Sublime

Projects. Seymour provocatively argued for “projects over problems.” Of course, Seymour understood the importance of problem solving. But he believed that people learn to solve problems (and learn new concepts and strategies) most effectively while they are actively engaged in meaningful projects. Too often, schools start by teaching concepts to st

I began to see how children who had learned to program computers could use very concrete computer models to think about thinking and to learn about learning and, in doing so, enhance their powers as psychologists and as epistemologists.

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

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

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

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.

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