Zoltan P. Dienes is a Hungarian mathematician whose ideas on the education (especially of small children) have been popular in some countries. He is a world-famous theorist and tireless practitioner of the "new mathematics" - an approach to mathematics learning that uses games, songs and dance to make it more appealing to children.
He described his theory of six stages of learning mathematics:
Stage 1.
Most people, when confronted with a situation which they are not sure how to handle, will engage in what is usually described as “trial and error” activity. What they are doing is to freely interact with the situation presented to them. In trying to solve a puzzle, most people will randomly try this and that and the other until some form of regularity in the situation begins to emerge, after which a more systematic problem solving behavior becomes possible. This stage is the FREE PLAY, which is or should be, the beginning of all learning. This is how the would-be learner becomes familiar with the situation with which he or she is confronted.