of basic education is both confessional and defensive. Economists express concern, because they think of the maths skills needed to run a prosperous economy. Parents hunt for schools where their children may get a better deal.
We are scurrying around to find a better national deal. Researchers fervently write proposals and annual reports on their funded projects. We academics write articles and books and speak with much conviction at conferences such as the South African Association for Research in Mathematics Science and Technology Education annual gathering.
The higher education and training department initiated a programme targeting teacher education for foundation-phase (grades one to three) numeracy and literacy teaching with a national conference last year and a special issue of the South African Journal of Childhood Education to come this year on numeracy education for the early grades.
So the country is not sitting back merely worrying about the mathematics performance of the young: it is deliberately, almost feverishly, targeting "the maths problem". In the academic world where I live, we are like a bunch of detectives looking for clues of the things that go wrong. Some of us look systemically by interpreting the large-scale surveys of competence such as the matric results, the Timss and the ANAs. Others look at schools and teachers. Some, like the teams in the South African numeracy chairs at universities, combine their research with development programmes for teachers, doing admirable work at universities such as Wits and Rhodes. Education departments and non-governmental organisations also try to address the issue with teacher development projects.
But I wonder whether we are looking in the right places and in the right ways. We may be missing the young children themselves, especially in the foundation phase and what it is that we are actually teaching them when we say we "teach mathematics".
If you observe a grade one or grade two maths lesson in action, at any school, it may be worthwhile to ask yourself that question. Also observe children doing homework. Are these young children learning mathematics – the study of patterns and relationships of quantities, size, shapes, and so on – or are they learning to manipulate Arabic number symbols and verbal language symbols? Are they learning to be competent to work only with concrete objects, such as counters and abacuses, or are they initiated into understanding big numbers and number relationships that they can work with mentally?
We should ask what signs teachers show as they teach. Are they communicating their own understanding of, for instance, the concept of the part-whole relationships of numbers in a comfortable, logical flow of language? Are they talking clearly and unambiguously in their explanations? Or are they handing out worksheets and leaving it at that?
Worse still, do they communicate randomly, jumping from concept to concept? Is their communication systematic and focused? Are they teaching mostly symbol manipulation or are they teaching concepts? More importantly, what do the children do in these classes? Do they mostly just follow instructions for menial tasks, or are they thinking? Are they consistently working in groups or are they sometimes given the chance to just sit and think and puzzle?
Then there is the curriculum, with its deliberate pacing of classroom work and a specific number of minutes for maths learning, per topic, per day. I sometimes get the impression that teachers now teach so stringently to the curriculum – and the ANAs – that they get trapped, and their intuitive teaching and their spontaneity are overruled by curriculum compliance.
If these observations hold, what are the implications for research, its aims and its methods? How much of it is dedicated to finding out how children actually learn maths.
Some of the questions research should ask are: Which maths concepts are the most troublesome in the early grades. When do most children let go of concrete objects and start working abstractly with their "mind tools" alone?. What is the relationship between an early grasp of parts and wholes for working with fractions and decimals?. What core or innate knowledge do children already have when they come to school and how do we utilise this?. Why do many children "unlearn" their ability to estimate size and number once they enter school?
A massive question for us concerning research and its purpose is: Why does our country spend so much time and money on finding out whether teachers cover the curriculum (as in the ANAs), how our school learners perform in comparison with Singapore and South Korea, and how poverty and school performance correlate when we basically already know the answers?
These massive testing interventions could well be better spent on in-depth research that investigates where the trouble spots are in learning, first, and then in teaching. At present we are researching learning output (or outcomes, if you wish). There is a glaring void in "longitudinal" research – that is, studies of children's learning over a number of years that can identify general trouble spots. Few of the large-scale surveys are accompanied by smaller samples of in-depth inquiry, working with individual children and testing them in face-to-face interview style.
If all the finances available for the large surveys could be pooled into systematic studies of children, with samples from all over the country, we might find some of the cracks in the foundation that lead to our poor results. The methods with which to do this type of work are not rocket science and the instruments are available. At the University of Johannesburg we train third-year foundation-phase education students to conduct these tests over a few years with the same children. It is manageable and affordable to look deeply into learning.
Noam Chomsky said recently: "People tend to study what you know how to study – I mean, that makes sense." It does. In South Africa we now know so well how to conduct these large-scale and impressive surveys of learning outcomes. But Chomsky also said: "On the other hand, it's worth thinking whether you're aiming in the right direction. It's worth remembering that with regard to cognitive science, we're kind of pre-Galilean, just beginning to open up the subject."
Our direction has been to look at teaching and, of late, at learning output. We have not yet ventured enough into what goes on in the minds of young children when they enter formal schooling. We may be missing something in our "pre-Galilean" stumbling. We already see in our research on the maths competence of grade R to grade two learners that younger children do better on the more difficult items of the same test. Now that is something that should get us thinking.
Professor Elizabeth Henning is director of the Centre for Education Practice Research at the University of Johannesburg