Maths: Why don't we fathom young minds?
Conversations about mathematics education in this country pop up frequently in the media – and I have yet to come across anyone who is happy with the way things are in the learning of maths among the nation"s children.
Many try to find out what goes wrong by conducting research. South Africa has about 150 researchers in mathematics education, and there are a number of special mathematics chairs of research and development at various universities. Funding foundations are generally very keen to contribute to research, especially if it is linked to development programmes and if some impact can be measured.
So education authorities have put much into place to make it possible for children and youth to learn well. Yet we do not seem to get on to the right path. Why does maths education remain such a concern? Where do things go wrong?
Teachers are usually identified as the first set of "perpetrators". It makes sense to think that if they do their work "properly", then children will learn "properly". Teachers cause children to learn well; or teachers cause children to fail.
This is a simplistic view, of course. There are many factors that interplay in learning generally, and in maths learning specifically. Children struggle to learn mathematics because it is not in our nature to learn it, much as it is not in our nature to learn to read. Both maths and reading are cultural inventions and both are a very recent introduction in the development of humankind. Our brains are simply not wired to work in this way. Young children"s minds have to be gradually, and very systematically, "rewired" to be able to learn to work with mathematics – and with reading and writing. None of these competencies comes naturally at all.
When children are young, their first teaching has to be done very judiciously and systematically, because it lays the foundation for further incremental learning (and "wiring"). It has to be done according to a plan that takes into account the neuroscientific and psychological research information we have about the young human brain and its ability to "recircuit" for maths and literacy.
The plan that societies all over the world use to teach mathematics systematically is the school curriculum. In our country we have such a curriculum for mathematics education in the foundation phase (grades one to three). When reading it, teachers look out for topics they must introduce and for the order in which they should teach. They also look for clues about how they must schedule their work programme, and what methods they can use to teach and to assess the young children"s output.
So, questions teachers ask when they study this plan may be: "What do we teach; when do we teach a topic; how do we teach it; how do we assess the work of the pupils; how do we help children who struggle; what resources do we need in the classroom?" The 518-page curriculum has abundant answers to all these questions.
There are many directions and even prescriptions in the plan; the most obvious one being the pace at which the teaching (with the assumed learning as a result of the teaching) takes place. Nowadays the teachers work very closely with the national curriculum because the children in their class will be assessed in the annual national assessments (ANAs) in September of each year. They also have to record their classroom progress with evidence from children"s work outputin workbooks and worksheets.
So inevitably teachers focus on the curriculum pacing and its content as rigorously as they can. They do not wish to have a district curriculum official paying them a visit and then finding that they have been "playing around" with the curriculum too much.
More than anything, they don"t want the children to perform poorly on the 20 to 26 items in the September ANAs. This test is set on the basis that certain parts of the curriculum will have been covered. If a teacher has followed the curriculum directive in grade one, for instance, then by the time the ANAs are conducted, the children in her class will have learned everything they need to succeed in the test.
But this is where things go wrong. Having "taught" children something does not mean that children will have learned it. The skills to teach young children are highly specialised, and not all teachers have them because many were not educated and trained in the techniques of pedagogy for the early grades.
Nevertheless, teachers diligently assess children"s progress. Some do it daily. Some of them will know how to deal with children who struggle – but if the classes are too big, they may not have enough time. The curriculum says they have to teach 160 lessons a year. In those lessons they have to teach all the children all the concepts and procedures for "doing a sum" as prescribed in the curriculum.
They need to make sure that each child stores in their memory the factual knowledge and the operations for calculation. Few teachers ever refer to the fact that they need to be teaching thinking with mathematical concepts. Most teachers just wish to "cover the curriculum" and "prepare for the ANAs". That is their discourse.
In my own experience of research on pupils and teachers in foundation phase classrooms, I have found that this is, indeed, what teachers do. They "cover" the curriculum –with a label that says "done"! And then they move on.
Why do they do that? Why do they not dwell on difficult concepts such as the "part-part-whole" concept of number that has to be firmed up in grade one (and again later) because it is the foundation for so much that children will learn later on?
Why do they use the notion of the (mental) number line as if it is a fixed, linear tool (on paper), not realising that this concept develops very differently for each child and teaching it has to be done extremely carefully? Why do so many teachers think counting numbers in a class, chorus style, for 20 minutes or more a period (in the 160 periods a year) will add an understanding of something? (A clue here may be the 542 mentions of the word "counting" and 545 mentions of the word "count" in the foundation phase curriculum.)
Relations between numbers
Why do they not explore the relations that numbers have with each other in much more depth? Why do they introduce the use of the money system and an understanding of time sequence before children know parts and wholes as concepts well?
Why do they teach measurement in units before children understand intervals? Why is the concept of fractions not taught when most children are developmentally ready to grasp it? Why do they say a "symbol" is an Arabic numeral/sign (only)?
Why are six-year-olds taught unit measurement of volume, length and weight before they know at least some of the physics of magnitude? Why do so many pupils fail to develop an understanding of number place value?
There are some clues in the curriculum. I think it is too full and expects the pupils to progress too rapidly, not taking enough cognisance of children"s developmental capabilities.
There is one question that does not receive prominence in the curriculum. Seldom are teachers advised to ask: "Why?"
Why does it help me to understand children"s development from birth? Why can children identify a set of three objects without counting long before they come to school? Why do infants already know how to judge approximately between many and few objects? Why do three-year-old children struggle to understand what four is if they already know what three is? Why is it so hard to understand the "sixness" of six?
Why are hands and fingers important in learning maths? Why is the sequence of numbers in the counting "string" important only in some instances? What does it mean if a child can count? Why do we have to learn certain calculation operations by ongoing practice while we grasp others quickly? Why are the concepts underlying the operations and procedures of number calculation important precursors to building understanding? Why is memory so important in maths learning? Why do we need to know tables and bonds (or not)?
Some of us who research mathematical cognition in childhood ask: Why are most teachers not educated and trained to understand the developing mind of the child?
Professor Elizabeth Henning is director of the Centre for Education Practice Research at the University of Johannesburg"s Institute for Childhood Education, Soweto campus