ABSTRACT
In the last chapter we considered ways in which example spaces develop. We now look more closely at subtle but significant differences in the effects of pedagogic prompts on the structure of personal example spaces and on the creation of mathematical objects that are new to you. Before considering types of prompts, it is useful to classify types of examples by the roles they play. We use the experience of constructing new objects to address the question of how it is possible to construct new knowledge (the learning paradox). We end by revisiting the larder metaphor, emphasizing the dynamic nature of learning and example space construction.
