Caleb Gattegno

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Caleb Gattegno (1911-1988) is best known for his innovative proposals for teaching and learning mathematics , foreign languages The Silent Way and reading Words in Color.

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[edit] Caleb Gattegno’s pedagogical approach

Caleb Gattegno’s pedagogical approach is characterised by several radical propositions based on the minute observation of human learning in many and varied situations. This is a brief description of three of these propositions.

First, Gattegno noticed that there is an “energy budget” for learning. Human beings have a highly developed sense of the economics of their own energy and are very sensitive to the cost involved in using it. It is therefore reasonable to seek ways of learning which are “cheap” in terms of the amount of energy spent. He proposed a unit of effort in learning elementary maths, which he called the ogden. This is similar to the modern notion of computational complexity.

Second, Gattegno considers that only awareness is educable in human beings and therefore proposes pedagogical procedures based on awareness.

Third, he suggests that for pedagogical actions to be effective, teaching should be subordinated to learning.

[edit] Learning and effort

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From the point of view of our energy budget, learning can be of two kinds, depending on the quantity of energy we need to carry it out. Certain kinds of learning are very expensive in terms of energy, while others are practically free.

Every time we have to memorise arbitrary facts, we have to spend our own energy to do so because these arbitrary items have to be “stuck” in our memories. The energy cost can be very high especially when the content is of no interest to the learner. Many subjects studied at school are of this kind: history dates, tons of wheat produced in a given country in a given year, the names of rivers and mountains, mathematical formulae and theorems are all of this type. All these facts are arbitrary, at least from the point of view of the children.

But school is not the only place where this kind of learning is necessary. When we meet people for the first time, we have to learn their names which are arbitrary as far as we are concerned. Bob could just as easily have been called John or Peter. Telephone numbers are equally arbitrary. We have to use our own energy to make arbitrary facts like these stick in our memories. The “mental glue” necessary is expensive and this type of learning uses up a lot of energy.

Not only is this type of learning expensive, it is also very fragile. We all know how difficult it is to remember these kinds of facts. Even when we make great efforts we do not always succeed. We often recognise a face without being able to remember the name of the person. Not to mention all that we have forgotten of what we learnt at school. How many hours do we spend learning history at school? And how much of it remains a few years later? We forget much of what we memorise very quickly.

However, there is another way of functioning, which Gattegno called retention. An example of retention is the reception of sensory images. When we look at something – a street, a film, a person, a fine view – photons move from what we are contemplating and enter our eyes to strike the retina. When we listen to something, we create auditory images in a parallel way. In these cases, energy enters from the outside and we have to use only a tiny amount of our own to retain it; the amount is so small we are not aware of any effort. Such images are easily acquired and remain for long periods. We all have experiences similar to these:

First experience, "I recently visited a village in the south of France where I had not been for over 10 years and I was able to say, 'Oh, yes, I know. The pharmacy is over there beyond the baker’s.' I went to see and there it was. I had made no effort to memorise this village square. It had entered my mind during my previous visits and it had remained there."

Second experience, "I visit a supermarket and go down the aisles. I see an unexceptional woman with a trolley. Three aisles further on, I see her again. I have not tried to remember her, but I have seen her and I can recognise her again a little later."

This system of retention is extremely efficient. We keep in our minds a huge quantity of information simply because we have seen, heard, tasted, smelt or felt it. This ability is part of human nature. This is what enables us to walk about our town without getting lost, to ski or to read a book.

Gattegno proposes we base education, not on memorisation which has a high energetic cost and is often unreliable, but on retention. Learning should be based on retention whenever possible, that is to say, almost always. The learning tools and techniques Gattegno proposes rely systematically on retention.

[edit] Only awareness is educable

We are constantly becoming aware of new things. When it is something significant, the awareness is often audible in the form of the “Ah!” so typical of an important realisation. However, most realisations are made much more discretely. Indeed, as we live our everyday lives, we become aware of all sorts of things at great speed throughout the day: the price of bananas, that these bananas are not ripe enough, that the price of the yoghurts has been reduced because they are close to their sell-by date …. All our life is a succession of tiny awarenesses. Until we become aware of something, that thing remains totally unknown to us. As soon as we become aware of it and integrate into our lives, we often no longer pay attention to it. But, the moment of realisation, the act of learning is an act of awareness.

The role of the teacher in these acts of learning is not to inform their students of this or that piece of information, but to help them to discover it, to perform a conscious act to become aware of it.

Gattegno suggests that leaning takes place in four stages which can be described in terms of awareness.

The first stage consists in a single act of awareness: the realisation that there is something new to be explored. As long as I am unaware that there is something to be known, I cannot start to learn.

The second stage. As soon as I start to learn, I have to explore the situation in order to understand it. As I am not yet an expert in the field, I make many mistakes. These mistakes enable me to progress because by observing what happens and becoming aware of it I can adapt my attempts in relation to the feedback given by the environment. This stage ends when I know what I have to do, but I only succeed when I am wholly present in what I am doing.

The third stage is a transitional stage. At the beginning, I am able to do what I want if I pay attention at each instant. At the end of this stage I know longer need to pay attention: the new skill has become completely automatic and because it is automatic, I am free to give my attention to learning other things.

The fourth stage is that of transfer. For the rest of my life, what I have learnt can be used for all the new skills I may wish to acquire. When I learnt to run, I used the know-how I had acquired from learning to walk. Both of these, walking and running, were useful to me when I decided to learn cross-country skiing. Each skill remains available, except in the rare cases of accident or injury, for a lifetime.

[edit] Subordinating teaching to learning

Third, Caleb Gattegno suggests that to be efficient, teachers should subordinate their pedagogical actions to the learning of their students.

The role of teachers is not to try and transmit knowledge, but to engender acts of awareness in their students, for only awareness is educable. Gattegno created pedagogical materials designed to engender awarenesses. The materials are intended to be used along with techniques aimed at leading students through a succession of awareness. As the students progress, teachers who observe their students can see when and how they can induce a new act of awareness.

For example, he created Words in Color for learning to read. Briefly, it consists of a series of word charts using a colour code in which each colour represents a phoneme of the language. The charts are used to provoke the phonological awareness in students of the sounds they are making and the order in which they are making them thus engendering all the awarenesses of how the graphemes relate to the phonemes and of how the spatial order of writing reflects the chronological order of speech. Other charts, called Fidels, list the graphemes for each phoneme.

He also used this colour code in The Silent Way materials for learning foreign languages to enable students to identify and produce the sounds of the new language. Cuisenaire rods are used, particularly with beginners, to create visible and tangible situations from which the students can induce the structures of the language. The silence of the teacher both gives the students room to explore the language and frees the teacher to observe the students. The teacher is thus able to propose a sequence of pedagogical challenges adapted precisely to the evolution of the students’ learning.

In his approach to teaching mathematics, manipulatives, such as geoboards which he invented and Cuisenaire rods which he popularised, are part of a way of systematically developing students’ mathematical thinking through the exploration of clear and tangible problems.

All the materials created by Gattegno have been designed to allow teachers using them to place the accent systematically on the students’ learning rather than on what they, the teachers, do. Teachers watch their students deal with the challenges they are given, and provide them with feed-back on their trials and errors. Teachers thus actively base their work on the awareness and awarenesses of the students, in the here and now. It is therefore very difficult for a teacher to have more than a vague idea of what will happen in the classroom during any lesson, since the students are actively exploring the domain and have the freedom to take the lesson wherever they want it to go. The class becomes a kind of guided improvisation in which the teacher launches a challenge at a suitable level for the students, and if necessary nudges them into the awarenesses they need to have in order to learn. This is the case whatever the subject being dealt with, and is what is meant by Gattegno’s expression, “the subordination of teaching to learning”.

Classes are usually very stimulating for both the teacher and the students.

[edit] Timeline

  • Caleb Gattegno was born in Alexandria, Egypt, on 11 November 1911.
  • Doctorate in mathematics at the University of Basel: Les cas essentiellement géodésiques des équations de Hamilton-Jacobi intégrables par séparation des variables, 1937.
  • Founder of the International Commission for the Study and Improvement of Mathematics Education (CIEAEM) in 1951.
  • Docteur ès Lettres (Philosophy) at the University of Lille, 1952.
  • In 1952 he founded The Association for Teaching Aids in Mathematics (ATAM), which became The Association of Teachers of Mathematics (ATM) (4000 members), and its journal Mathematics Teaching which is published 4 times a year.
  • In 1952 he also participated in the founding of the Société Belge des Professeurs de Mathématique d'expression française and its journal Mathematica et Paedagogia
  • Founder of The Cuisenaire Companyin England, 1954; director until 1986. Production of the Cuisenaire materials and the accompanying manuals
  • Member of a United Nations (Technical Assistance) mission to Ethiopia with the object of finding a solution to the problem of illiteracy, 1957-58
  • Mathematics at Your Fingertips 1961, film.
  • Founder of Educational Solutions in 1968 in New York where he lived until his death in 1988
  • From 1947 on, he ran seminars for international groups, mainly in Europe, in North and South America and in Japan
  • From 1971 on, he published the Educational Solutions Newsletter five times a year
  • He is the author of pedagogical works, books on psychology and books of reflection on different subjects (the brain, awareness, energy, death, health, love, economics...)
  • Between 1944 and 1988 he published almost 120 books and 500 articles in scientific and other journals in a dozen countries. See the bibliography of his works
  • He created pedagogical materials for the teaching of reading (Words in Color, Infused Reading), foreign languages (The Silent Way) and mathematics ( geoboards)
  • He died in Paris in 1988 two weeks after having run the seminar Le mystère de la communication near Grenoble.

[edit] Brief Bibliography

  • (1954) "The Gattegno Geoboards" in Bulletin of the Association for Teaching Aids in Mathematics, N°.3.
  • (1954) with Georges Cuisenaire, Numbers in colour, Heinemann
  • (1962) Words in Colour - Teachers' Guide. Educational Explorers
  • (1970) What We Owe Children, The Subordination of Teaching to Learning. Outerbridge and Diensfrey, New York.
  • (1974) The Common Sense of Teaching Mathematics, Educational Solutions, New York.
  • (1975) The Mind Teaches the Brain, Educational Solutions, New York. pp. 246. (rev ed 1988)
  • (1976) The Common Sense of Teaching Foreign Languages, Educational Solutions, New York
  • (1985) The Common Sense of Teaching Reading and Writing, Educational Solutions, New York

[edit] External links