It is a strange feeling, teaching the new maths syllabus.
On the hand one is teaching a course that is actually very worth while - in the sense that the maths that allows one to fill in a tax return or work out a fuel consumption is always good, always useful. More than that it, teaching the kind of methods that one needs to work out real world situation demands one actually teaches thought, rather than simple 'you do this then that, then this.' The philosopher me really revels teaching this syllabus, as it really demands pupils think and presents the teacher with the challenge that we teach the links between topics, rather than the formal topics itself.
On the other hand, it is very very strange to teach, if one understands teaching in its old formal sense. That definition of teaching was very class room based, and what it taught reflected the classroom situation. One taught methods inside topics and during formal lessons - one did fractions then percentages, then ratios, and left it to minds of the smartest to work out that these are really the same thing. One could use the connection between the different elements of the syllabus as a signifier for smartness: A's were given to those who link topics, and as teachers we conspired that it was so.
The strangeness for me, is that while the first stratagem for teaching is for me preferable, it is as a teacher much harder to work out both what you are doing, and what the long terms effect of what teaching be. I mean you are teaching to something that is integral to humans, namely their real understanding. The pupils therefore really comprehend what you are saying, which is just as well as the bite sized ' you do this then that in this case' approach cannot be formally taught as such. There are no simple methods or internal 'one-size-fits-all written answer calculators (that is very few formal written methods). One is therefore never really sure, until the next week or week after, of the power ones teaching:- If you like one is always flying blind, as one cannot read another's mind, and there nothing on paper to read. If you like maths teaching has become intuitive! Which for my money is no bad thing....
The only trouble is, of course that this being blind makes the teaching slightly weird for the teacher as it is (potentially) good for the pupil- and problem is that education is run by adults, as is basically for adults: Teaching is so often an expression of adult anxiety, and not what is good to learn. It is then surely only a matter of time before we turn back to what is easy for adults to teach, asses and so judge both pupils and teachers. A fact that makes teaching the new approach all the more odd. I know even as I really get my teeth into how to teach it, how to think it, that the knowledge will soon be useless, and swept away in the interest of tradition.
Monday, October 8, 2012
Tuesday, October 2, 2012
Leaders....Follow the leaders
It is one of the strange, and very hidden dangers of teaching - any teaching - namely the problem of power.
Power is always at stake in teaching; without it the very ability of the teacher is questioned - authority breaks down, and with it trust in what is being taught; and once that has gone, then all teaching ceases: all that are imparted are a random sequence of half truth.
Power matters therefore to teachers, we need it.
And yet, power warps the powerful, of course it does. It is so easy for a teacher to assume that somehow the power they wield is justified and right. All the more so as the power is often hard won, and potentially problematic in itself. It needs therefore to be substantiated, by an assumption that the power is somehow justified and simply 'right'; the implication then being what that power breeds, what abuses or assumptions are also necessarily right.
Now in the past the relationship was of crisscrossed by voilence. Teacher could wack children and did often. It then went through a period where work itself became the issue. If one wanted to enforce authority, then one made the students work harder, or pointlessly. And now of course we express the same abuse in terms exams, and endless regulation. we make kids feel small, by making them feel stupid: By revealing that stupidity, not only to them, but also their peers...And at the same time of course, on a slightly bigger picture, the 'powers that be' in education (politicians and regulators) wield their own power over teachers. The struggles of kids and teachers, are then caught up in a wider struggle of politicians, with all that entails...
Of course one has to be so very careful in all this. Power and teaching goes together, of course it does - and power and abuse goes together, just as naturally; for once one has power it is next to impossible to pitch it right. Indeed the anarchist in me thinks it is impossible for power to be otherwise. There is no point, one moment its righteous exercise becomes an abuse. On the contrary, the two sides of power are caught up together, abuses are justified, from other angles, or if the mood music changes...
The problem any epoch in education faces is therefore where it draws its lines of power - and how it links learning to discipline and so to thought. There is probably no right and wrong here, only exercise and consequence. The fatal mistake that adults make is that kids do know what is happening and why. Of course they do, they are just pragmatists and accept it all - but then of course of judge it and its justifications in their own way and in their own time. A thought I think that is so difficult for adults to encompass, that they ignore it - much to the cost of the over all system.
Power is always at stake in teaching; without it the very ability of the teacher is questioned - authority breaks down, and with it trust in what is being taught; and once that has gone, then all teaching ceases: all that are imparted are a random sequence of half truth.
Power matters therefore to teachers, we need it.
And yet, power warps the powerful, of course it does. It is so easy for a teacher to assume that somehow the power they wield is justified and right. All the more so as the power is often hard won, and potentially problematic in itself. It needs therefore to be substantiated, by an assumption that the power is somehow justified and simply 'right'; the implication then being what that power breeds, what abuses or assumptions are also necessarily right.
Now in the past the relationship was of crisscrossed by voilence. Teacher could wack children and did often. It then went through a period where work itself became the issue. If one wanted to enforce authority, then one made the students work harder, or pointlessly. And now of course we express the same abuse in terms exams, and endless regulation. we make kids feel small, by making them feel stupid: By revealing that stupidity, not only to them, but also their peers...And at the same time of course, on a slightly bigger picture, the 'powers that be' in education (politicians and regulators) wield their own power over teachers. The struggles of kids and teachers, are then caught up in a wider struggle of politicians, with all that entails...
Of course one has to be so very careful in all this. Power and teaching goes together, of course it does - and power and abuse goes together, just as naturally; for once one has power it is next to impossible to pitch it right. Indeed the anarchist in me thinks it is impossible for power to be otherwise. There is no point, one moment its righteous exercise becomes an abuse. On the contrary, the two sides of power are caught up together, abuses are justified, from other angles, or if the mood music changes...
The problem any epoch in education faces is therefore where it draws its lines of power - and how it links learning to discipline and so to thought. There is probably no right and wrong here, only exercise and consequence. The fatal mistake that adults make is that kids do know what is happening and why. Of course they do, they are just pragmatists and accept it all - but then of course of judge it and its justifications in their own way and in their own time. A thought I think that is so difficult for adults to encompass, that they ignore it - much to the cost of the over all system.
Wednesday, September 26, 2012
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.
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.
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.
Subscribe to:
Posts (Atom)