A KINDER WAY TO TEACH: TO LEARN: A history of heroic failure

Dec 14, 2015 by


A KINDER WAY TO TEACH: TO LEARN: A history of heroic failure

Colin Hannaford
Oxford, England

I always knew that my spectacularly successful career as a classroom mathematics teacher must end eventually. I imagined it would be celebrated with an award from a grateful European Union for rescuing mathematics teaching in Europe, another in the United States for restoring belief in government of the people, by the people, and for the people, and perhaps another by UNESCO for saving all of humankind from existential despair.

It was more like a train crash.

I had become sufficiently proud one of my youngest classes: twelve to thirteen year-olds, girls and boys, multi-national, and multi-lingual, that I invited a deputy-director to a lesson.

Pride before fall.

For some time he had been showing anxiety about the reports he would have heard about what was going on. Now he would find out: first-hand.

After ten years of practice, I was now teaching all my pupils to learn mathematics directly from their textbook. They would continue like this until Baccalaureate. All the pupils in this particular class still enjoyed working with others, but many were already virtually self-directed. I was happy to invite him.

“You remember what you’ve been telling us,” one eleven year-old had told me, or rather whispered one day after asking to speak to me alone.

A little nervously, I had agreed. “You remember about reading aloud, and then asking ourselves ‘What does this mean?’” I admitted that I did remember.

“Well,” and now his voice trembled, as he was imparting the secret of World Peace, as, indeed, it might be, “I’ve discovered it works with other subjects!”

But the deputy-director was incensed.

“If you carry on teaching children like this,” he told me, although he had at least the grace to wait until they had left the room, “in a few years time they won’t need a teacher at all! You must stop teaching them like this at once!”

I could only stare in silence. If his face had peeled away to reveal clicking mandibles drooling slime, I might have been more surprised, but not much.

He had much more to say. I waited silently. He was comparatively young for position of such responsibility, of such authority. I knew that his own subject as a teacher had been geography. He had probably taught geography for less than ten years. I had been teaching mathematics for twenty-six years: twenty-four in this school.

After my army service, in which I had once been an instructor of young army apprentices: a tough bunch, but all eager to learn. I had begun teaching at Magdalen College School in Oxford. My specialism is remedial mathematics so that in the English section of our newly created European School I generally took the youngest classes, some in between, then the weaker senior pupils in the final two years before their Baccalaureate.

For the last decade, our School had never fallen below the highest average Baccalaureate results in our entire group of twelve international schools. Whatever did he imagine I had done to contribute to this success? What did he suppose is the purpose of a school? And, finally, I was one of the highest paid mathematics teachers in Europe, possibly in the world. I had been told at the outset, officially, that I was expected to find a better way to teach mathematics. If not, why was I being paid this munificent salary?

In the moments in which he drew breath, I attempted to suggest that if indeed I could produce classes capable of learning mathematics by themselves, this was my aim; and if, at this age, they are able to explaining mathematics satisfactorily to each other, as they would, should not both achievements be regarded as generally good educationally – and socially valuable too.

He must be a fool not to know this. Not to know that children in schools are usually taught to be selfish with their own understanding, conditioned to believe competition is the fast route to success; very soon conditioned to despise any more able than themselves and contemptuous of those less able. Then we wonder why our societies are full of selfish, angry, frustrated, and mostly disappointed people!

If instead, I should also not have tell him, children learn the pleasures of learning co-operatively, knowing the pleasure of helping, and receiving thanks from, the less able than themselves, they may be less inclined as adults to ignore injustice and to treat the less fortunate with derision.

Both of these aims seemed to me valuable additions to any school’s curriculum. My pupils were learning both. With me.

Neither entered into his notion of good teaching. He was still explaining to me passionately, banging the flat of his hand on a desk to emphasize each point.

The good teacher must write everything their pupils need to know on the blackboard. The good teacher’s pupils should copy this into their notebooks; take their notebooks home; and there complete the exercise which their good teacher has set for their homework, to be tested again in their next lesson.

This,” he told me triumphantly, “is how I succeeded at school!”

“But,” I was finally allowed to reply, “if their lessons are mainly spent copying notes from the blackboard – of what is already printed perfectly clearly in their textbook – they will not have time to discuss what it means; some of them will make mistakes in copying from the board; will make more mistakes at home, and when the exercises show that they do not understand, they have no other source of information, and no way to develop their understanding, because they have never learnt to use their textbook as a resource!”

This was nonsense. He waved it aside. If all teachers followed his instruction any failure by their pupils must be the result of the pupils’ laziness or their stupidity.

It could never be blamed on their teachers, or their teachers’ instruction.

“Most important of all,” he concluded, “once your pupils have left with their notes, your responsibility has ended. And so has mine!”
There was a little more from this modern Pontius Pilate. He had said enough about the damage I was doing to my pupils’ futures. He was even more worried that my teaching would damage of other teachers’ futures.

I was removing their employment!

He must surely know that schools cannot get enough teachers to teach mathematics. When they can, and when new teachers teach as they have been trained to teach, half of them will quit within two years.

They are not killed. They don’t die. They quit. This is a casualty list that only the seriously mad can possibly allow. But they also don’t know how to stop it.

My heart was sinking. Right here in front of me was the kind of idiot failing children everywhere; failing their nation’s future everywhere. In desperation many schools are buying computers. But what computer teaches children to be generous with others; to laugh together, to learn together, to succeed together?

What I was doing should never have surprised him. Published articles explaining my method – and praising it – had twice appeared in The Times Educational Supplement; once in the New Scientist. An entire two-year European Union project had been devoted to it in Germany. I had written its fundamental thesis in which I had revealed, to a somewhat startled audience, the historic link between mathematics arguments and democracy.

It is delightful simple. But it had to be explained to me by an eminent Cambridge classicist; and supported further by an equally famous neuroscientist.

Mathematical arguments are not intended to command obedience. They are intended to persuade that certain statements or true: or, at least, are useful. Lessons in which mathematics is taught mainly through instruction: instruction which has only to be uncritically obeyed to be rewarded; in which any pupil’s admission of failure understanding is an obstacle to the ‘progress’ of the entire class, this will certainly produce a fine crop of young fascists, and eventually adult fascists too, all with little respect for intelligent discourse, for other opinions, for different opinions.

This, I had first pointed out some years before at a mathematics education conference in Ingolstadt in Germany, then again in Budapest in Hungary, and again in the Comenius Institute in Prague, was the common method of teaching mathematics in the late 19th and early 20th century in Germany and Russia. It produces a fine respect for rigid authority: perfect order: final solutions.

In another year I had been invited to explain this to a class of young women, all beautiful, all in headscarves, in the American University in Istanbul.

I explained to these brave young ladies, as I have to all my listeners,that respect for democracy is best created in lessons in which mathematics is mainly taught through patient, reasoned, thoughtful discussion, eventually through reaching a collective agreement.

This, my Cambridge classicist had explained to me, was why what we now forms of mathematical arguments were first developed over two thousand years ago in Athenian Greece. Not to encourage ordinary Greeks to study mathematics, but to give them more confidence in democratic argument.

Their forms are simple. Describe the evidence; show the connection; state the conclusion. Eventually all mathematics was to take this form. Mathematics should be taught as argument. One plus one equals two. Is this always true? After thoughtful reflection, one small boy offered a contradiction. “Well, we once had two guinea-pigs.’ He paused, perhaps enjoying his ‘Eureka Moment’. “Now there are ten.”

Careful university research, especially in Hungary, has proved such lessons in argument to be far more effective in teaching real mathematical understanding. They are also lessons in honest, critical discourse, in democratic courtesy and manners.
Many schools in Germany were now using this approach under the direction of my German colleagues. It was for this reason that an earlier school director asked me to teach ethics as well as mathematics.

Throughout these years, I was of course enjoying the enormous freedom of being required to think ‘out of the box’. But I also tried my best to keep other British teachers informed. In the before year the British National Literacy Trust published an article in its journal ‘Literacy Today’ with an editorial praising it. It also published statistics showing that the kind of teaching he was demanding is up to ten times less effective than when children are encouraged to explain their ideas to others. .

“I am very disappointed,” were my visitor’s parting words. “I shall have to come back, and see you again!”

What do children most complain at school? Boredom. And, of course: of not understanding their teacher’s explanations.

But what is more boring than endlessly copying notes? Who is more likely to succeed: the pupils who depend on understanding a teacher who has tried to explain once or thrice in the classroom, whilst many are either daydreaming or are distracted by others misbehaving; or the pupils who have been taught to read and understand their textbook, which they can consult alone and undistracted, anywhere, at any time?

I was deflated, discouraged, dispirited. I was brassed off, disgusted. Up with this nonsense I would not put. I did not know that my visitor had gone back to his office and written to my ministerial employers demanding that I be removed from my classroom at once.

Knowing this before I did, the school’s director, previously a state inspector of schools in Portugal, and a mathematician, told me that she did not expect me to change my methods.

But I had had occasional spasms of angina for a year, and this encounter triggered an attack that woke me the next night, and the next. My doctor stopped me working. Further investigations kept me off work for months. The first of the specialists I saw, one of the best in Britain, gave an immediate explanation of the cause. “It’s just stress.” he told me. “Twenty-five years of teaching has an effect. You are feeling in your heart.”

He wrote in his report that my workload should be immediately reduced.

The British education ministry insisted that I should see its own doctor in London. He advised the same: this teacher’s workload must be reduced.

The beginning of the next school year brought another civil servant down from London to discuss my timetable. Before I could speak, however, he had already told my director, in my presence: “I am entirely satisfied that the school has done everything necessary to respond to this problem.”

But, I pointed out: nothing had been done! My timetable was exactly the same as the year before. Same classes, same pupils. They, at least, were glad to see me.

But all my ethics classes were taken from me, and replaced with more maths. I had always enjoyed having a few ethics lessons. The increase of workload would be considerable.

In the ethics lessons, as in my maths lessons, I was most successful in getting my pupils to talk. One of my pupils came back to school one day to tell me how much she had valued this more than anything I had said. “You listened. We never really get asked to talk about our ideas to someone who listens seriously. You did.”

This is probably true in many homes today. The most effective way to help children to mature is to treat them as if they are mature. To develop mature opinions, they need to talk. Democracy needs mature opinions too.

  But I was becoming convinced – actually for the first time – that nothing that I was doing was seen to be valuable by my own government. I was not regarded, as in Germany, France, Spain and Hungary – and still more recently in the United States – as a valuable innovator but rather more as a nuisance and a malcontent.

And I was causing my heart condition by working too hard! “It’s the obvious reason.” the senior civil servant told me. “You are doing far too much beside teach!”

To show, I think, her sympathy, the lady director added: “You may not do anything more without my permission!”

The ministry in London then offered to renew my contract only for a further year instead of the usual four: “Because your medical condition makes your future uncertain.”

This was the final absurd, insulting, careless nail driven into the coffin of my career that made my decision for me. I was clearly no longer wanted.
But lazy, I decided, I certainly could be. I estimated that my work had actually been increased by twenty percent. I responded by reducing my effort by twenty-five percent.

From that day on I wrote very little on the blackboard except the day’s date. Everything was now read out of the textbook: line after line; one pupil after the other, some of them stumbling over the English, always aloud.

This meant that their English improved as well. The meaning of the text, the diagram, or the demonstration, all were then discussed and defined, and when their understanding satisfied them – and satisfied me – they chose the exercises to test themselves; and they, finally, they marked their results.

I explained very little myself. To any seriously perplexed individuals who came to me for individual help, I would ask where they had previously felt happy with the text. “Then go back three pages, and start reading again from there.”

As always, I gave regular tests, marked and told them the results: but I marked almost nothing in their exercise books. In most cases they would already have found their own errors – and had corrected them.

The results of this total abuse of my visitor’s idea of my responsibilities were astonishing. My classes got even better. The day-dreamers woke up, and began to work. The most irritating stopped being irritating, and began to work. The most distracting lost some of their friends, and began to work.

Meanwhile my angina became sharper for some months; but drugs – and possibly my newfound routine – got the better of it. By the end of this year my cardiologist told me I had now no problems with my heart. But by this time my mind was fully made up. When a further year was offered, I refused.
It was towards the end of this last year that the classroom door was opened and two tall young men stood there. I had last seen them when both were about fifteen. They were now nearer twenty.

The darker of the two wore black, with a gold chain at the neck. The taller, dressed less dramatically, was a blond colossus. Both beamed at me shyly.

“Come back in twenty minutes, lads”, I told them, and they left. They were back in twenty minutes, and I invited them to address the class; suggesting they start with their names.

“Well:” began the dark one. “My name is William Anastasiadis. I’ll spell that for you!” Which he did by counting off the letters on his fingers as he advanced to stand by me: “A- N-A-S-T-A-S-I-A-D-I-S!”

The class sat as if petrified. “And this,” he turned to point at me, “is the best teacher we ever had.” His tall and silent companion, who I now remembered as a much smaller blond Scott Walker, nodded solemnly in agreement.

And then they left

On the very last day another reward was left behind by a girl of one my senior classes as she and her friends left for the summer. “Good-bye, Mister H,” she wrote on my blackboard, “We love you.”

I had not had the courage to tell them that they would not be seeing me again. I was afraid there might be tears, some of them mine.

I am not really sorry not to be teaching. I shall miss my pupils. I did not desert them willingly. I was not actually treated badly. No-one was unkind. Only stupid; only hidebound, only utterly careless of their responsibility for the future of the youngsters in their charge.

In this last few weeks another deputy director, a Dane, went out of his way to tell me how often parents had told him of their thanks for my work with the children.

I had begun to feel suffocated. Despite its astronomical costs, and the even greater cost of its continued and obvious failure, those who control children’s education neither look for new ideas nor want them. It does not discuss them; will not notice them, test them, or promote them. They find new ideas disturbing. Their reputation, and the reputations of whole generations of academic ‘expert’s who have ‘done the research’ and have advised them, must be protected. Far better to ditch anyone unorthodox, than to find out whether unorthodox methods work.

Bitterly I realised that for years I had been living with the delusion that my approach was being noticed, and valued. Two years before a magazine devoted to school education had contained an article by me called ‘Programmed to fail – or taught to succeed?’

This is the real and unavoidable choice. Virtually all attempts to teach mathematics by instruction will leave some, then more, then most, pupils puzzled by what it is they are supposed to be doing.

Absent the most talented or slavishly obedient, the anxiety of the many over their actual incomprehension becomes eventually so serious that they start to lose heart and to fail.

This careless destruction of young people’s confidence, this humiliation of hundreds of thousands by their failure to copy meaningless routines, is as disgusting and senseless as any carnage in war.

I had found an elementary way to stop this carnage: easy to use with children as soon as they can read. In my classroom I had proven repeatedly that this method not only works, but that it produces better mathematical understanding, enjoyably! Yet from this first British European School – in the words of its first British director, “now part of the most important development in education in European history” – it was not allowed to leave my classroom. Learning of my plight, an American educational journalist, being himself a professor of educational psychology, published a sympathetic interview in the world’s largest online education journal ‘EducationViews’ His title, ‘A prophet without honour in his own land’, said it all. No-one, in my own country’s government was interested in my success.

And it was this, in the end, that was unacceptable.

No matter that I had been officially invited to find a better way for children to learn mathematics; no matter that I was paid like a nabob – no job can remain interesting when there is no possibility of progress in it.

When my own ministry of education refused to champion my efforts, they dismissed me. The author of my dismissal was later promoted. At least showed me my delusion plain. As he told to me at the time: ‘I must report what I see.’
This, then, is my report.

His method of teaching is used in many schools. Its most important benefit, as he pointed out with such passionate conviction, is that no-one can blame their pupils’ failure on the method their teachers are using, or on their schools, and on the ultimate governors of those schools, on the grandly titled ‘Secretary of State for Education’ or

the hundreds of feckless minions and useless advisers.

Many pupils will fail. Needlessly, shamefully, disgracefully.

But no-one who is responsible will be blamed.

Teaching by instruction, especially of mathematics, the key subject of all the science, is in every other sense, a bad method.

It is not just a bad alternative. It is criminally, irredeemably, hopelessly stupid. The first painful truth is that teaching by instruction protects all but the most appalling teachers and dreadful schools from being blamed for their pupils’ failure.

It is the worst way to learn how to understand anything.

Understanding is achieved through creating associations with other knowledge: through discussion; through argument; most of all through provoking individual questioning and responses.

Teaching by instruction creates no association. It does not create understanding. It provokes only boredom.

The second painful truth is that most teachers are obliged to do only what they have been trained and are required to do. They are the lowest in their profession’s food chain. But everyone above them, the school directors, the national inspectors, the government ministers: all want to say, as my visitor explained, “Once your pupils have left your classroom, your responsibility has ended. And so has mine!”

The third, which is my own belief, is that many of those who have the power to make the change simply do not care. Or perhaps they want selfishness and ruthlessness to continue to succeed; for contempt for the less able to continue; for those to be punished who ‘have not tried’.

There is no real benefit for them in improving on the present situation. They will make noises about ‘improvement’. They will spend vast sums on ‘initiatives’. They will continue to insist that all that is necessary is to attract ‘better teachers’ into classrooms. They may buy more computers.

But without changing the whole strategy of teaching in the classroom, without giving children more autonomy in learning how to learn, they will achieve, essentially, nothing.

What can I offer to anyone who wants their own children to avoid the horrors which most schools will blithely inflict on them, is how youngsters can learn maths alone, or with friends, from any literate textbook. ‘Literate’ means more text; not more silly cartoons.

In a few years they should not need a teacher. It is called the Socrates Workbook for Nine to Nineteen Year Olds, and there is also a Teacher’s Guide. The first, incidentally, was originally ‘for Nine to Eleven Year Olds’; but the senior German student who translated it, as did others into other languages for a pound a page, told me: “It’s terrific, Mister Hannaford. But your title’s wrong. Every one of us needs to know what’s in this book.” Hence: Nine to Nineteen year-olds.

Both can be downloaded free in any of five languages from the section ‘Core Materials’ in my archived website: http://web.archive.org/web/20060902011441/http:/www.gardenofdemocracy.org .

For braver teachers and educationalists a more formal explanation was published in 1997 by the leading English language journal International Reviews on Mathematics Education, and this article, entitled ‘Mathematics Teaching is Democratic Education’, may be downloaded from www.zblmath.fiz-karlsruhe.de/. The proceedings of the two-year European Union project with much the same title may be obtained from LEU, the Landesinstitut für Erziehung und Unterricht, Stuttgart. The NLT journal Literacy Today published the article Read Aloud – and Learn! in Summer 2003. The TES and New Scientist have of course their own archives.

And, finally, as the lives of millions of people are being disrupted and destroyed by religious strife, is there any spiritual value in this approach? I believe there is, for I did not begin unprompted. There are two books that you may like to look in, both published privately by Trafford. The first, ‘473959’, my old army number, is basically an account of the lectures I was invited to deliver in Mercer University in Georgia, and of my reasons for giving them. The second ‘Educating Messiahs’ has a rather longer explanation and has its own YouTube presentation, at ‘Trafford Educating Messiahs Hannaford’.

Be warned that both contain a report of God in action, not dead.

Any parents who decide to take their children out of school and educate them at home will find, as my eleven year-old confided in me: “It works with other subjects!”

Together with all my other pupils, over the best twenty-five years of my life, he was discovering what the French philosopher Michel de Montaigne noticed five centuries ago: ‘The best method for teaching children is to give them space to teach themselves.’

By using this method, with math and any other subject, they can help their children to become happier and more successful in learning than ever before.

It’s actually very simple. Try it. They will love you for it.

Colin Hannaford,
Oxford, 6-11
th September 2004; 9-14th December 2015.

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