Second
Qatar Foundation Symposium Series
Innovations in Education 2006
TECHNOLOGY, EMPOWERMENT, AND EDUCATION.
Panel III: Empowerment in Scientific Reasoning (3)
Dr Eva Vásárhelyi; Dr Bahaa Darwish; Dr Hani Khoury; Mr
Colin Hannaford
Moderator: Dr Farhan Nizami, Director, Oxford Centre of Islamic Studies
Introducing a Socratic Methodology in Schools: Evaluating Change
by
Colin Hannaford,
Institute for Democracy from Mathematics, Oxford OX20QT, England
Reporting on his work in America, my colleague Professor
Khoury has emphasised the importance of leadership both inside and outside
the classroom. I am going to continue and reinforce this emphasis. The
most important element of successful leadership is to ensure that everyone
in an enterprise understands the aim of the whole task, together with
their own responsibilities within it, and how the latter may change
as progress is made.
Let us first of all understand what the technology
truly signifies that we are here to study and discuss in this Symposium.
Our modern notion of the sense of 'technology' has
become severely limited. English dictionaries typically define it as:
'the study and use of the mechanical sciences'. The original sense was
very much greater.
To the early Greeks - who first made a study of it,
and who later transformed it into a major discipline of their own academies
- techne logos meant 'reasoned speech, or logical argument'.
They needed this important distinction - and needed
it urgently - because their attempts to include more of their citizens
in the processes of open government were being swamped by the teaching,
to just a few, of a very much more sophisticated but also, at times,
deliberately confusing form of argument called 'rhetoric'.
The teachers of rhetoric - they actually called themselves
'Sophists' - boasted that - for their fee - they could teach their pupils
to argue that black is white or that true is false, or any similar variation
on this theme for any different day of the week.
Naturally enough their fees were being paid by those
who wanted to win arguments in their own interests: and not in the interests
of the people as a whole. Confidence in open debate was collapsing.
Even those most critical of ordinary citizens - and
Plato was one - warned that rhetoric had become too powerful. The people
needed to be taught a new, far simpler form of argument. It must begin
with the least number of essential facts; they must be fitted into a
familiar and dependable form of argument; which must produce a conclusion
which could then be reviewed and tested by anyone familiar with these
forms of argument.
These forms eventually became our mathematics. Their
first purpose, however, was never to do mathematics; it was to give
ordinary people confidence in their own powers of thinking, of criticism,
and of expression. This is what techne logos really means - and the
aim of the Socratic approach to learning is to teach technology in just
this sense.
Because this is a very real innovation, the necessity
of careful leadership will be especially important in introducing the
Socratic methodology undramatically and gradually in schools, and then
in evaluating the progress of pupils in acquiring it. I will therefore
suggest that, from the very beginning, the following responsibilities
must be understood and accepted by everyone involved:
· The first task of the school's
directors is to ensure that the pupils and parents understand that the
final aim of their education is not just to pass the school's examinations.
It is for the pupils to progress from learning mainly from their teachers,
as they do when they are young, to being able to learn independently
and alone in their last years at school, in order to be ready for further
study at university or in their employment. Learning in a modern society
must be life-long, and it is this ability to continue to learn throughout
their lives that the school must help all its pupils achieve.
· The first task of the teachers is
then to explain to their pupils, as early as possible, the modern understanding
of how their brains learn; why the ability to learn and remember a written
text is increased by reading aloud and listening to oneself; why this
ability increases again on listening to others and trying to understand
them; and why it increases yet again when one tries to explain, in one's
own words, the meaning of what one has heard. At every stage more of
the brain's secondary functions of cognition, logical analysis, combination
- and, finally, of speech, are brought into action, to join with the
primary functions of perception, recognition, and association.
· The first task of the pupils is to
understand that this process will produce difficulties for everyone
from time to time; and that they are required to show patience with
others; to retain their good humour; and neither to resent nor reject
the honest efforts of anyone to correct or criticise. Their teacher's
aim is not the success of a fraction of the class. Her aim is now for
the class to learn as best it can together.
· The Socratic approach to whole class
learning is generally enjoyed and appreciated by children, even at a
very early age. It can be deeply resented, however, by parents of the
cleverest children. They may protest - most vigorously - that the natural
advantage of their own child or children is being reduced, is even being
damaged, by the teacher's attempts to help the less clever children!
A further task of the school directors must then be to explain to parents
- equally firmly - that a class teacher is responsible for the learning
of the whole class, not a fraction of it. It may also be added that
the cleverest children also learn faster - and more thoroughly - when
required to explain their understanding to others, as any teacher will
confirm!
The Aim of the Socratic methodology in schools:
All
the work attempted should be at a natural pace and should be enjoyed.
In any class there will always be a natural range of abilities. In time
this will be recognised as to the advantage of the class, for it obliges
everyone thoroughly to explore and share their understanding. At first,
however, especially if competitiveness has been encouraged very strongly,
it may be expected to produce selfishness and jealousy.
It is true that a few children do have a special aptitude
in mathematics. But this fact should not be turned on its head to assert
that most children have none. That very few children ever really enjoy
mathematics, that even fewer develop any real interest in it, is not
because the majority lack this magic 'aptitude'. It is more likely because
most have been taught to reproduce a repertoire of mysterious mechanical
actions with no real understanding of their logic; even more rarely,
of how or why they were first invented; and least of all that there
is almost certainly far more mathematics yet to be discovered than has
yet been found. They have never been helped to feel that they 'own'
their mathematics. Consequently, very few will ever believe that they
could continue to learn it - or anything equally challenging - alone.
The aim of the Socratic methodology is to supply pupils
with this opportunity: to experience independence and autonomy in learning
- of mathematics first, but subsequently of any discursive subject.
Although this kind of learning must be carefully introduced,
their teachers will find that they and their pupils have a very comfortable
'window' in which classes can succeed.
In an unusually able class - for example - the majority
may become practically autonomous in learning their mathematics from
a suitable text-book by the age of 13 to 14 years: that is, within their
third secondary school year.
In a less able class, a class which will naturally
exhibit more variation, the majority should be beginning to find their
own way by end of the fourth year.
An unusually slow class, or slow minority, may not
become sufficiently confident to work alone until the fifth year. Whatever
the actual rate of progress, once the method has been made clear to
them, all pupils will be found able to maintain their own rate of progress
and be able to improve it. The remarkable sensation of being actually
in control of their own progress is as exciting for the majority of
pupils as it is novel. It is rewarding for them all.
If, by the beginning of their penultimate year in
school and beginning study for university entry, any pupils have still
not learnt to work in mathematics independently, they should only be
advised that a career in the sciences is probably not for them. This
does not mean, and it should not be assumed to mean, that they lack
ability in other fields. There may also be very many reasons for their
lack of achievement, reasons which have nothing to do with intelligence,
or its application.
Evaluating change: in the transition from primary to secondary
The aim of their last year in primary school should be to ensure that children are not afraid of reading aloud, even whilst making occasional mistakes, and that they are accustomed to being asked to comment on what they have read themselves, or have heard others read.
Before leaving primary school, pupils should have learnt to read texts silently, at a suitable level for their age, and most should also be expected to read confidently aloud. Their teacher must have accustomed them to be questioned about the text, about any ideas it contains or what it describes. Individual work for the pupils should consist of summarising a story or writing something similar themselves. In arithmetic, the children should be able to explain - in simple terms and in their own words - the purpose of the various manipulations of whole numbers: that is, of addition, subtraction, multiplication, division - and should be able to say what they expect to see after they perform these operations. They should also know by now what a number is!
Secondary school: The First Year:
The aim of this year's practice is to increase the confidence of the class in using the text-book as their secondary learning resource.
The teacher should introduce her pupils to their math text-book: as a book. She should cause them to notice that it is written by an author, and that it is his obvious intention to teach them everything they need to know. The teacher then should frequently refer to the author by name in order to emphasize that his book, like any other book, is the product of human minds. It is not very likely to contain many imperfections - but these are possible. This is not the only reason why they need to learn to read a math book carefully - but it must always be born in mind. People are fallible: even experts.
A suggested dialogue:
"How
many teachers are there in this class-room today?" "One? Soon
you will know that there are two. Where is the second?" "Yes:
in the text-book." "And soon there will be even more. Where
will they come from?" "Good: soon there will be as many teachers
as pupils in this class - plus two. With the help of this book, and
with my help, you are all going to become teachers!" "What
is the advantage of having so many teachers in the classroom - and yet
another in the book? How many can go home with you?" "Right!
Whenever you leave this classroom, this teacher you can take home with
you!" "From today you are going to learn from me, as you are
used to; but sometimes you are also going to be helping each other;
and eventually you will all know how to learn from this special private
teacher in your text-book. You are going to learn how to get him to
talk to you; how to ask him questions; how to find his answers; and
how to check whether you have really understood him properly."
"What did I say is the advantage of your having a private teacher
in your text-book?" "Exactly: this is going to be the teacher
you can take home with you whenever you like!"
*
Lessons should then proceed in the usual fashion.
The teacher should do most of the teaching; but the pupils should be
shown that there are lots of chapters in their text-book - and they
should be asked why. Then they should understand why. It is because
there are many different kinds of mathematics, and in past centuries
many different kinds have been found to be ever more useful or powerful
in different human endeavours. From time to time these histories should
be discussed.
Increasingly now, however, whenever a new chapter
is begun, the teacher should ask the more and less confident readers
to read portions of the text aloud, and then the teacher - not the pupils
- should try to rephrase the same text in her own words.
The aim is for the pupils to begin to realise that
their text-book contains ideas - some of which are very basic, and often
very old - but that these ideas may be expressed in many different ways,
and that some ways, like some people, are easier to understand than
others.
Occasionally the teacher can ask the class to help
her with these explanations, but she should always be able to show that
the text-book's explanation is invariably sufficient, and is often the
simplest. The text should rarely be criticised. (It is not for this
reason alone that the book used must be selected with great care, but
this is already a sufficient reason.) Now the aim is for the class to
be helped to believe that so long as the text is read aloud, so long
as the words are listened to carefully, reflected on thoughtfully, perhaps
trying different interpretations and comparing them others, its meaning
will eventually become clear. This should not be made to appear either
automatic, or easy. It is neither.
The Evaluation of Change:
The evaluation of individual pupils in this year should not be very different from the teacher's usual practice, but with the addition of her private observations of individual pupil's confidence and ability in literacy. These comments may also be shared privately with individuals - but never at this stage openly - whilst any observation of serious weakness in reading or in comprehension should be communicated to their appropriate teachers of reading and literacy.
The Second Year:
The aim of this year's practice is to confirm the confidence of the class in using the text-book in the classroom as a learning resource almost equal in value and importance to their teacher - but becoming of far greater importance when working alone or outside the classroom.
By
the start of the second year it should have become routine for the beginning
of every new chapter to be read aloud by selected pupils. They should
be selected by the teacher - not predictably, but not at random - so
that everyone has this task at least every month - now with the additional
innovation that more time is spent by the pupils explaining what it
means.
This process is always slow at first, and hesitant;
but, as the pupils realise that no attempt is ever wrong, and that every
attempt can build and improve upon previous attempts, their responses
should become less inhibited.
As the year progresses, and as the class becomes more
accustomed to the practice, the teacher should become increasingly less
helpful, whilst her questions become more specific. Helped by her occasionally,
helped by other volunteers, selected pupils should try to explain the
meaning of the text aloud to the class without either altering or losing
any of its original sense. Remaining always sensitive and responsive
to the mood of the class, and never allowing embarrassing delays to
develop for any particular individual, the teacher will begin to demand
of pupils more confidently: "Lizzy," - for example - "what
do you think that means?"
The teacher's manner should indicate that she does
not expect an immediate response, and certainly not a perfect response,
but that she does expect some response from someone. If no attempt is
offered by anyone, she should unhurriedly and calmly direct either the
same or another pupil to read the passage again, always being careful
to avoid embarrassment, and always making it clear that their hesitation
is natural and expected. She may even explain why at first this almost
always happens: that most people can read aloud perfectly well but without
their brain actually realising what the words mean. (I have often demonstrated
this by reading French aloud. This I can do quite impressively; but
I can only rarely understand what I read.)
The sentence or the paragraph may thus need to be
read again, and again, and even once again, before eventually some sense
percolates through to someone in the class. If, for some reason - for
classes can get tired, like people - no useful response appears, it
may be sensible for the teacher to turn to her blackboard and give her
own explanation and example. In the next lesson, however, she must without
fail return to the text, repeat the exercise, and extract from the class
the admission that they can now understood this text just as well.
By the end of the second year - except for additional
elucidation or, occasionally, for entertainment - for much of the time
the teacher's blackboard should be empty.
In contrast, by now every paragraph of the text-book should be read,
discussed, and explained by the pupils themselves to themselves. Increasingly,
the teacher should be acting solely as the director, referee, and final
judge.
The aim is now for the class to know that although
its author may sometimes expressed an idea awkwardly, or even badly,
their text-book only very rarely contains mistakes. When class and teacher
both agree that the explanation they have developed themselves is better
that the text, the teacher may direct them - but again very rarely -
to "take a pen and a ruler, and cross out what he has written,
and write in instead what [name the child] has just said - which we
think is better."
Nobel prizes are not usually won in the Second Year
- but they are also not more appreciated than this!
The Evaluation of Change:
By
the end of the second year most pupils should have emerged from their
defensive shells or have abandoned selfishness. Most will attempt to
explain a meaning of whatever they have read or heard at the first request.
There may still be some who will insist, either mischievously or with
far more critical intent that this method 'is not proper teaching When
this once happened to me, one young girl, previously a friend of my
critic, whispered to me afterwards: "She and her lot don't like
what we are doing, because you make them all work harder!"
A better response is that 'proper teaching' is what
you needed in the Primary School. Now what you are doing is 'proper
learning'.
None of these very varied verbal responses can be
quantified in individual evaluations together with the pupil's test,
exam, and homework marks - but a subjective evaluation should be made
on a suitable scale: perhaps of 1 to 10. This mark should be recorded;
and should again discussed with your literacy teaching colleagues, especially
now that the pupils' ability in literacy begins to affect their numeracy
ever more obviously. (One of my successes in the UK has been to persuade
the British National Literacy Trust that the two are inescapably connected!
Those who do not recognise words very well - which is what literacy
is about - will also not understand very well any explanation, in words,
about numbers - which is what literacy is about!)
In this year also, and in schools in which there is
a year pass mark: of, say, 60% overall - it will found very effective
for the teacher to let her class know - well within the year - that
she is reserving a margin of 20% to be either awarded, or deducted,
according to their individual efforts to help others understand. (This,
incidentally, is something that the pupils can do themselves. A simple
secret ballot will produce results very surprisingly similar to the
teacher's appraisal.) The aim here is to ensure that no very clever
child will receive 100% if continuing to be selfish and refusing to
help others. It also means that no slow thinker, but one who has been
more often ready to attempt an explanation, ever needs to fail.
Third Year:
The
aim of this year's practice is to transfer the responsibility of their
learning almost entirely from the teacher, with her knowledge, to the
textbook, and the information it contains. This distinction between
information and knowledge should now have become much clearer to the
pupils. It should certainly be discussed. This understanding is vital.
The textbook certainly contains information, but this information can
only be converted into knowledge when it has been incorporated in a
mind, and when the mind has then learnt to develop, to associate, to
elaborate, and to apply it both constructively and inventively.
This degree of progress is achievable by any generally able class in
their third secondary year. If it is not achieved in this year, it should
be possible by the same class in the fourth year, or in the fifth. The
confidence of the core of the class that they can achieve precisely
what their teacher believes they can is their most precious resource.
Allied with their ambition - and being always open to honest, critical
appraisal - their confidence and their teacher's qualities of leadership
will carry them through most of their difficulties.
In this phase the leadership of their teacher is their most important
asset. This means that the teacher must know when the class is weary,
when it has possibly been disheartened by other subjects, when it may
be time to switch to a different emphasis in learning, and even to revert
to the simplest kind of learning: copying from the board and doing endless
examples.
Every kind of teaching has its place. Every kind of teaching should
be available at need. The essential thing is not, never to stop; it
is only never to lose momentum in learning. Ideally, in every lesson
every child should know that it has learnt something new. It should
expect to learn something new in every further lesson - to be stretched;
to be tested; and, occasionally, also it should expect to fail!
Once
a sizeable minority has learnt the freedom of being able to learn unsupervised
from the text-book - and this is a freedom which many find euphoric,
and which can lead to over-confidence and over-reaching - the main difficulty
for their teacher will be to keep some unity of the class!
This is best done by systematising the Socratic procedure.
Every paragraph of every chapter must be thoroughly discussed and analysed.
The cleverer pupils maybe challenged to invent their own exercises.
By now - if they have not had them already - all the pupils should have
free access to the correct solutions of all the problems they attempt
at all times. They should be marking their own solutions themselves
and, when these are not correct, they should know that it is their responsibility
to know why. They should know that this is also why they should set
out all the steps of their solution clearly and completely. It is so
that they can find out for themselves - or so that they can ask a partner
to look and to see - where, exactly, they went wrong.
The teacher's role is still to lead the class - but
by now her actions should be mainly supervisory. She should see the
pupils' work regularly; and of course must also set and mark both regular
and random tests. The marks for the latter need not be recorded, but
are very useful for keeping pupils working within realistic limits.
There will still be the occasional private plea for
help. The teacher can deal with these requests according to her assessment
of the need. She may respond, occasionally, by a brief explanation of
her own. If this is satisfactory, she will not repeat the favour for
some time. If, however, she feels sure that the pupil is able, but lazy,
she should ask where in the text-book the pupil felt secure, and should
then direct the pupil: "Go back three pages, and read on again
to where you got stuck. That should help!" If she feels that another
pupil is too far ahead, she may ask that pupil to help the first out
of the difficulty. If she knows that yet a third pupil is in a state
of even greater perplexity, she may send the first to help the third,
explaining: "The best way for you to understand where you are stuck,
is to help another who is stuck even earlier!"
As always, the teacher must be alert, and avoid being
used as a crutch, but, finally, if the obstacle is obviously common
to several pupils, she may either ask one of the more forward pupils
to explain it to the others; or she may call the whole class to order
and explain the problem herself - best of all with reference to the
text-book, and only using her blackboard from real necessity.
Many text-books provide a summary of what is expected
to have been learnt from it at the end of any chapter. A useful finale
to the Socratic study can be to invite all the pupils to prepare an
oral summary, then to ask a number of pupils to stand up, one after
the other, to deliver a complete explanation of the whole, with the
blackboard available for their illustrations, and being also prepared
to answer questions!
The Evaluation of Change:
Once
the habits of learning which have been outlined in this paper have taken
hold in a class - and whether this is achieved satisfactorily in the
third, fourth, or fifth year - a very radical change in the atmosphere
and activity in the classroom should be obvious to a visitor.
First is the reading aloud of the text, line by line,
by pupils named by the teacher. Then there should be a general discussion,
ending with a general agreement of its meaning. Then the teacher should
indicate the exercise from which the pupils should select problems to
test themselves - and then the teacher should tell the class to continue.
She may visit different pupils in the classroom, or, if this is impractical,
she may call individuals to her desk with their book to be examined.
The class should be generally very busy, working alone or talking with
each other about the work. There should be no need for movement, or
shouting, or loud argument, or any other deliberate disturbance. The
class should look cheerful, but not subdued, and the general impression
should be of industrious enjoyment!
Individual marks may now given for a number of formal
reasons: the most important and objective will still be the accumulation
of successive long test marks; next, the standard of written class-work
and home-work; next, the suggested 20% for positive and intelligent
contributions to the class's discussions (also a useful opportunity
for discussion privately with the pupil); whilst a final decimal point
may be awarded according to a vote by the class of who has been the
most cheerful influence throughout the year.
Fourth, Fifth, or Sixth Year:
The
aim in these years must be to continue or consolidate the progress already
made in persuading the pupils that they do have the ability and - although
it is getting shorter - that they do still have the time to abandon
an increasingly desperate hope that their teacher can be responsible
for their learning of mathematics and their passing - or failing - its
examinations. The more mature will have already accepted the obvious:
that only the person who goes into the examination room can ever be
properly responsible for the results. All that the teacher can do is
to direct and help each pupil to learn to study and to learn in the
most efficient and effective way.
The Socratic Method is not the actual method
of Socrates. It uses his name, with very great respect, because Socrates
was determined to show his countrymen - eventually, as is well known,
at the cost of his own life - that they had all the capacity to think
for themselves.
The Socrates Method has been developed to show any child that this is
true as soon as they have been taught to read. By using the textbook
as the basis for free discussion, it then combines the ability and the
energy of any teacher with the expert authority of the authors of their
textbooks.
Used intelligently, sensitively, and with affection
for the spirit of honesty and the wish for truthful understanding that
is born in every child, it cannot fail.
Colin
Hannaford,
Oxford, April 2006;
for the Qatar Foundation,
Qatar, May 2006.
The following may be downloaded from www.gardenofdemocracy.org :
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Appendix A:
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The Socrates Method Workbook for 9 to 19 year olds, English text; also available by free download in Core Materials, currently in English, French, German, Italian, Russian, and Spanish.
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Appendix B:
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Teaching the Socrates Way: a four page A5 guide for teachers, parents, student teachers, and senior pupils.
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Appendix C:
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The Religious Education and Philosophy Departments' Problem: Social and Moral Implications of Mathematics Teaching.
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