This article is about experimentation in both practical and mental activity and uses data from a series of studies with preschool children. The article focuses on personal experimentation, which is aimed at discovering relations, rather than the more utilitarian experimentation that is aimed at solving practical tasks. Personal experimentation increases children's knowledge which in turn increases the complexity of experimentation and the role of goal setting within it. In the process of experimentation, children develop new skills and also acquire indefinite or "emerging" knowledge which is flexible and volatile. In the first study, children rolled balls down two chutes of differing length with variable incline. Previously, they had been tested for an understanding of kinetic dependencies, and the experimenter used leading questions to encourage them to experiment. Once children discovered that they could make the ball rolling down the long chute overtake the ball rolling down the short chute, the quality of their experimentation changed, and became richer. In subsequent tasks they easily learned more complex kinetic dependencies. Children have great potential for developing experimentation but in normal pedagogic situations the familiarity of objects gives little stimulus for the development of this potential. Special devices can be designed to stimulate this development. Children experimentation leads to an experience in which stable knowledge (images and categorical knowledge) is challenged by unstable knowledge (motives, questions, hypotheses). The interplay of these two leads to a creative development of new knowledge, as inner contradictions emerge and transform knowledge which subsequently becomes stable, but at a higher level. The proportion of these two kinds of knowledge varies, but when unstable knowledge predominates, children's experiences have a heuristic character. Four pedagogical principals derive from this: (1) optimal balance between adult-determined and child-determined development; (2) create a development-promoting environment; (3) develop intrigue so that children actively forecast, hypothesise, and experiment; and (4) encourage creativity and experimentation with new study material.