This translation aims to provide interested psychologists and mathematics educators with a new catalyst for research in cognitive development. It should also prove useful to the mathematics teacher at the precollegiate level who has an interest in the theory of cognitive development and who teaches probability in the classroom. It is, in fact, one of the few works by Piaget that the beginner can read profitably, without needing too much help from the critics, because it gives a relatively clear example of the development of his techniques and thought.