Mindstorms: Children, Computers, And Powerful Ideas

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

In pursuit of our theme of using the computer to understand scientific knowing as rooted in personal knowing, we shall next look at ways in which scientific knowledge is more similar to knowing a person than similar to knowing a fact or having a skill.

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 danc

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

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 prerequisite

What is true historically is also true for the individual: An important part of becoming a good learner is learning how to push out the frontier of what we can express with words. From this point of view the question about the bicycle is not whether or not one can “tell” someone “in full” how to ride but rather what can be done to improve our abili

PLATO WROTE OVER HIS DOOR, “LET ONLY GEOMETERS ENTER.” TIMES have changed. Most of those who now seek to enter Plato’s intellectual world neither know mathematics nor sense the least contradiction in their disregard for his injunction. Our culture’s schizophrenic split between “humanities” and “science” supports their sense of security. Plato was a

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