The difference between what he “could” and “could not” learn did not depend on the content of the knowledge but on his relationship to it.

Slowly I began to formulate what I still consider the fundamental fact about learning: Anything is easy if you can assimilate it to your collection of models. If you can’t, anything can be painfully difficult.

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 commonsense knowledge about what to do when confronted with a new gadget, a new

As a mathematician I know that one of the most powerful ideas in the history of science was that of differential analysis. From Newton onward, the relationship between the local and the global pretty well set the agenda for mathematics.

In retrospect, we know that the road that led from nineteenth-century transportation was quite different. The invention of the automobile and the airplane did not come from a detailed study of how their predecessors, such as horse-drawn carriages, worked or did not work. Yet, this is the model for contemporary educational research.

Like other builders, children appropriate to their own use materials they find about them, most saliently the models and metaphors suggested by the surrounding culture.

Let us begin with a closer look at the problem of prerequisites. Someone who wanted to learn about aerodynamics might lose interest upon seeing the set of prerequisites, including mechanics and hydrodynamics, that follow an exciting course description in a college catalogue. If one wants to learn about Shakespeare, one finds no list of

Out of the crucible of computational concepts and metaphors, of predicted widespread computer power and of actual experiments with children, the idea of Piagetian learning has emerged as an important organizing principle. Translated into practical terms this idea sets a research agenda concerned with creating conditions for children to explore

The process reminds one of tinkering; learning consists of building up a set of materials and tools that one can handle and manipulate. Perhaps most central of all, it is a process of working with what you’ve got. We’re all familiar with this process on the conscious level, for example, when we attack a problem empirically, trying out all the