In a recent post I poured scorn on Michael Gove’s tinkering with the maths curriculum. Having done so, I thought it only fair to outline what would be necessary to improve school maths teaching. Since what I am saying needs to be detailed, I am first going to confine what I say to one group of children – those who cannot do arithmetic reliably and, as a result, are unable to get a C grade in GCSE maths.
The current GCSE, that is before Mr Gove’s tinkering, has provided in its Foundation Level GCSE Maths an excellent examination for weaker students. By taking the Foundation GCSE Maths, children can get any grade from G at the bottom to C at the top. The exam tests the basic numerical skills that one would hope that most school leavers would have. It includes questions like calculating percentages, perimeters, areas and volumes, drawing and interpreting graphs and tables, angles and basic geometry. There are questions on simple algebra like Factorise y² – 2y.
There is a non-calculator paper. It requires children, as well as adding and subtracting, to be able to use their tables for multiplying and dividing in real contexts. Bearing in mind that the Cameron, Osborne, Morgan trio together have refused to demonstrate that they can multiply 8 x 9, 7 x 8 and give the cube root of 125, these Foundation Maths questions are not trivial. One is reminded of the occasion in 2009 when Ed Balls, responding to Michael Gove’s criticism of GCSE’s, threw a few GCSE questions at Mr Gove – none of which he was able to answer.
At the sharp end of education, in both state and independent sectors, a maths teacher’s job depends on children passing GCSE. Teachers sweat blood to get children through the exam. There are, of course, children with very limited intellectual ability that will never be able to show much achievement in maths. But there is a broad swathe of children who, at the moment, get D, E or F grades. These children are totally failed by current mathematics teaching and in most schools teachers are powerless to help them improve. These are the children who never understood the basics of mathematics in the first place. Their first encounter with maths happened before they were ready to learn maths.
A good proportion of children at the age of five do not understand the concept of two. They are not ready for any maths teaching. If one tries to teach them maths at that age, they will simply learn that they cannot do maths. Forever they will be confused. Come the age of eight when tables appear, maths will seem to them to be a complete foreign language. Expecting them to learn their tables off by heart is like getting them to recite Mandarin poetry. It’s nonsense to them and it is very hard to remember nonsense accurately. But this is what the current maths curriculum requires. It’s bonkers. When these children reach maths GCSE their basic arithmetic is so poor that they get a low GCSE grade – and breathe a sigh of relief that they never have to do maths again.
The solution to poor numeracy is simple. Those who cannot remember their tables need to go back to their number bonds to 10. This means learning, re-learning and over-learning that the number that needs to be added to 7 to make 10 is 3, and so on for all the other numbers from 1 to 9.
Then these children need to learn to stop counting on to perform addition, a method that is so inaccurate that prevents children seeing any pattern in number. They need to learn how to add numbers by partitioning. This means that, when adding 7 to 28, they need to split 7 into 2 + 5; then add 2 to 28 to make 30 and, with the remaining 5, they get 35. Only by adding by partitioning can one understand the rungs of, in this case, the 7-times table. Being able to add by partitioning turns the learning of tables from random chanting to the much easier task of learning something that makes sense.
If the above sounds simple, it is because it is. Test any child who is having significant number difficulty and you will find that they don’t know their number bonds and they can’t add by partitioning. Unless you correct these faults they will never make progress. You don’t get children to learn tables by getting them to chant tables. You first need to give them the skills to understand tables.
Of course, none of this chimes with current government policy. Maths exams must be made harder! Standards must be raised! It’s nonsense of course. Without a clear understanding of the fundamentals of any subject, going faster does no good at all.
One excellent primary school teacher I know, a post-takeover victim of an over-ambitious academy chain, was challenged by a maths inspector: ‘Why were you teaching them number bonds to 10? You were doing that in the last lesson I saw!’
In schools one seldom dare speak the truth, even to maths inspectors with no primary school experience. It would have been lost on him, and have been regarded as downright rebellious, to say that children don’t get some of the basics of maths the first time and one needs to go over and over the foundations of mathematics because children cannot make any progress at all until they first understand the basics.