Piaget’s great insight was that knowledge is not delivered from teacher to learner; rather, children are constantly constructing knowledge through their everyday interactions with people and objects around them. Seymour’s constructionism theory adds a second type of construction, arguing that children construct knowledge most effectively when they

First, there was the continuity principle: The mathematics must be continuous with well-established personal knowledge from which it can inherit a sense of warmth and value as well as “cognitive” competence. Then there was the power principle: It must empower the learner to perform personally meaningful projects that could not be done without it. F

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 thing

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 “nat

Thus this book is really about how a culture, a way of thinking, an idea comes to inhabit a young mind.

The analogy of the dance class without music or dance floor is a serious one. Our education culture gives mathematics learners scarce resources for making sense of what they are learning. As a result our children are forced to follow the very worst model for learning mathematics. This is the model of rote learning, where material is treated as mean

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.

is not uncommon for people with no knowledge of computers to use such concepts as “input,” “output,” and “feedback” to describe their own mental processes. We shall give an example of this process by showing how programming concepts can be used as a conceptual framework for learning a particular physical skill, namely, juggling. Thus we look at pro

Robert, a seventh grader, expressed his conversion to this style of programming by exclaiming: “See, all my procedures are mind-sized bites.” Robert amplified the metaphor by comments such as: “I used to get mixed up by my programs. Now I don’t bite off more than I can chew.” He had met a powerful idea: It is possible to build a large intellectual