In 1957, Van Hiele published his study on levels in learning mathematics. In this article we present an elaboration of the theory on levels in learning and an illustration of this theory based on empirical results. We distinguish between three levels: The first is the formation of an image out of a range of familiar examples or experiences. Second, on the basis of the image a schema can be built, which includes all kinds of interrelated details. Third, a theory can be developed with basic assumptions, definitions, and logical inferences. Before entering the next level, the learner should be sufficiently experienced on the actual level. It is shown that the theory on levels in learning can be integrated with other learning principles, such as notions from constructivism.