In my columns I have been continually stressing the need for sense-making and understanding.
Children need to be exposed to situations from which they can make meaning and, in the process, recognise patterns and relationships.
I have stressed the role of the teacher in creating and managing learning situations so that children are provided with the opportunity to develop mathematical concepts and skills. Yet there is also another ingredient: practice.
One of the most frequent complaints teachers voice is that children forget. Teachers claim that they taught a lesson well yesterday, last week, last term and even last year. They claim that the children “knew” the work then, and yet the children cannot do a thing today. They have forgotten everything.
Let me try to use an analogy to explain. There was a time when I ran quite a bit. I set reasonable times in the races (half-marathons, marathons and even a few ultra-marathons) that I ran. I trained at least six days a week for at least an hour a day — sometimes for three to four hours. I stopped running a while back.
Recently, I watched the runners in the Two Oceans Marathon running 56km and realised that at present I cannot run 10km. Nobody is surprised. If you do not train, you do not gain and maintain the levels of fitness required to be able to run long distances.
Why is it, then, that teachers are so surprised that children have “forgotten” everything they did last year when they revisit the topic for the first time a year later?
If you don’t practise or use a skill, there are chances that you will lose your touch. We are unsurprised when we read about top musicians, sportsmen and -women, dancers and actors, chefs and artists and discover that they spend hours and hours practising their trade.
In the book Outliers, Malcolm Gladwell proposes a 10 000-hour rule. He demonstrates that success in any field involves, to a large extent, a great deal of practice. He specifically claims that it takes at least 10 000 hours of practice for people to reach the top of their field.
Mathematics is no different. Children need to practice if they are to reach the top of their class. I get the opportunity to visit many schools and mathematics classrooms across South Africa each year.
There is no doubt that there are many different and complex forces at play across the wide range of schools that I visit and success or not in mathematics is determined by a wide range of factors. And yet, quite apart from these forces, there are also some simple yet striking differences between those schools in which children perform better in mathematics and those where children do not achieve their potential.
The most striking difference lies in the amount of mathematics that children do each day. In some classrooms, children will do no more than four to five problems/sums a day, whereas in others children will do up to 30 questions in the lesson and then do another 20 for homework.
If children do not use the mathematics that they have learnt over and over again in a wide range of different ways they will not internalise the knowledge and grow in confidence. Mathematics is not a spectator sport.
We do not get better at doing mathematics by watching a teacher doing sums on the board. We do not get better by doing one sum every 15 to 20 minutes. We get better by doing many hundreds of problems each week.
Something else I have observed is that in schools serving more affluent communities, parents often enrol their children in extra mathematics lessons and/or mathematics coaching programmes. Parents, wanting the best for their children, have noticed that the children in the school who attend these programmes often do better in mathematics than the children who don’t.
They believe these programmes teach or develop special skills that the school somehow does not succeed in teaching and they spend fortunes ensuring that their children will not be left behind. The only real difference between the children who attend these programmes and those who don’t is the extra hours that those attending the programmes spend doing mathematics each week.
It would be silly to suggest that simply doing more mathematics each week is enough. It is more complex than that. You have to know what you are doing, you have to be doing the right kinds of activities and you need to be doing the work in a reflective manner — learning from what you are doing. We can say that doing more mathematics is a necessary but not sufficient condition for success in mathematics.
Before I am misunderstood, I am not undoing all I have said in previous columns about the need for children to experience mathematics as a meaningful, sense-making problem-solving activity.
I am not suggesting that the meaningless drilling of rules and procedures is sufficient. I am simply making the observation that it is unrealistic to expect that children will still be able to do next year what they can do today if they do nothing with what they can do today between today and next year. These remarks have important implications for the planning of teaching.
Mathematics programmes that assign a week or two once a year to a particular topic are letting children down: one way or another, children need to revisit topics frequently and the younger the child the more frequent the revisiting. In terms of teaching and daily lessons, there is a direct correlation between the number of problems/sums/questions that children do each day and their performance in mathematics.
Aarnout Brombacher is a private maths consultant. For more information go to
www.brombacher.co.za
Teachers’ tips
- Children need to practice their mathematics skills if they are to reach the top of their class.
- The most striking difference between schools in which children perform better in mathematics and those where children do not achieve their potential lies in the amount of maths that the children do each day in the classroom.
- Doing more mathematics is a necessary but not sufficient condition for success in mathematics. Children also need to experience mathematics as a meaningful, sense-making problem-solving activity.
- In planning mathematics programmes, teachers need to revisit a particular topic frequently, not simply once a year for a week or two.