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A Gattegno Anthology
A remarkable, seminal contribution to the understanding of the learning process
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 A Gattegno Anthology - PDF
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A Gattegno Anthology
Caleb Gattegno grew up in Alexandria, lived in Cairo, London and New York, but worked all over the world.
He was a world citizen who in a life-long study of learning not only created a number of important innovatory techniques for the teaching of languages and of mathematics, but also made a remarkable, seminal contribution to the understanding of the learning process at all ages. His personal influence was profound and there are many people whose lives have been changed by the experience of working with him in seminars in various countries over the last few decades.
The first English translator of Piaget, he was influential in spreading awareness of developmental psychology.
He invented geoboards; and he introduced teachers to Cuisenaire rods and the mathematical films of Nicolet. Use of these aids was developed in classrooms - he would teach children of any age or ability, anywhere, at any time, and do so publicly in front of other teachers.
ISBN 0 900095 77 6
A few months before he died, Gattegno gave a moving talk at the 1988 ATM Easter Conference.
This anthology opens with an edited transcript of his final talk to the Association. The selection from published articles is then presented in four sections. The first contains edited versions of the various articles that were specially written for anniversaries and other occasions; these are given in chronological order. The second section may be loosely described as being devoted to curriculum issues, covering technical aspects that range from early counting to the calculus. The third section groups together various writings that are devoted to aspects of learning experience.
One article forms the final section: this is the very powerful and condensed account of a new epistemology: Understanding the nature of mathematics is not just a job for mathematicians. Teachers need to be involved so that mathematics is properly based on psychological, human foundations.
“...there is only one instrument in research in order to find answers. One instrument: and that is to raise questions, to ask questions. To question is the instrument. And if you don’t question, then don’t be astonished that you don’t find anything.
“There are questions that are trivial and don’t serve any purpose: What’s the time? Five to nine. It’s finished, it’s a useless question. What’s your name? It’s a useless question. But there are important questions and we have to learn to ask them. One important question is: why is it that every one of us did not speak until the ninth month or the tenth or the twenty-fourth month after birth? This is an important question. Why is it that we don’t speak for many months and then a year, or a few months, later, we do speak? It is disturbing to have a question of this kind: why is it that I did not speak? The answer is so rich, in terms of your own education, that I hope you will put it to yourselves.
“Another question is: why do I sleep every night? This is one of the most stupid questions, yet one which has the greatest profundity and a tremendous yield. Why is it that I sleep every night? Another question is: what is the cost of learning anything? Is there an objective way in which we can know what it costs to be as good at addition as Weierstrass. Weierstrass was a great mathematician and he must have been good at addition. (laughter) Why is it that it takes so long to teach long division and that it’s not understood by so many? The cost of learning anything is an important question. It is included in a wider challenge, which you may perhaps want to work on: what is the economics of education?”
