““progressive enrichment of children’s intuitions, leaning heavily on their precocious understanding of quantitative manipulations and of counting. One should first arouse their curiosity with some amusing numerical puzzles and problems. Then, little by little, one may introduce them to the power of symbolic mathematical notation and the shortcuts it provides — but at this stage, great care should be taken never to divorce such symbolic knowledge from the child’s quantitative intuitions. Eventually, formal axiomatic systems may be introduced. Even then, they should never be imposed on the child, but rather they should always be justified by a demand for greater simplicity and effectiveness. Ideally, each pupil should mentally, in condensed form, retrace the history of mathematics and its motivations.””
