Caleb Gattegno

Caleb Gattegno (1911–1988) was an Egyptian educator, psychologist, and mathematician.

He is considered one of the most influential and prolific mathematics educators of the twentieth century.

He is best known for introducing new approaches to teaching and learning mathematics (Visible & Tangible Math), foreign languages (The Silent Way) and reading (Words in Color).

Gattegno also developed pedagogical materials for each of these approaches, and was the author of more than 120 books and hundreds of articles largely on the topics of education and human development.

Gattegno was born November 11, 1911, in Alexandria, Egypt.

His parents, Menachem Gattegno, a Spanish merchant, and his wife, Bchora, had nine children.

Because of poverty, Gattegno and his siblings had to work starting from a young age.

The future mathematician had no formal education until he started to learn on his own at the age of 14.

He took external examinations when he was 20 years old and obtained a teaching license in physics and chemistry from the University of Marseille in Cairo.

He moved to England, where he became involved in teacher education and helped establish the Association of Teachers of Mathematics and the International Commission for the Study and Improvement of Mathematics Teaching.

He taught at several universities including the University of Liverpool and the University of London.

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 of Jean Piaget and worked on introducing the implications of the latter's cognitive theory on education.

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.