Wednesday, 27 March 2013

Every Single Child Can Pass Maths

As the coalition government pushes forward with reforms to the National Curriculum in England, the spotlight is once again on the debate around the 'right' mathematics curriculum.
The desire is, of course, to raise standards (whatever that might mean) and there are arguments and counter arguments aplenty. What shocks me is that on all sides of the debate, the ever present excuse that 'some kids' will never be successful in mathematics rears its ugly head.
This has got to stop.
Enough is enough.  No more excuses.
Except for the rarest of child, we are all born with the same capacity to learn. Every single child, on the day of their birth, has it within them to leave the schooling system mathematically literate. I'm not talking about everyone being a Fields Medalist or mathematical genius, just that everyone can attain a level of mathematics that ensures they have access to all other learning and can continue to learn if they wish. A level of mathematics useful and practical in their future lives.
And one of the main reasons that so many do not achieve this level at the moment, is that so many people in the education world seem hell bent on setting the bar far too low and excusing under performance.
When children enter the education system, say at 3 or 4 or 5, when we are first able to influence their path through learning, they are no longer equal. The experiences that they have had in their early childhood have changed them. They are at different starting points.
But here's the thing: so bloody what.
It is not good enough to use this pathetic excuse to consign thousands of children to a life of being mathematically subnormal. It is not good enough for a profession to throw its hands in the air and say 'well it's not our fault'.
And just while I'm on this, if one more person says to me that these children are from 'certain types' of background, if one more person tries to tell me that being poor means you are screwed before schooling even gets its hands on you, then I will clench my fist as tight as I can and smack that person firmly in the face.
When I hear apparently intelligent adults writing off kids 'from the estate', I want to scream, I want to drag them from their comfortable lives and show them that poverty is not an excuse – there are millions of parents around the world facing the most incredibly challenging circumstances who love their children dearly and do an amazing job at raising them, including instilling a love of learning and a desire to be successful. It has nothing whatsoever to do with income level and everything to do with bad parenting – and these people are in every walk of life.
Regardless, it is a pointless argument. The fact is the children arrive the way they arrive. It is what we then do to them that matters.
During their short time in school, the average child attends 1600 hours of mathematics lessons.
Let's take, for ease of argument, a benchmark of success as Grade C at GCSE (though this is, frankly, a joke). If anyone pauses for just a few moments, looks at the requirements for gaining a Grade C and then considers that each child has 1600 hours of instruction to get there, they would quickly come to the conclusion that this MUST be possible. Absolutely must be. Geez, a trained monkey could get there in that time. Grade C mathematics is not taxing. It just isn't.
So why do thousands of children find it so incredibly taxing? Well, the simple answer is that the 1600 hours of instruction that they receive isn't doing the job for them. Kids fail GCSE mathematics not because they can't do the stuff that forms the Grade C checklist, they fail because they haven't got a clue what is going on in mathematics. They, at some point along the way, dropped the ball.
Recently, I have been writing a curriculum for mathematics designed to take any person learning mathematics from the point of starting to understand numbers and counting all the way through to calculus. I firmly believe that every single child being born today has the capacity to, and with the right journey could, achieve this level by age 15 (far beyond the expectations of the current curriculum).
Mathematics is not an arbitrary set of topics for study. It is a discipline founded on well-defined axioms. Like playing a piano concerto, writing a great novel, or baking a cake, you cannot produce the goods without understanding and knowing the foundations.
And the really irritating thing is that we know, and have known for hundreds of years, what the journey through mathematics needs to look like, what it needs to consist of, if one is to be able to use mathematics fluently.
I cannot say this strongly enough, but if you do not have a full grasp of numerosity, place value, the base 10 system, arithmetic and proportional reasoning, then you are... well... fucked.
And, just to add at this point, with regards to the axiomatic nature of mathematics, at the level of foundations there is no namby-pamby way of 'discovering' this knowledge.  They are axioms, that's the point.  You just need to know them.  Someone needs to tell you, and you need to remember.  The numbers are 1, 2, 3, 4... and that just is so.  A square is called a square, nothing is going to change that.  Numbers in place value columns are linked by a scale of 10, get over it.  Later on in mathematics, once these fundamental elements are known, then the excitement begins and one can construct all sorts of new knowledge from these axioms combined with logic and imagination.  But if you don't know these things, you can never ever get there.  Just in the same way that if you don't know the English languge, you can never ever write Hamlet.
Yet, even though we know this, for some inexplicable reason, the curriculum and the teaching of it, seems to ignore the fact that these fundamentals are non-negotiable. The curriculum, especially when enhanced by the inspection regime, puts mathematics, as a set of skills, on a fast moving conveyor belt that is impossible to stop or rewind.
Except for the fact that the current National Curriculum is so low in its aspirations and expectations, the topics there are all fine and good, nothing controversial. But it just pays no attention whatsoever to how mathematics must be mastered at each level before moving on.
I am sick to the back teeth of meeting 15 year olds who are being asked to solve algebraic equations or analyse graphs, when they can't even perform basic arithmetic or know how the number system works. What the hell are we doing to these kids.
And they are not rare – these kids are everywhere.
Somewhere along the line, the conveyor belt served up arithmetic, say, but they didn't grip it, they didn't get it, they didn't get there. For the moment, forget why. It doesn't matter, it's just an excuse. Yes, maybe they are a pain in the arse, or were away, or they have mental parents, or the most difficult lives. It does not matter. What matters is that, by simply continuing on with the next topic, we are screwing these kids over for life.
Mathematics teachers need to be brave. They need to ignore Ofsted or idiotic SMT who haven't a clue what they are talking about. Mathematics teachers need to know mathematics. They need to know their kids. They need to know who has and who hasn't mastered the foundations and they need to ensure that every single child does so.
You see, the thing is, it might seem scary because the curriculum powers on and you might feel that you are behind, you might feel someone will 'tell you off', but for Christ's sake, the only thing that should matter in teaching is doing what is right for learning. Sometimes you need to rise up.
And you know what, it isn't rocket science. When kids understand and know the basic grammar of mathematics, they are able to accelerate through the other stuff.
Instead of trying to shoe horn every kid in to learning what the scheme of work says they should be learning because of the year group they are in, actually bother to sort the problem.
And everyone blames everyone else. Secondary teachers blame primary teachers, who blame policy makers, who blame the mathematics society and on and on and on...
But the truth is, it's our fault. All of us. As a society we have all been complicit in allowing expectations to fall so dreadfully low.
If you are a teacher and you have a child in your class (doesn't matter how old they are) who doesn't know and understand the foundations I listed above, please, please, please stop the conveyor belt and get them to master these. They all can. All. Do not accept the nonsense some peddle that some types of kids can't. It's not true. They can. Have that as your expectation and aspiration (and if you don't, then perhaps teaching is the wrong career).
I often refer to mathematics as a giant Jenga. At the top, the wooden blocks represent those mathematical concepts that we want the kids to be able to do at the end of their schooling, aged 15 or 16. The GCSE topics. But they are not failing mathematics because they don't know these topics. They are failing because the blocks much further down, the foundations, are loose, wobbly or completely missing and so the whole tower tumbles.
We should all feel really ashamed that we allow young people to leave schooling without these foundations. For it is these that will enable them to learn more. Without them they are imprisoned for life.
I hope that a new curriculum for England will be high in its expectations and aspirations. I hope that teachers will see that there is no point in moving children on from one skill to the next to the next if they don't have at their disposal the basic grammar, the language of mathematics that allows them to learn. I hope that headteachers will tell their staff to ignore the age of a child and instead focus on diagnosing what they do and do not understand so that they can ensure each child leaves schooling able to be successful in mathematics. I hope that Ofsted take their head out of their arse and stop bleating on about age related expectations and instead focus on making children better at mathematics.
I hope that a new curriculum will bring about real improvements in the life chances of the children being born today so that, by the time they reach age 15, the current GCSE grade C topics look like an amusing set of piddling easy tasks because they have gone so much further and mastered the subject in a way that everyone of them is capable of doing.

This blog led to a discussion on the TES forum.