Caleb Gattegno

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.

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.