ON LEARNING MATHEMATICS WITH LESS ANXIETY

ON LEARNING MATHEMATICS WITH LESS ANXIETY

4th talk for students and teachers of philosophy and education
at Mercer University, Georgia, USA: 30 September, 2005.

   Good evening, everyone. I am really very honoured to be asked to talk with you about learning mathematics. It is of course exciting for an Englishman to be invited to America to talk about anything. It is quite some time since Americans felt that there was anything they had to learn from England, but I have to tell you that I would not be here except for my admiration for Dr Khoury.
   Teaching is an extremely conservative profession. Most professions are, of course. That is why they are called professions. The professors teach their undergraduates; the undergraduates graduate; use what they have learnt from their professors; then some of them become professors, and they teach what that they have learnt that has worked for them. There is really very little room for actual invention.
   It may not look quite like that it teaching. There are always these new ideas; new approaches; fancy new fashions; initiatives of this, initiatives of that. But if you look at these apparently new ideas closely, you usually find there is very little there which fundamentally affects two essential relationships in the classroom: the dominance of the teachers as instructors of the subject and the internal social dynamics of the class.
   Internal social dynamics! Hoo-hoo! That sounds just like one of these fancy new buzzwords, doesn't it? Maybe it does. It means something that destroys more good teachers than any education system can afford to lose.
   In the good old bad old days when a teacher - to use the words of your President Teddy Roosevelt - could talk softly and carry a big stick: and, just occasionally, use it, are long gone. Then there was no need to both with any internal dynamics of a class. Everyone just sat down; shut up; and kept their mouth closed until told to speak. There might be the occasional shove or push: even fight in the playground - but in the classroom the teacher was the boss.
   Today you need to know about internal social dynamics. In other words, teaching today is rather like trying to keep the attention of a bucketful of frogs.
   Personality is supposed to be the answer. The teacher is supposed to have such a force of personality, such powers of persuasion and inspiration and innovation and dedication and communication and empathization - and I don't know what other kinds of 'actions' : but you can be sure they are written down in a job description somewhere - that an entire class remains just fascinated and enthralled by everything the teacher does, says, or writes.
   How many of you have ever been in a class like that? Well, I used to have a colleague who has this effect on his classes: using a kind of radiation. Elmore Leonard wrote about it for Chili Palmer in Get Shorty. Did you ever read that book? Chili was a loan collector and he used to talk about 'washing' his customers - 'hosing them down' - with fear. My colleague was like that. I used to envy him a lot. He had his classes paralysed most of the time. I couldn't do it. I had been in the Army, however, and the Army teaches its officers to 'manifest' a kind of total, unquestionable authority. This would be like Colonel Kurtz in Apocalypse Now, or Jack Nicholson as Jessep in All the Good Men.
   I couldn't frighten my classes to death, but I had just that kind of authority. At least, I did - and it worked: until the year I came up against a class that decided to show me that it was tougher than I was. With this class I use to wake at four in morning, sweating, thinking about that class. "Oh God, I've got the Fourth Year in the morning!" These were fifteen year old kids. They were a monster with twenty-five head: and I had only one. I could bite one: twenty-four would bite back. I lost that fight.
   I nearly quit teaching too at that time. But then I began to think there must be a better way to do this: so that I stay happy - all the time; nearly all the time - so that I can carry on teaching, because I believe in teaching. In that film I just referred to Nicholson as Colonel Jessep is trying to explain to Tom Cruise why he, Cruise, as prosecuting officer, does not want to hear the truth. "You can't handle the truth," he says and he is very angry. "I have a greater responsibility than you can possibly fathom. We live in a world that has walls. Those walls have to be guarded by men with guns."
   Now I think this is true. I know this is true. But I also know now that the first line of defence of any society against its destruction is not the men who stand and guard the walls that hold the barbarians back on the other side. It is the teachers who stop the barbarians - or who should stop the barbarians - appearing inside the walls.
   And this is what brought me here. Because Dr Khoury invited me? No, not just that. I have lots to do at home. I have frogs in my pond. I think I do. They were there in the spring, but the pond is now so thick with weed that they must be wondering whether global warming is getting to them as well.
   I am here because Dr Khoury started to do something new - with you and his other classes - without telling me; and without looking for any encouragement from me or any grant from the Ford Foundation or the Rockefeller Trust. He just went ahead and did it: and what he did turns every fashion that I know about in education right around through one hundred and eighty degrees and destroys the potential of the usual internal social dynamics of the class - well, let me give that a simpler name: the bucket of frogs - to wreck your chances of learning. This is why I admire him.
   At first it may appear that he may be asking you to do more than before. I hope so.
    You see, in the frog bucket scenario: with twenty or thirty frogs all waiting for a chance to jump, you never know who is actually listening or watching - do you know that the brain of a frog is in fact so connected to its eyeballs that until something actually moves into their line of sight it is not seeing at anything at all! Wire up even a very bright and usually perfectly thoughtful frog to an ECG machine - a brain wave machine - and until something moves out there right in front of it; and something, furthermore, that it will want to eat - and it will flat-line! How many hours do you suppose I have spent talking, writing, drawing in front of a class - only to find that they have all been flat-lining?
   And then when they're all quiet like that at the bottom of the bucket, all apparently deeply thinking their own thoughts about what you are saying, you never know who is going to jump next - Ooop!, like that - and set off all the rest in a great tangle of activity and a terrible great waste of time. More time is wasted like this than is ever spent learning. This is the real tragedy of all those methods in which the teacher is supposed to be dominant. The teacher is not allowed to dominate any more. Colonel Jessep lost his fight to guard the walls. Teachers are supposed to inspire: twenty percent of the time. The rest of the time is frog-jumping time.
   What I think Dr Khoury will be trying to get you to do together when you work in his class is not to listen to him. But the fact is that almost no-one can do that several hours a week for months at a time. Instead he is more likely to ask you to listen to each other talking about what you understand of what you are doing or what your textbook - or he - expects you to do.
   This is easier on you - and on him. But it is also more interesting. You will learn faster, with less anxiety, with less likelihood of being intimidated by the others or silenced by shyness. You will discover - I hope without too much pleasure - that even the most confident and most articulate big-mouth is just as often lost for the exact words which will describe what he or may be she is thinking as you may be.
   This is why it's so exciting, you see. This is okay. It takes time for a frog's brain just to work out if anything is moving. Do not be surprised that it takes any brain time to begin to describe what it may actually see itself doing. Imagine trying to explain to someone else what you have to do to do a knot in your shoelaces. That's hard enough. Do any of you skateboard? Explaining exactly what your whole body has to do to get your board to jump up a step would be hard for an expert physicist.
   The good thing about what we try to do with a Socrates Method class is that everyone gets an exactly equal chance either to be a genius or to make a complete fool of themselves. Let me tell you how it started.

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ON LEARNING MATHEMATICS WITH LESS ANXIETY 4th talk for students and teachers of philosophy and education at Mercer University, Georgia, USA: 30 September, 2005. Good evening, everyone. I am really very honoured to be asked to talk with you about learning mathematics. It is of course exciting for an Englishman to be invited to America to talk about anything. It is quite some time since Americans felt that there was anything they had to learn from England, but I have to tell you that I would not be here except for my admiration for Dr Khoury. Teaching is an extremely conservative profession. Most professions are, of course. That is why they are called professions. The professors teach their undergraduates; the undergraduates graduate; use what they have learnt from their professors; then some of them become professors, and they teach what that they have learnt that has worked for them. There is really very little room for actual invention. It may not look quite like that it teaching. There are always these new ideas; new approaches; fancy new fashions; initiatives of this, initiatives of that. But if you look at these apparently new ideas closely, you usually find there is very little there which fundamentally affects two essential relationships in the classroom: the dominance of the teachers as instructors of the subject and the internal social dynamics of the class. Internal social dynamics! Hoo-hoo! That sounds just like one of these fancy new buzzwords, doesn't it? Maybe it does. It means something that destroys more good teachers than any education system can afford to lose. In the good old bad old days when a teacher - to use the words of your President Teddy Roosevelt - could talk softly and carry a big stick: and, just occasionally, use it, are long gone. Then there was no need to both with any internal dynamics of a class. Everyone just sat down; shut up; and kept their mouth closed until told to speak. There might be the occasional shove or push: even fight in the playground - but in the classroom the teacher was the boss. Today you need to know about internal social dynamics. In other words, teaching today is rather like trying to keep the attention of a bucketful of frogs. Personality is supposed to be the answer. The teacher is supposed to have such a force of personality, such powers of persuasion and inspiration and innovation and dedication and communication and empathization - and I don't know what other kinds of 'actions' : but you can be sure they are written down in a job description somewhere - that an entire class remains just fascinated and enthralled by everything the teacher does, says, or writes. How many of you have ever been in a class like that? Well, I used to have a colleague who has this effect on his classes: using a kind of radiation. Elmore Leonard wrote about it for Chili Palmer in Get Shorty. Did you ever read that book? Chili was a loan collector and he used to talk about 'washing' his customers - 'hosing them down' - with fear. My colleague was like that. I used to envy him a lot. He had his classes paralysed most of the time. I couldn't do it. I had been in the Army, however, and the Army teaches its officers to 'manifest' a kind of total, unquestionable authority. This would be like Colonel Kurtz in Apocalypse Now, or Jack Nicholson as Jessep in All the Good Men. I couldn't frighten my classes to death, but I had just that kind of authority. At least, I did - and it worked: until the year I came up against a class that decided to show me that it was tougher than I was. With this class I use to wake at four in morning, sweating, thinking about that class. "Oh God, I've got the Fourth Year in the morning!" These were fifteen year old kids. They were a monster with twenty-five head: and I had only one. I could bite one: twenty-four would bite back. I lost that fight. I nearly quit teaching too at that time. But then I began to think there must be a better way to do this: so that I stay happy - all the time; nearly all the time - so that I can carry on teaching, because I believe in teaching. In that film I just referred to Nicholson as Colonel Jessep is trying to explain to Tom Cruise why he, Cruise, as prosecuting officer, does not want to hear the truth. "You can't handle the truth," he says and he is very angry. "I have a greater responsibility than you can possibly fathom. We live in a world that has walls. Those walls have to be guarded by men with guns." Now I think this is true. I know this is true. But I also know now that the first line of defence of any society against its destruction is not the men who stand and guard the walls that hold the barbarians back on the other side. It is the teachers who stop the barbarians - or who should stop the barbarians - appearing inside the walls. And this is what brought me here. Because Dr Khoury invited me? No, not just that. I have lots to do at home. I have frogs in my pond. I think I do. They were there in the spring, but the pond is now so thick with weed that they must be wondering whether global warming is getting to them as well. I am here because Dr Khoury started to do something new - with you and his other classes - without telling me; and without looking for any encouragement from me or any grant from the Ford Foundation or the Rockefeller Trust. He just went ahead and did it: and what he did turns every fashion that I know about in education right around through one hundred and eighty degrees and destroys the potential of the usual internal social dynamics of the class - well, let me give that a simpler name: the bucket of frogs - to wreck your chances of learning. This is why I admire him. At first it may appear that he may be asking you to do more than before. I hope so. You see, in the frog bucket scenario: with twenty or thirty frogs all waiting for a chance to jump, you never know who is actually listening or watching - do you know that the brain of a frog is in fact so connected to its eyeballs that until something actually moves into their line of sight it is not seeing at anything at all! Wire up even a very bright and usually perfectly thoughtful frog to an ECG machine - a brain wave machine - and until something moves out there right in front of it; and something, furthermore, that it will want to eat - and it will flat-line! How many hours do you suppose I have spent talking, writing, drawing in front of a class - only to find that they have all been flat-lining? And then when they're all quiet like that at the bottom of the bucket, all apparently deeply thinking their own thoughts about what you are saying, you never know who is going to jump next - Ooop!, like that - and set off all the rest in a great tangle of activity and a terrible great waste of time. More time is wasted like this than is ever spent learning. This is the real tragedy of all those methods in which the teacher is supposed to be dominant. The teacher is not allowed to dominate any more. Colonel Jessep lost his fight to guard the walls. Teachers are supposed to inspire: twenty percent of the time. The rest of the time is frog-jumping time. What I think Dr Khoury will be trying to get you to do together when you work in his class is not to listen to him. But the fact is that almost no-one can do that several hours a week for months at a time. Instead he is more likely to ask you to listen to each other talking about what you understand of what you are doing or what your textbook - or he - expects you to do. This is easier on you - and on him. But it is also more interesting. You will learn faster, with less anxiety, with less likelihood of being intimidated by the others or silenced by shyness. You will discover - I hope without too much pleasure - that even the most confident and most articulate big-mouth is just as often lost for the exact words which will describe what he or may be she is thinking as you may be. This is why it's so exciting, you see. This is okay. It takes time for a frog's brain just to work out if anything is moving. Do not be surprised that it takes any brain time to begin to describe what it may actually see itself doing. Imagine trying to explain to someone else what you have to do to do a knot in your shoelaces. That's hard enough. Do any of you skateboard? Explaining exactly what your whole body has to do to get your board to jump up a step would be hard for an expert physicist. The good thing about what we try to do with a Socrates Method class is that everyone gets an exactly equal chance either to be a genius or to make a complete fool of themselves. Let me tell you how it started.
	*
This method started about two and half thousand years ago. Since then it has been forgotten, remembered, forgotten and remembered I don't know how many times. It tends to get remembered when someone like Dr Khoury or me stop being satisfied with being the ringmaster of a just bucketful of frogs: when we want to believe our pupils actually know and can do something - that they can learn more than just what we tell them! In those days, in Greece, they really did have walls to hold back the barbarians. They were called the Long Walls, and they ran from Athens all the way down to the harbour where the Athenians kept their navy so that, as a last resort, they could always put their men to sea in their ships and attack a land enemy from behind. This is what General Douglas MacArthur did in North Korea, at the Inchon Landings in 1950. These Greeks were pretty superior people. Really stuck-up, you might say. They called everyone a barbarian who was not a freeborn Greek. There was some discussion amongst them whether these barbarians could actually think as they did at all. One day the first Socrates offered to demonstrate that everyone's brain has a whole store of memories from before they were born, and that working anything out just meant recalling what the brain already knows. He got hold of a young slave boy - obviously a barbarian - as a pupil, and got him to talk about the difference between the lengths of the sides of a triangle. Now at first I thought that this was a pure demonstration of the 'Socratic Method'. But if you read it through it is more like the sort of thing that a really bossy teacher will do to persuade you that you have thought things out for yourself when all you are actually doing is being made to answer the way the teacher wants you to. The teacher asks questions to which there are really only obvious answers. For example: "Do you see that this triangle has three straight sides?" "Yes." "Do you see that there must be two shorter sides and one long one?" "Yes." "And isn't it obvious that the two short sides and the one long one connect the same two points? "Yes." "And which is usually the shortest distance between two points?" "A straight line." "So what can you tell me about the total length of the two short sides compared with the one long side?" "Ooh, you are clever! And I: I am such a good teacher!" Socrates was really quite a sly old man. It got him into deep trouble in the end because his enemies were able to accuse him of doing exactly the things he was against: 'of making the weaker argument appear stronger'. This was actually one of the accusations at his trial: that he deliberately confused honest people. But the method he uses with the slave-boy is so obviously not going to help anyone to think for themselves that it is now reckoned to be a spoof demonstration of how not to teach! What Socrates is really famous for is continually asking people what they mean by words like 'courage', 'honest', 'loyalty' and so on. He made people think about ideas that they thought they understood perfectly well. He made them realize that they only knew how words like this are most often used - not they really mean! They had skills in using words, but they had not much knowledge to go with the skills. A lot of people liked what Socrates was doing. Far too many found him irritating. He called himself 'a gadfly'. Eventually they decided he had to be swatted!
	*
I want now shift from discourse like this to anecdotes to try to suit the interest and humour of the class. For example: How did I begin? The boy who told me: "I've finished." How do people really learn: correspondence with Chomsky/Barlow. Skills are non-verbal; knowledge is language. What we now know of the brain: semi-specific functions. What we know about learning: complex pathways; value of humour/contexts. Maths explanations are arguments: connection with democracy; Lloyd/Stewart. Maths taught as orders: "bullshit!" from Columbia; methods in the RPC. European School Senior Maths Inspector Dethier: "Use the textbook!" Learning use the text book: "You're supposed to teach us this rubbish!" Autonomy at eleven: "I've discovered a secret: it works with other subjects!" Germany: "Gentlemen, I've come here today - " The Stuttgart project; continuing. Hungary: Eötvös Lorand research; Eastern Europe, national divisions.. Istanbul: Director of Basic Research; Bosphorus U. Zeldin: The Socrates Workbook; New Scientist; TES; Literacy Today. Dr H. Khoury, Mercer U. HH Sheikha Mozah, Qatar. ... and I can also ad lib! 24/09/05 If you have arrived from an external link click here.