Reflections on ICME IVAuthor(s): Eric GowerSource: Mathematics in School, Vol. 10, No. 2 (Mar., 1981), pp. 11-12Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30213629 .

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experience with ease and charm; Ivan Niven (Maxima and Minima without Calculus) and Arnold Ross (What Mathematics for Gifted Young People?) were good examples of this. Other highly polished and stimulating presentations included those of Arthur Engels (The Impact of Algorithms on Mathematics Teaching), Douglas Hofstadter (Analogies and Metaphors to Explain G6del's Theorem) and a team from Bell Laboratories (Exploratory Data Analysis). On the whole the mathematical education sessions I attended were less rewarding than those on mathematics. It was interesting to hear of other countries' problems and preoccupations (I thought more than once that a dose of Godfrey-and-Siddons-type geometry might work won- ders), but, as Geoffrey Howson pointed out at the end of his session on Language and the Teaching of Mathematics, despite all the talk not much progress seems to have been made on many major questions since ICME III in 1976. It was notice- able that while there were 21 sessions on relating mathematics education to special groups of students (with a welcome emphasis on women) there were only three on mathematics and employment.

The exhibitions and displays made a refreshing change from

all the talk. The British contingent were prominent, and I particularly enjoyed the Nottingham Shell Centre collection and the very entertaining "Images in Mathematics" presentation by a group led by David Roseveare. It would be very good to have both of these repeated here so that a wider British audi- ence could see them. The ATM Primary Workshop was buzzing with eager participants (including a few children), and the Thursday afternoon poster session gave a good opportunity for anyone with something to pronounce to attract an audience. The Mathematical Association's posters were well supported, as the photograph shows.

Was it worth attending ICME IV? Answer definitely yes, though as usual the informal contacts and "talking shop" seemed to matter most. The planners had done well to provide opportunities for this, aided by the generous meals in the halls of residence and the plentiful variety of tempting restaurants in Berkeley and San Francisco. I enjoyed the week, I learnt a lot (and was not discouraged by British efforts in comparison with others), I strengthened old friendships and started new ones. Why not begin to think of a trip to Adelaide for ICME V in 1984?

Reflections on ICME IV

by Eric Gower

The University of California at Berkeley, USA, would be a beautiful setting for anything in August, nestling, as it does, under the hills overlooking San Francisco Bay and the Golden Gate Bridge. This August it was the setting for the fourth International Congress on Mathematical Education and I was fortunate to be one of the participants who enjoyed both the surroundings and events of the Congress. Each one will have taken away his own impres- sions and my attempt to record mine will doubtless be coloured by the number of firsts I associate with that week, my first flight, my first visit to the USA, my first paper at an international conference, my first ICME and so on. Any conclusions which I draw may therefore be hasty, but I record them nonetheless.

San Francisco International Airport proved to be a good place to begin the sort of reflection which a good conference should encourage. As I left the plane I noticed an unpunctuated sign on a door "NO EXIT DOOR IS PERMANENTLY LOCKED". The compelling logic of this statement makes you look again to see what it was intended to say. In much the same way I found myself reflecting during the conference on what professional, cultural, political and other messages lay behind what was being said. Often a presentation seemed almost absurd simply because one's experience and knowledge is limited to one culture and language. Only at a conference like this does one begin to glimpse the many different ways in which people around the world are tackling apparently similar problems in teaching and learning mathematics. I believe the whole thing was worthwhile for the fact that it gave such opportunities for reflection, since it is this which sharpens the focus on one's own experience and intentions and this can only be good.

There were disappointments, however. At 93, Professor Polya must be able to take a balanced look at a subject like "Mathe- matics improves the mind", but illness cheated us of his presence and his contribution on this matter. Technical prob- lems made for difficulties, with overhead projectors proving to be stumbling blocks for the most eminent speakers. Even a great geometer like Freudenthal suffered problems of spatial relationships with his transparencies, and whilst what he had to say more than made up for these difficulties one couldn't help feeling that such irritations were unnecessary at such an event. The Japanese speaker on "Distance education for school

age children" (the use of educational broadcasting) underlined the fact that such visual aids can be quite a hindrance when he had to ask his audience to move to the front of the room in order to see the screen - such is "distance education"!

Other disappointments had to do with the workshops and exhibitions staged by the various national associations, projects and institutions. I felt these should form a central feature of a congress like this, instead of which they were placed virtually at opposite ends of what can only be termed a vast campus. The profusion of roller skates, skateboards and bicycles (not manned by ICME participants, I hasten to add) was testimony to the problems of distance. This robbed the projects and their workshops and exhibits of their vital role and meant that those involved in staging them were somewhat trapped and isolated from whatever else was happening. Some serious thought must be given to the location of such presentations at ICME V.

Lest anyone should feel I have only complaints about the projects, I should say that I felt they revealed more clearly than most things what good and exciting things are still being done around the world in developing the mathematics cur- riculum. In this, the United Kingdom featured large with major contributions from SMP, ATM, OU, Leapfrogs, BBC and the Shell Centre.

There were other important opportunities for individuals to make statements via large posters strung along the long corri- dors of one of the large University buildings. I've often wondered what you could use such a waste of space for and having seen such a gallery of posters and statements I now

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know. It would be a great idea if some of our institutions could make this sort of personal presentation on the large scale a permanent feature of their normally very boring passageways.

As usual on such occasions as this it was personal contacts and informal conversations which proved most fascinating and beneficial. Successive breakfast companions included an English comprehensive school-teacher, an Australian college lecturer, an American college professor and a Welsh University professor of physics! Perhaps the definition of a congress as a series of meals and coffee breaks interrupted by lectures and presentations is not so ridiculous when one analyses its real value.

It is precisely the fact that one can mix with people of such vastly different backgrounds and positions which makes it such a pity that more practising teachers in ordinary British schools were not at Berkeley. Of the 70 or so British people who took some part in the programme (and this was not by any means all those who travelled from the UK) only three or four of us admitted to a school as being our place of work. The decision of some of the sponsoring bodies in this country to give priority to practising teachers should have meant more were able to go - certainly many schools and children would have benefited directly had their teachers gone to ICME IV. I believe that there should be a concerted effort before 1984 - the year of ICME V - to enlarge the number of schools repre- sented. It will certainly take a few years to redress the balance between the schools and other institutions so perhaps this article will set the ball rolling.

Answers to the following questions might help establish what our priorities ought to be.

1. How many mathematics teachers know enough about the scope of ICME to even consider attending? I certainly knew very little indeed before being invited to participate. 2. How can LEAs be persuaded that national and international conferences are a vital part of in-service education for teachers, and that they have a responsibility to see that their teachers are supported in attending them?

3. Since, in the end, availability of funds will be the deciding factor for teachers considering attending events like ICME, how can the number and scope of funding agencies be improved?

Attending ICME V could be more of a problem financially for teachers since it is due to be held in Adelaide. However if we can get it right for 1984 then there should be little difficulty in this direction for subsequent ICMEs!

If you go, then be prepared for the instant promotion which the ICME organisation arranges. With professors of every hue so thick on the ground, those in charge appeared to find it hard to believe that there were any lesser mortals attending ICME IV. I found myself referred to as Professor on a number of occasions and, on my refuting claim to such a title, was there- after referred to as "Dr Gower". At that point I gave up trying to decline undeserved titles. So if you have been trying un- successfully to persuade Jimmy Saville to fix it for you to be professor for a week try ICME - they'll do it for no extra charge at all!

So has it made any difference attending ICME? Of course there are personal benefits which are difficult to quantify. The widening of horizons, the opportunities to mix with mathe- matics educators of widely differing backgrounds and experience, the chance to sample some of the curriculum developments around the world. These are bound to give a fresh view of what you are trying to do in your own classroom. There are ideas which I will want to turn into classroom activities. There were resources which I want to use to improve my own teach- ing. There are contacts with people around the world which I want to follow up.

Above all ICME re-opened my eyes to the fact that often the best curriculum development is taking place in unspectacular ways in ordinary classrooms in places as far apart as Argentina and Holland. Ordinary teachers who have their fingers on the pulse of what is happening. I hope that more of these vital people and their contribution can be seen in Adelaide in 1984.

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