Many teachers are interested in fostering creativity, and there are good reasons for doing so. However, the question of how to do it is made difficult by the paradoxes of creativity: mutually contradictory findings that are, nonetheless, simultaneously true (e.g. convergent thinking hampers creativity but is also necessary for it). These paradoxes can be resolved by dividing the process of creativity into seven phases that depend upon different cognitive processes (e.g. divergent versus convergent thinking) and personal properties (e.g. openness versus compulsiveness), are facilitated by different environmental conditions (e.g. tolerance of errors versus demands for accuracy) and lead to different kinds of product (e.g. something radically new versus novelty that nonetheless fits into the conventional framework). Mapping the four Ps of creativity (person, process, product and press) onto the phases provides a system for analysing both teaching methods and learning activities of individual students. (Contains 1 figure and 3 tables.)