I HAVE DEFINED mathetics as being to learning as heuristics is to problem solving: Principles of mathetics are ideas that illuminate and facilitate the process of learning. In this chapter we focus on two important mathetic principles that are part of most people's common-sense knowledge about what to do when confronted with a new gadget, a new dance step, a new idea, or a new word. First, relate what is new and to be learned to something you already know. Second, take what is new and make it your own: Make something new with it, play with it, build with it. So for example, to learn a new word, we first look for a familiar "root" and then practice by using the word in a sentence of our own construction.
We find this two-step dictum about how to learn in popular, common-sense theories of learning: The procedure described for learning a new word has been given to generations of elementary schoolchildren by generations of parents and teachers. And it also corresponds to the strategies used in the earliest processes of learning. Piaget has studied the spontaneous learning of children and found both steps at work -- the child absorbs the new into the old in a process that Piaget calls assimilation, and the child constructs his knowledge in the course of actively working with it.