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.
What an individual can learn, and how he learns it, depends on what models he has available.
The gear can be used to illustrate many powerful " advanced" mathematical ideas, such as groups or relative motion. It is this double relationship both abstract and sensory that gives the gear the power to carry powerful mathematics into the mind.
Many cultural barriers impede children from making scientific knowledge their own.
there is a world of difference between what computers can do and what society will choose to do with them.
In my vision, the child programs the computer and, in doing so, both acquires a sense of mastery over a piece of the most modern and powerful technology and establishes an intimate contact with some of the deepest ideas from science, from mathematics, and from the art of intellectual model building.
Programming a computer means nothing more or less than communicating to it in a language that it and the human user can both " understand."
Every normal child learns to talk. Why then should a child not learn to " talk" to a computer?
It is possible to design computers so that learning to communicate with them can be a natural process, more like learning French by living in France than like trying to learn it through the unnatural process of American foreign-language instruction in classrooms. Learning to communicate with a computer may change the way other learning takes place.
Much of what we now see as too " formal" or " too mathematical" will be learned just as easily when children grow up in the computer-rich world of the very near future.