tool kit maths

Now I loath myself for sounding like Michael Gove but....

 One of my pet hates is the current craze sweeping primary schools for 'intitutive maths'. Put simply we are teaching kids the hidden structure rules of numbers , to enable then to do division and multiplication. So 7 times 15, becomes 70 plus 35, and they do it all in their head. Or again 480 divided by 5, becomes  450 divide 5 plus 30.
 It means you can give a method very quickly. It gives you also a lovely touchy feely approach to counting. In terms of confidence wonderful them - and I cannot fault it. Likewise as an adult means of counting it is faultless - I might go further the best mathematicians are the ones that see numbers in this way: they feel and love the structure, and we are now teaching it. We are making then 10 years old think like Gauss, and is beautiful in its way,- and if with Gove zeal gets rid of it  I will yell and yell and yell....
 The trouble though, if you are not Gauss (and most ten year olds are not, they are merely playing at being him) - is what the method can not do, and what it does not teach, and what it does not show.
 The first of these problems I always call the sneeze rule. If the method you are following does not survive me putting you off, by sneezing, coughing or simply talking, then it cannot be your only method. I have put off numerous kids using this method, and no one has ever come back and remembered where they are. It might sound trivial, but in the real world a method you cannot pick the threads to if you are made to forget for a moment is louzy. It simply cannot be your only method (Gauss could use it, as he could think so quickly you could not put him off....)
 Secondly, I think it creates the wrong impression of what maths is. The problem kids have is not working things out in their head, but reading and writing. All the trendy methods in the world do not help this fact. They simply do not set out mathematics in a way that helps kids think. We need trendy methods to solve the real problem that algebra (and maths in general) involves writing down not what you are thinking, but what you have thought and are about to think. That is what makes it hard. That is what makes it fun! For there is nothing like it....
 What is more the kids I see, who work things out in their heads all the time, are clueless when we given (as we do the minute they hit secondary school) anything that requires detailed writing. A problem that gets worse again the minute we turn to algebra. The point is algebra  is easier and easier the more you are used to writing stuff down formally. If you like, what makes algebra so great is that it is the naughty breaking of apparently formal and eternal rules. It is the point you break the rules, as you see how they work. We are trying to teach that point rather earlier in the process. Its effect on how you think of an equation is then problematic I think.
 Oh I am not saying there are are not trendy methods to solve equation, there are. I know many. That is not the point though. The problem is rather, that unless we really do produce a generation of kids who can think like Gauss and so see numbers, and can palpably feel their connection with algebra ( and maybe we will - or work out a way to teach as if we did), the methods we are currently teaching will  in the end break down. There are no trendy methods to differentiate equations or complete the square. At some point maths has devolve into a tradition form. I council would be kinder in the long run to kids it we make this change earlier than later -  and sweeter and funnier ( It seems sensible to do it when kids still believe what adults say, and not when they assume adults always lying anyway)...All the more so, as this will help them  cope with the kind of questions that require a lot of writing that have already crept in by 10!
 Finally I spend my teaching life telling kids to write working it  down - as insurance, against getting the answer wrong. It seems then rather rich if we are early on in their career conspiring to prevent writing it down at all!
Now again I am not knocking something in these methods. What they do brilliantly is be on the kids side. They are methods to make maths feel easy, and happy. Great, I am all for that. But the sad old adult in me knows this is not totally the case.We are simply not on the kids side  or not totally. Our exams are often rather opposed to kids, and they know it, and fear it. Putting off the fact that this is so, is not good, let us be honest about it all a little more...
The point here is actually substantitive. What matters in the end, in, maths as we teach (if not live) it, are  written methods. Or to be more philosophical about it, what maths is all about  is the way writing  takes control from the thinker's head  and puts the thoughts onto the paper;  and how in doing so our thoughts are  externalize and simplified, even as we loose absolute control over them.
 So for me the gift of real teaching is getting the kids to trust (and then love) paper. This is not easy, they do not naturally do it. They all want to keep thinking 'in house', and trust their brains, not the their writing, which open them to criticism external and internal. Good teaching, is therefore what allows kids to navigate this potentially difficult process and makes it feel easy ( I find history and stories great at this) : But what they simply do not need is  anything that conspires with their reliance on in house maths. Such maths has its place, and utterly necessary, but it misses the challenge, and simply will not get you through your maths career...
The only thing I can say is perhaps the present craze for chunking and the rest was invented by a maths tutor, such as myself, for we are the only ones going to make good business from it...and that is awful, I ought to be marginal, and scratch around for a living.