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.
Wednesday, September 26, 2012
Monday, September 24, 2012
What is maths Teaching for?
With maths teaching it seems to me there are two main approaches. The first, the traditional approach, really has Maths down as the great initiation rite of our country. It is the Bar we put up to stop just anyone being anything. You have to be able to solve these random puzzles, some with some relevance to here and how, some dating from Ancient Greece, some from even older than that.... - no matter- to prove you are one of us.
This method is good for elites, as pupils very quickly work out whether they are one of us or not. It is good for universities, who ensure that only pupils who can think in a very certain very prescribed way come into to the institutions. It is good for politicians who get an exam they can claim is difficult. It is good for Maths teachers (and tutors), who get an exam that is easy to teach (or next to impossible for the uninitiated). The people it lets down of course are the pupils -most of whom are not able to get those grades, and have to rest content with the fact they somehow it is all their fault.
The exam then is then very much a passion play, in which a social order based on an arbitrary selection and partial (if highly obscure) merit is re-enacted, and enforced in the same moment. What is lacks any notion is maths as we live as adults with all richness, and complexities (from filling in tax forms, to guess measurements - its all maths). Rather than any of this richness we are presented, as a necessary truth, a maths exam that is the stale, sterile exam. the product of empire and tradition, and utterly valueless in itself.
The other approach, the one we have just moved to sacrifices the obscurities of mathematical rigour and the elegancies of of a single exam, for continued modular assessment, using questions that are based on real life adult experience. Now there is a real sacrifice here, if you understand maths only in terms of a tradition exam, where a certain number of universally acknowledged truths must be imparted (or else some one somewhere has failed). The modern exam, with its emphasis of reading and actually thinking, will not have space for such truths. But instead it teaches the really very valuable skills of how one reads different maths questions, how one thinks about them, and one one is reflex about what one is writing.
The importance (and uniqueness) of this reflexive complex method of reading and thinking is difficult to over emphasize. You see maths needs to be read and written in a way utterly different to the way you read english. Is so many many ways maths reading and writing is unique and different: In maths one reads and reads questions, as one is solving it (and as it starts to make sense); one does not necessarily start at the beginning; one plays with meaning, resolving it careful, part by part, and only at the end creating a whole (which makes sense); one checks the links of algebra and grammar, finding different ways thought can be described; one creates accords between drawing, writing, thinking and reading, accords that are hard to express, but easy to grasp.
In short this is an exam where one must really think and one reads and writes, and do so without let up. What is more one thinks about thins one has a handle on, that one can see are useful, and do matter. In In addition to this the unit version of some of the exams allow pupils to really get the bit between their teeth. They do well in one part of the exam, and suddenly wake up and work. Pupils in such circumstances will start to feel that the exam is for them, and that is enough to make them think differently. It gives them an impetus to engage. It is not then that unit exams are easier, they are not; they merely inspire people to work, people the old exam would necessarily fail....
Now the exam is messy. It does not produce simple 'product'. Pupils with 'A' might excel at different parts of the rich exam, and so universities (and politicians) can not guarantee what a grade 'means'. Likewise the rest of europe, which has kept the initiation approach, looks on in amazement at the sheer 'wierdness' of our exams (I actually teach European students, who have done very well in the Baccs, but cannot get their head round exams that make you think). It goes without saying that the exam is hard to teach, and so does maths tutors at least no favours.
But the people who respond well to it are the pupils (and their parents), for them the exam opens out endless new possibilities and new worlds. Is that not the point?
No of course not.
The exam is bad for the social repression element of a maths exam, - for lots of people, from many different backgrounds, might do well in it, and we no longer have the select brotherhood of 'mathematicians' (Good I say even as a member of that group). But it is of course this last element, the role of maths in the social institution and enforcement of a particular kind of meritocracy, that really matters. Which is probably why the power that be, when they wake up to the change, need to suppress it. Maths is our initiation rite. The idea that 'standards have slipped', and the maths of Ancient Greece is going by the board, feels significant, feels like a diminution in some manner, and lessoning of the magic of the old exam, and the power of the initial initiation. And therefore, to defend the status quo, we need to destroy this new exam, and do so even as we deny the reasons why we must do so. Our system of exam-ocracy masquerades as a more open meritocracy, and we would defend it as that.
The real problem for me at least, is not the defence of a social order, but the clear political (and anthropological) hypocrisy, that this defence involves. To undermine kids in the interests of a social order is common place (that is what societies do), but we ought at least to be honest about it - and accept the choice between different ways to teach and think about maths, is nothing to do with quality, or merit.
This method is good for elites, as pupils very quickly work out whether they are one of us or not. It is good for universities, who ensure that only pupils who can think in a very certain very prescribed way come into to the institutions. It is good for politicians who get an exam they can claim is difficult. It is good for Maths teachers (and tutors), who get an exam that is easy to teach (or next to impossible for the uninitiated). The people it lets down of course are the pupils -most of whom are not able to get those grades, and have to rest content with the fact they somehow it is all their fault.
The exam then is then very much a passion play, in which a social order based on an arbitrary selection and partial (if highly obscure) merit is re-enacted, and enforced in the same moment. What is lacks any notion is maths as we live as adults with all richness, and complexities (from filling in tax forms, to guess measurements - its all maths). Rather than any of this richness we are presented, as a necessary truth, a maths exam that is the stale, sterile exam. the product of empire and tradition, and utterly valueless in itself.
The other approach, the one we have just moved to sacrifices the obscurities of mathematical rigour and the elegancies of of a single exam, for continued modular assessment, using questions that are based on real life adult experience. Now there is a real sacrifice here, if you understand maths only in terms of a tradition exam, where a certain number of universally acknowledged truths must be imparted (or else some one somewhere has failed). The modern exam, with its emphasis of reading and actually thinking, will not have space for such truths. But instead it teaches the really very valuable skills of how one reads different maths questions, how one thinks about them, and one one is reflex about what one is writing.
The importance (and uniqueness) of this reflexive complex method of reading and thinking is difficult to over emphasize. You see maths needs to be read and written in a way utterly different to the way you read english. Is so many many ways maths reading and writing is unique and different: In maths one reads and reads questions, as one is solving it (and as it starts to make sense); one does not necessarily start at the beginning; one plays with meaning, resolving it careful, part by part, and only at the end creating a whole (which makes sense); one checks the links of algebra and grammar, finding different ways thought can be described; one creates accords between drawing, writing, thinking and reading, accords that are hard to express, but easy to grasp.
In short this is an exam where one must really think and one reads and writes, and do so without let up. What is more one thinks about thins one has a handle on, that one can see are useful, and do matter. In In addition to this the unit version of some of the exams allow pupils to really get the bit between their teeth. They do well in one part of the exam, and suddenly wake up and work. Pupils in such circumstances will start to feel that the exam is for them, and that is enough to make them think differently. It gives them an impetus to engage. It is not then that unit exams are easier, they are not; they merely inspire people to work, people the old exam would necessarily fail....
Now the exam is messy. It does not produce simple 'product'. Pupils with 'A' might excel at different parts of the rich exam, and so universities (and politicians) can not guarantee what a grade 'means'. Likewise the rest of europe, which has kept the initiation approach, looks on in amazement at the sheer 'wierdness' of our exams (I actually teach European students, who have done very well in the Baccs, but cannot get their head round exams that make you think). It goes without saying that the exam is hard to teach, and so does maths tutors at least no favours.
But the people who respond well to it are the pupils (and their parents), for them the exam opens out endless new possibilities and new worlds. Is that not the point?
No of course not.
The exam is bad for the social repression element of a maths exam, - for lots of people, from many different backgrounds, might do well in it, and we no longer have the select brotherhood of 'mathematicians' (Good I say even as a member of that group). But it is of course this last element, the role of maths in the social institution and enforcement of a particular kind of meritocracy, that really matters. Which is probably why the power that be, when they wake up to the change, need to suppress it. Maths is our initiation rite. The idea that 'standards have slipped', and the maths of Ancient Greece is going by the board, feels significant, feels like a diminution in some manner, and lessoning of the magic of the old exam, and the power of the initial initiation. And therefore, to defend the status quo, we need to destroy this new exam, and do so even as we deny the reasons why we must do so. Our system of exam-ocracy masquerades as a more open meritocracy, and we would defend it as that.
The real problem for me at least, is not the defence of a social order, but the clear political (and anthropological) hypocrisy, that this defence involves. To undermine kids in the interests of a social order is common place (that is what societies do), but we ought at least to be honest about it - and accept the choice between different ways to teach and think about maths, is nothing to do with quality, or merit.
Sunday, September 16, 2012
Well - we didknow that it happened
One of the sad facts about the current education security is he has tendency to view with suspicion everything that was not around when he was at school. And so he argues that modular exams, multiple boards, GCSE's all of it, must go, and the clock must firmly be set back fourty years or so, for as Dickens himself said (in the mouth of Simon Tappit) 'it is only in going back we truly go forward'..
Now it is no that my do not think the current system is problematic. The endless retakes at A level are a problem, but att GCSE, I think not- they simply show working hard has its rewards. I have had many pupils who have really tried in a system where they can see themselves improve, and would be lost in the single exam system - which ironically rewards the flyby nights idols individuals who are good at exams (of which there are very many). To change the system is therefore to privileges the idle over the workers....
Likewise the problem of grade poker related to schools swapping boards, is a problem, But its cause in not the exam, but rather the way schools are assessed. Unless we going to abolish (and it might take that) Ofsted, and rework how we understand what schools do, and how we (as a nation) ask them to endless do they do better, we are always going to get the distortions of grade poker (which the driver of grade inflation, not the exams themselves). Grade poker is then the creation of education ministers who want to prove they are doing something, and has little do to with schools themselves. That is why is is such a despicable game!
But in the hubbub of reform something wonderful will be certainly lost- namely the Brand New maths GCSE. This GCSE is maths as it has never been taught before - for it is the maths we live by and use every day of lives. Maths made real, edgy, difficult, a maths that does not need 'right' answer, only estimates, a maths that allows us to actually understand the world we live in. The radicalness of this approach, and its ability to change pupils lives (once they get the hang of it) is very hard to appreciate. It is no exaggeration to say that for the first time in twenty of teaching I feel like I am teaching something worthwhile, useful and even good. And this will now be swept aside in the name a reform which will set the clock back thirty years or so, and back to a system of examining and thinking about maths that seemed to delight in making it obscure, tricky, abstract, and about as far from everyday life as it is possible to go. Its loss will be heavy.
But then perhaps it is hypocritical of me to really mind. For one thing is certain, the old system with its sudden death exam was very good for maths tutors. If they reforms go ahead, my business will boom, as it always does when the system does not suit the pupils very well. But I am for at least big hearted enough to see beyond my greed. I just politicians were the same...
Now it is no that my do not think the current system is problematic. The endless retakes at A level are a problem, but att GCSE, I think not- they simply show working hard has its rewards. I have had many pupils who have really tried in a system where they can see themselves improve, and would be lost in the single exam system - which ironically rewards the flyby nights idols individuals who are good at exams (of which there are very many). To change the system is therefore to privileges the idle over the workers....
Likewise the problem of grade poker related to schools swapping boards, is a problem, But its cause in not the exam, but rather the way schools are assessed. Unless we going to abolish (and it might take that) Ofsted, and rework how we understand what schools do, and how we (as a nation) ask them to endless do they do better, we are always going to get the distortions of grade poker (which the driver of grade inflation, not the exams themselves). Grade poker is then the creation of education ministers who want to prove they are doing something, and has little do to with schools themselves. That is why is is such a despicable game!
But in the hubbub of reform something wonderful will be certainly lost- namely the Brand New maths GCSE. This GCSE is maths as it has never been taught before - for it is the maths we live by and use every day of lives. Maths made real, edgy, difficult, a maths that does not need 'right' answer, only estimates, a maths that allows us to actually understand the world we live in. The radicalness of this approach, and its ability to change pupils lives (once they get the hang of it) is very hard to appreciate. It is no exaggeration to say that for the first time in twenty of teaching I feel like I am teaching something worthwhile, useful and even good. And this will now be swept aside in the name a reform which will set the clock back thirty years or so, and back to a system of examining and thinking about maths that seemed to delight in making it obscure, tricky, abstract, and about as far from everyday life as it is possible to go. Its loss will be heavy.
But then perhaps it is hypocritical of me to really mind. For one thing is certain, the old system with its sudden death exam was very good for maths tutors. If they reforms go ahead, my business will boom, as it always does when the system does not suit the pupils very well. But I am for at least big hearted enough to see beyond my greed. I just politicians were the same...
Thursday, September 13, 2012
Grade Poker - part 2
Let's face it - grade poker is a heartless game. I call it grade poker when pupils face repeated entries into GCSE exams (often beginning in year 10 or even 9), with the sole aim that the school maximises its grades, and so does not face an ofsted investigation. Time after time I first meet a pupil when they are demoralised and reeling from a particularly inappropriate bout of poker. They have been entered into an exam too early, and before their own personal ability to read, to think and to count, are lined up in the necessary conjunction to sit an exam, The result 'shot across the bows' has nearly sunk them. And I spend weeks getting their confidence up, before ever we open a paper.
The roots of Grade poker lie I think in the difference twenty years ago or more, between public school and comprehensive. Almost all privates schools played grade poker. But then they had the freedom to do so. The creamed off the best students in the 13+ exams, and got them wired in to a great exam sausage machine straight away - and those who rebelled were asked to leave. The result was that grade poker, particularly when played against 'bog standard' schools, was a very successful game. But then some time in the nineties it was decided that the public school model ought to be unwound for everyone if possible. The Creaming of talent and the ruthless removal of failure were clearly not appropriate in the state schools system- But grade poker was a game everyone could play. Everyone who really mattered in eduction (I mean ofsted, government, governors, exam boards,teachers ad even parents) were happy. Here a way to import the public sausage machine into the state system.
The only people who screamed were the kids - but then of course we could all yell back, that the exam were character building, and anyway to got them off their X boxes..... Well Maybe - but grade poker to my mind has long since stopped being appropriate or funny. Kids are simply too smart for it. They know they are being led through a series of exams, not for their own benefit but for the schools and for the 'collective good'. More than that they know they in the end the school will not make decisions based on them as living, breathing kids, but merely on the schools own need to get an As. So they have simply become used to the fact that their exam board has to change half way through their course, or that the exam has changed half way through their course or they are 'required' to sit the exam early or late, or miss it or do it in april of over Christmas (all of which I have known in the last three years). Kids then have stoically and to my mind heroically accepted that their education is nothing about them, and is all about the school and the government.
And yet, and yet, and yet, as I am called to see yet another lovely kid, who needs to get a C to go to farmers academy, and would get it quite easily, in the normal course of things, at the end of a GCSE course; and yet who is being forced to take the exam a year early, and has the prospect of taking it again and again (unless I can make a difference), and is panicking at the thought; I start to dream of the old system. You that one with an exam at sixteen - or at least a single set of modular exams, and perhaps even a maths project systems or two, a system that might have been dull, but seldom caused this level of panic. For the current world of perpetual exam, might be good for the government and for ofsted (Michel Gove you note is not talking about changing the exam regime), and is absolutely wonderful for maths tutor like me (it is my bread and butter), but it is loathsome for the people who really matter- the kids - and turns what could be fun and certainly (potentially) life changing namely learning (even maths should be engaging) into an endless grind, through a perpetual game of exam poker.
The roots of Grade poker lie I think in the difference twenty years ago or more, between public school and comprehensive. Almost all privates schools played grade poker. But then they had the freedom to do so. The creamed off the best students in the 13+ exams, and got them wired in to a great exam sausage machine straight away - and those who rebelled were asked to leave. The result was that grade poker, particularly when played against 'bog standard' schools, was a very successful game. But then some time in the nineties it was decided that the public school model ought to be unwound for everyone if possible. The Creaming of talent and the ruthless removal of failure were clearly not appropriate in the state schools system- But grade poker was a game everyone could play. Everyone who really mattered in eduction (I mean ofsted, government, governors, exam boards,teachers ad even parents) were happy. Here a way to import the public sausage machine into the state system.
The only people who screamed were the kids - but then of course we could all yell back, that the exam were character building, and anyway to got them off their X boxes..... Well Maybe - but grade poker to my mind has long since stopped being appropriate or funny. Kids are simply too smart for it. They know they are being led through a series of exams, not for their own benefit but for the schools and for the 'collective good'. More than that they know they in the end the school will not make decisions based on them as living, breathing kids, but merely on the schools own need to get an As. So they have simply become used to the fact that their exam board has to change half way through their course, or that the exam has changed half way through their course or they are 'required' to sit the exam early or late, or miss it or do it in april of over Christmas (all of which I have known in the last three years). Kids then have stoically and to my mind heroically accepted that their education is nothing about them, and is all about the school and the government.
And yet, and yet, and yet, as I am called to see yet another lovely kid, who needs to get a C to go to farmers academy, and would get it quite easily, in the normal course of things, at the end of a GCSE course; and yet who is being forced to take the exam a year early, and has the prospect of taking it again and again (unless I can make a difference), and is panicking at the thought; I start to dream of the old system. You that one with an exam at sixteen - or at least a single set of modular exams, and perhaps even a maths project systems or two, a system that might have been dull, but seldom caused this level of panic. For the current world of perpetual exam, might be good for the government and for ofsted (Michel Gove you note is not talking about changing the exam regime), and is absolutely wonderful for maths tutor like me (it is my bread and butter), but it is loathsome for the people who really matter- the kids - and turns what could be fun and certainly (potentially) life changing namely learning (even maths should be engaging) into an endless grind, through a perpetual game of exam poker.
Friday, September 7, 2012
I broke one of the unwritten rules about maths teaching yesterday. Never however much you are tempted contact those people who said they you get back to you, but did not. It is usually because they have not got the results they wanted, and do not want to tell you about it....
The trouble is then that you can live in a bubble of good results. It is the ones you never hear about you have also to worry about. And I do ( I reckon, from experience, around haf of them are merely inertia on the part of the pupil - they would tell you but....and the other half are those who have not done it).
The problem of course is that one so wants to make a difference - of course one does - but sometimes it is not possible. The case result in point, was was a weird one- the pupil had a genius in plausibly being wrong. I mean he was so plausible in not noticing something, or starting from the wrong place, and so generated such plausible readings, that he would catch me out: I would find myself agreeing within him, and only them say No.
The problem was therefore very clearly one of reading and thinking about the questions for his actauly theoretical maths was rather good. He misread questions, wanting them to be harder or just different from how they were, and all else followed. The problem then is of course exactly how does one address those who misread in this way? A real teaching problem, and one as unique as the pupil. What one then does is of course ones best. One goes through questions, one teaches lessons to the way they read must be read, one talks about putting distance in between them and the thought, and talks about reflexivity, and the joy of self correction, and does so repeatedly. One talks about the power of reading a question carefully, but also how to read bearing in mind the examiner, and the nature of a questions themselves... Finally one gives them lots a really difficult papers, and trues to get them to think under stress in a way that will get through an exam.
All of which can work - but with a plausible misheaded thinker it is always touch and go. For they might help, but they do not tackle the real problem. That problem is that the pupils has just mistook the nature of maths. They are thinking of it too abstractly just at the moment when you need to think of it as a problem-solving enterprise. This means they are quite literally reading it wrong. - they are if you like actually mistaking the nature of Number in the context of a maths exam. What makes the problem tricky is that the pupil is not wrong. Maths can be abstract, it is just not in GCSE! or to put it better translating something into maths, into the abstract world of symbols is only half the problem. One also has to translate abstract maths into actual questions, and make sure then you meet up.
It is this the inspired reader could not do - and I could not seem to show him how to do. He got the point that he was reading wrong, and that it was something to do with the way he was thinking about the maths, but could not stop, could not change - and so got a B not an A. Not awful, but he would have got a B without me... A good reminder to me as a teacher than sometimes it does not work, and one has to keep on learning how to teach, and thinking about how to make sure that next time...
For the pupil? well the grade did not stop him doing what he wanted to do,and he has time to go back to it if he wants to it. Moreover it does happen that only a bolt from beyond, a result cocked up, can give the impetus to really rethink how one thinks (which is never easy). Maybe he needed that result. If he did then the structures I went through with him of how to use maths to think, in terms of questions should help.
So in the end nothing is lost but parental hope and the dignity that goes iwith it. But perhaps that is not as bad as that to loose.
The trouble is then that you can live in a bubble of good results. It is the ones you never hear about you have also to worry about. And I do ( I reckon, from experience, around haf of them are merely inertia on the part of the pupil - they would tell you but....and the other half are those who have not done it).
The problem of course is that one so wants to make a difference - of course one does - but sometimes it is not possible. The case result in point, was was a weird one- the pupil had a genius in plausibly being wrong. I mean he was so plausible in not noticing something, or starting from the wrong place, and so generated such plausible readings, that he would catch me out: I would find myself agreeing within him, and only them say No.
The problem was therefore very clearly one of reading and thinking about the questions for his actauly theoretical maths was rather good. He misread questions, wanting them to be harder or just different from how they were, and all else followed. The problem then is of course exactly how does one address those who misread in this way? A real teaching problem, and one as unique as the pupil. What one then does is of course ones best. One goes through questions, one teaches lessons to the way they read must be read, one talks about putting distance in between them and the thought, and talks about reflexivity, and the joy of self correction, and does so repeatedly. One talks about the power of reading a question carefully, but also how to read bearing in mind the examiner, and the nature of a questions themselves... Finally one gives them lots a really difficult papers, and trues to get them to think under stress in a way that will get through an exam.
All of which can work - but with a plausible misheaded thinker it is always touch and go. For they might help, but they do not tackle the real problem. That problem is that the pupils has just mistook the nature of maths. They are thinking of it too abstractly just at the moment when you need to think of it as a problem-solving enterprise. This means they are quite literally reading it wrong. - they are if you like actually mistaking the nature of Number in the context of a maths exam. What makes the problem tricky is that the pupil is not wrong. Maths can be abstract, it is just not in GCSE! or to put it better translating something into maths, into the abstract world of symbols is only half the problem. One also has to translate abstract maths into actual questions, and make sure then you meet up.
It is this the inspired reader could not do - and I could not seem to show him how to do. He got the point that he was reading wrong, and that it was something to do with the way he was thinking about the maths, but could not stop, could not change - and so got a B not an A. Not awful, but he would have got a B without me... A good reminder to me as a teacher than sometimes it does not work, and one has to keep on learning how to teach, and thinking about how to make sure that next time...
For the pupil? well the grade did not stop him doing what he wanted to do,and he has time to go back to it if he wants to it. Moreover it does happen that only a bolt from beyond, a result cocked up, can give the impetus to really rethink how one thinks (which is never easy). Maybe he needed that result. If he did then the structures I went through with him of how to use maths to think, in terms of questions should help.
So in the end nothing is lost but parental hope and the dignity that goes iwith it. But perhaps that is not as bad as that to loose.
Thursday, September 6, 2012
The second result I got yesterday was an A. Now this was an interesting one. The exam was the easy exam in a three part modular GCSE. So it matters but is only worth 30% of the whole. The pupil was originally forecast a D, so again a real result. But has left us all with a problem. She is now out performing her class (she is bottom to mid range in her setting), so much so that the school (partly because the poker-game now being imposed by an interventionist central government...) wants to change the exam she is in. She is doing well in the modular exam, but the rest of her class need to go on the linear,(end of year)version of the exam. She is therefore at risk of losing her A and having to sit the exam again, because the paper has changed!
This is of course where it all gets hard. The pupil herself is about the fourth most able natural mathematician I have ever taught - who in spite of 'doing a dizzy blond act' sees the structure of numbers, and can tell you the right answer very quickly and without really knowing how she does it, and does it for sums I have to right down ( her mum I discovered is the same, but never was encouraged at school)! So within reason we can do our worst to her- she can cope! And yet, she is very prone to being disheartened and assuming she is daffy after all.
The problem is therefore whether she gets promoted out of the set she she in to a set where they are going to stay in the modular exam - but are likely to go quickly be algebraic, and where it will be assumed, that she, prompted as she is form 'down below' is daft when she does not understand stuff in the same way. Moreover the move would mean she would loose the teacher who she is rather fond of, and works well with, and be seperated from all her mates. So this is clearly a no brainer, I told her mum, keep her where she is happy, where she is a star, and do so even though it means that she will be being taught for a different exam from the one she wants to take. The difference between the two papers is actually rather small. Indeed I think with my teacher head on she will probably do better as a result of this move, and the fact that now the school is going (apparently) to enter her in to two exams at once - both versions! It will give her two chances.
But it will do so only if we can keep her motivated, and wanting to do well, and keep her sprits us in the face now of two exams in the summer. This might be difficult, and yet it is better than the alternative, of a promotion to a class where the Dizzy Blond will take over in the face of algebra, or simply pulling her out of an exam she is on target to get an A in and into an exam where she has all to prove all over again. It all should be possible, and yet it does mean I will have my work cut out, and - will keep you posted.
But more than that it explains the problem of any exam system (and all reforms) - they only work sometimes - and easily do not pick the most able students if those students are not typical, and do not know that they are any good (and why should they)! They are the ones thatall too easily get lost, and left to assume they are daffy.... it is only I think when this happens in the second generation, that they picked up because their parent is desperate that the same does not happen to their kids as did happen twenty years ago or so to themselves....
This is of course where it all gets hard. The pupil herself is about the fourth most able natural mathematician I have ever taught - who in spite of 'doing a dizzy blond act' sees the structure of numbers, and can tell you the right answer very quickly and without really knowing how she does it, and does it for sums I have to right down ( her mum I discovered is the same, but never was encouraged at school)! So within reason we can do our worst to her- she can cope! And yet, she is very prone to being disheartened and assuming she is daffy after all.
The problem is therefore whether she gets promoted out of the set she she in to a set where they are going to stay in the modular exam - but are likely to go quickly be algebraic, and where it will be assumed, that she, prompted as she is form 'down below' is daft when she does not understand stuff in the same way. Moreover the move would mean she would loose the teacher who she is rather fond of, and works well with, and be seperated from all her mates. So this is clearly a no brainer, I told her mum, keep her where she is happy, where she is a star, and do so even though it means that she will be being taught for a different exam from the one she wants to take. The difference between the two papers is actually rather small. Indeed I think with my teacher head on she will probably do better as a result of this move, and the fact that now the school is going (apparently) to enter her in to two exams at once - both versions! It will give her two chances.
But it will do so only if we can keep her motivated, and wanting to do well, and keep her sprits us in the face now of two exams in the summer. This might be difficult, and yet it is better than the alternative, of a promotion to a class where the Dizzy Blond will take over in the face of algebra, or simply pulling her out of an exam she is on target to get an A in and into an exam where she has all to prove all over again. It all should be possible, and yet it does mean I will have my work cut out, and - will keep you posted.
But more than that it explains the problem of any exam system (and all reforms) - they only work sometimes - and easily do not pick the most able students if those students are not typical, and do not know that they are any good (and why should they)! They are the ones thatall too easily get lost, and left to assume they are daffy.... it is only I think when this happens in the second generation, that they picked up because their parent is desperate that the same does not happen to their kids as did happen twenty years ago or so to themselves....
More Results
So the great ring round produced two more results.... This time B and an A, both with a story behind them.
The B grade (Apparently 'nearly' an A) was from a student you I had seen for a year. She had been forecast a D, taken off the modular version of the exam, and moved from the higher paper to the foundation - hence the mum called me. The school was of course playing 'grade poker'. They were simply trying to ensure she go at least a C (or their own purposes - pupils failing does not look good). The pupil was therefore when I first saw her throughly demoralised, and already justifying why she was such a failure....and yet, and yet I soon discovered she was quite good at maths.
My aim in teaching her was therefore not really one of instruction - to be honest she already knew and understood it all. The task was rather to allow her to feel she was good (again) at maths, and give her the space to recover the shock of the degrade. More in particular the immediate job was to ensure that her ability to read (which in lay life was formidable) was carried over into her maths ability- because that was what has slipped: Her apparent failure had meant that she somehow was now ashamed to be a 'reader' - and assumed reading was somehow shameful in a maths exam....The immediate target was a foundation exam in January, which she got a C in. That actually was easy once I got her up and reading (that took a few months), and really she did the rest, I was just the appreciative audience!
The much more difficult task was to get that grade up in the full exam she was now taking in June. She wanted -I checked with her when her parents were away - a B, and wanted it quite a lot, but not desperately, she was happy with the C..... which meant she was more relaxed at least. Trouble was by now in terms of her maths and reading, if I could get them union I knew she really ought to get an A. But here there was an added problem - namely the new exam with its emphasis of scary long real world questions, where there are no rights or wrongs. None of us had ever taught an exam that looked like this, and I had no idea how pupils would react to it. Again technically (if it was not maths) she would be good at that kind of idea - but in maths? It felt tricky...
In the end She and I kept her going and kept her trying through successes and failures in mocks, and through a perplexing exam, and she did it (for herself - which is what matters).
The result was probably very fair. She got a B and was delighted, all the more so because it was just off (like 3 marks) an A - and so much better than she thought she would do, and has convinced she really can do it - and so she was clever after all: she Could Do Maths! So a real result. Her motehr was likewise so grateful, and so chuffed.
And that is actually of course all that really matters. It is only us grown (nerds) who get obsessesed with those grades and regret the missing 3 marks....
The B grade (Apparently 'nearly' an A) was from a student you I had seen for a year. She had been forecast a D, taken off the modular version of the exam, and moved from the higher paper to the foundation - hence the mum called me. The school was of course playing 'grade poker'. They were simply trying to ensure she go at least a C (or their own purposes - pupils failing does not look good). The pupil was therefore when I first saw her throughly demoralised, and already justifying why she was such a failure....and yet, and yet I soon discovered she was quite good at maths.
My aim in teaching her was therefore not really one of instruction - to be honest she already knew and understood it all. The task was rather to allow her to feel she was good (again) at maths, and give her the space to recover the shock of the degrade. More in particular the immediate job was to ensure that her ability to read (which in lay life was formidable) was carried over into her maths ability- because that was what has slipped: Her apparent failure had meant that she somehow was now ashamed to be a 'reader' - and assumed reading was somehow shameful in a maths exam....The immediate target was a foundation exam in January, which she got a C in. That actually was easy once I got her up and reading (that took a few months), and really she did the rest, I was just the appreciative audience!
The much more difficult task was to get that grade up in the full exam she was now taking in June. She wanted -I checked with her when her parents were away - a B, and wanted it quite a lot, but not desperately, she was happy with the C..... which meant she was more relaxed at least. Trouble was by now in terms of her maths and reading, if I could get them union I knew she really ought to get an A. But here there was an added problem - namely the new exam with its emphasis of scary long real world questions, where there are no rights or wrongs. None of us had ever taught an exam that looked like this, and I had no idea how pupils would react to it. Again technically (if it was not maths) she would be good at that kind of idea - but in maths? It felt tricky...
In the end She and I kept her going and kept her trying through successes and failures in mocks, and through a perplexing exam, and she did it (for herself - which is what matters).
The result was probably very fair. She got a B and was delighted, all the more so because it was just off (like 3 marks) an A - and so much better than she thought she would do, and has convinced she really can do it - and so she was clever after all: she Could Do Maths! So a real result. Her motehr was likewise so grateful, and so chuffed.
And that is actually of course all that really matters. It is only us grown (nerds) who get obsessesed with those grades and regret the missing 3 marks....
Wednesday, September 5, 2012
Here we go!
it is that time of year - the one that I always dread most. It is the day that I will contact all tuitions from last year and find out how they did, and arrange for tuitions for this year, if they still need them.
I dread it on so many levels. Firstly it is simply the case that I do not know as yet how busy I am next week, in some years the start has been so slow, while in other years I have started with such a bang, it is not true..... So who knows? Secondly I always want my pupils to do their very best - and teach them to do that, and so actually finding my out results is as nerve wracking as if they were my own results, and this my GCSE year,,,. I actually dread knowing- though i must know.... Finally I guess it is natural to fear the kind of phone call you do not know the result of even as you make it. I mean no one has ever been nasty- in fact usually the calls the nicest I make all year. People are often happy to hear from me, and curious about the summer - and that is wonderful, but never assume it is the case, I am just a maths teacher after all!
And yet I still the fear calls. So think of me, and all other tutors today and tomorrow, andkeepyour fingers cross....
it is that time of year - the one that I always dread most. It is the day that I will contact all tuitions from last year and find out how they did, and arrange for tuitions for this year, if they still need them.
I dread it on so many levels. Firstly it is simply the case that I do not know as yet how busy I am next week, in some years the start has been so slow, while in other years I have started with such a bang, it is not true..... So who knows? Secondly I always want my pupils to do their very best - and teach them to do that, and so actually finding my out results is as nerve wracking as if they were my own results, and this my GCSE year,,,. I actually dread knowing- though i must know.... Finally I guess it is natural to fear the kind of phone call you do not know the result of even as you make it. I mean no one has ever been nasty- in fact usually the calls the nicest I make all year. People are often happy to hear from me, and curious about the summer - and that is wonderful, but never assume it is the case, I am just a maths teacher after all!
And yet I still the fear calls. So think of me, and all other tutors today and tomorrow, andkeepyour fingers cross....
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