Background
Gattegno was born November 11, 1911, inPedagogical approach
Gattegno's pedagogical approach is characterised by propositions based on the observation of human learning in many and varied situations. This is a description of three of these propositions. He was also influenced by the works ofLearning and effort
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 essential to teach in ways that are efficient in terms of the amount of energy spent by learners. To be able to quantitively determine whether one method was more efficient than another, he created a unit of measurement for the effort used to learn. He called that unit an ''ogden'', and one can only say an ''ogden'' has been spent if the learning was done outside of ordinary functionings, and was retained. For example, learning one word in a foreign language costs one ''ogden'', but if the word cannot be recalled, the ''ogden'' has not truly been spent. Gattegno's teaching materials and techniques were designed to be economical with ''ogdens'', so that the greatest amount of information can be recalled with the least sense of effort. In 1970s, he collaborated with the film maker Joeseph Koenig. They produced one-minute television films that featured animation contents that presented: 1) raw data on how the English language works; 2) the language's spatial ordering; 3) the effects of transformations; and, 4) the concepts of insertion, reversal, substitution, and addition. For Gattegno, certain kinds of learning are very expensive in terms of energy, i.e., ''ogdens'', while others are practically free. Memorization is a very expensive way to learn. The energy cost can be especially high when the content is of no particular interest to the learner. Memorizing dates in history or major exports of foreign countries is like that, for most people. School is not the only place where that kind of learning is found. Learning somebody's name or telephone number is equally arbitrary. We have to use our own energy to make such arbitrary items stick in our memories. The "mental glue" necessary is expensive, since that type of learning uses up a lot of energy. Not only is that type of learning expensive, it tends also to be fragile. It is typically difficult to remember those kinds of items. Even when we make a great effort, 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 almost all of us have forgotten much of what we "learned" at school. It is not unusual for us to forget much of what we memorize. However, there is another way of functioning, which Gattegno called natural 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 similar way, that is, through energy that enters our system, rather than energy we allocate from inside, to memorize an arbitrary item. To retain an auditory or visual image, we have to use perhaps only an insignificant 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 generally remain for long periods. We all have experiences similar to the following examples Gattegno offered: ''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."'' Our system of retention is extremely efficient. We keep in our minds a huge quantity of information simply because we have seen, heard, tasted, smelled or felt it. That ability is part of human nature. It enables us to walk about our town without getting lost, to ski or to read a book. Gattegno proposed that we should base education, not on memorization, which has a high energetic cost and is often unreliable, but on retention. The learning tools and techniques Gattegno proposed rely systematically on retention.The subordination of teaching to learning
Gattegno argued that for pedagogical actions to be effective, teaching should be subordinated to learning, which requires that as an absolute prerequisite teachers must understand how people learn. Rather than present facts for memorization, teachers construct challenges for students to conquer. If the student cannot conquer the challenge easily, the teacher does not tell the answer, but observes and asks questions to determine where the confusion lies, and what awareness needs to be triggered in the student. His methodology is based on the idea that education is built around the acquisition of awareness obtained from the elements of learning. The role of teachers is not to try to transmit knowledge, but to engender acts of awareness in their students, for only awareness is educable. Gattegno created pedagogical materials designed to provoke awarenesses. The materials are intended to be used along with techniques aimed at leading students through a succession of awarenesses. 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 createdOnly awareness is educable
Gattegno found that only awareness is educable in human beings. On the path to learning, several awarenesses must be reached. The first is the awareness that there is something to be learned, some unknown to become known. The next awarenesses are triggered by experience with the subject matter. For example, rather than ask a student to write "2+2=4," Gattegno might ask them to create the number 4 in as many ways as possible with colored rods. The student can then clearly see, feel, and describe the characteristics of the number 4. Instead of memorizing "2+2=4," the student has had a mathematical experience, and become aware that "4" can be broken into parts, and that the process of breaking apart and putting together can be described in several ways. 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 it 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 acts of learning is not to inform 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 learning 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 no 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.Timeline
*1911 - Caleb Gattegno was born in Alexandria, Egypt, on November 11. *1932 - Mathematics teacher at the Lycée Français in Alexandria until 1936. *1937 - Earned a Doctorate in mathematics at the University of Basel: Les cas essentiellement géodésiques des équations de Hamilton-Jacobi intégrables par séparation des variables. *1944 - Began publishing books and articles in scientific and other journals. By 1988, he had written about 120 books and 500 articles. *1947 - Began running seminars for international groups, mainly in Europe, in North and South America and in Japan. He continued these seminars until his death. *1948 - Earned a Master of Arts in education at The University of London. *1951 - Founded thBibliography
*(1954) "The Gattegno Geoboards" in ''Bulletin of the Association for Teaching Aids in Mathematics'', N°.3. *(1954) with Georges Cuisenaire, "Numbers in colour," Heinemann *(1960) "Now Johnny Can Do Arithmetic," Educational Explorers, Reading. *(1962) "Words in Colour - Teachers' Guide," Educational Explorers, Reading. *(1963) "Teaching foreign languages in schools - the Silent Way," Educational Solutions, New York. *(1969) "Towards a Visual Culture," Outerbridge & Dienstfrey, New York. *(1970) "What We Owe Children, The Subordination of Teaching to Learning," Outerbridge and Diensfrey, New York.References
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