Anything is easy if you can assimilate it to your collection of models. If you can't, anything can be painfully difficult.
The understanding of learning must be genetic. It must refer to the genesis of knowledge.
What an individual can learn, and how he learns it, depends on what models he has available. This raises, recursively, the question of how he learned these models. Thus the "laws of learning" must be about how intellectual structures grow out of one another and about how, in the process, they acquire both logical and emotional form.
I find myself frequently remind- ed of several aspects of my encounter with the differential gear. First, I remember that no one told me to learn about differential gears. Second, I remember that there was feeling, love, as well as understanding in my relationship with gears. Third, I remember that my first encounter with them was in my second year. If any "scientific" educational psychologist had tried to "measure" the ef- fects of this encounter, he would probably have failed. It had pro- found consequences but, I conjecture, only very many years later.
A modern-day Montessori might propose, if convinced by my story, to create a gear set for children. Thus every child might have the experience I had. But to hope for this would be to miss the es- sence of the story. I fell in love with the gears. This is something that cannot be reduced to purely "cognitive" terms. Something very personal happened, and one cannot assume that it would be repeated for other children in exactly the same form.
My thesis could be summarized as: What the gears cannot do the computer might. The computer is the Proteus of machines. Its es- sence is its universality, its power to simulate. Because it can take on a thousand forms and can serve a thousand functions, it can ap- peal to a thousand tastes. This book is the result of my own at- tempts over the past decade to turn computers into instruments flexible enough so that many children can each create for them- selves something like what the gears were for me.
I shall be talking about how computers may affect the way people think and learn.
In this book I discuss ways in which the computer presence could contribute to mental processes not only instrumentally but in more essential, conceptual ways, influencing how people think even when they are far removed from physical contact with a computer (just as the gears shaped my understand- ing of algebra although they were not physically present in the math class).
It is about using computers to challenge current be- liefs about who can understand what and at what age. It is about using computers to question standard assumptions in developmental psychology and in the psychology of aptitudes and attitudes.
For example, although babies learn to speak their native lan- guage with spectacular ease, most children have great difficulty learning foreign languages in schools and, indeed, often learn the written version of their own language none too successfully. Isn't learning a computer language more like the difficult process of learning a foreign written language than the easy one of learning to speak one's own language? And isn't the problem further com- pounded by all the difficulties most people encounter learning mathematics?
If we had to base our opinions on observation of how poorly children learned French in American schools, we would have to conclude that most people were incapa- ble of mastering it. But we know that all normal children would learn it very easily if they lived in France. My conjecture is that 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.
I can quote this
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Difficulty with school math is of- ten the first step of an invasive intellectual process that leads us all to define ourselves as bundles of aptitudes and ineptitudes, as being "mathematical" or "not mathematical,' ' " artistic" or "not artis- tic," "musical" or "not musical," "profound" or "superficial," "in- telligent" or "dumb." Thus deficiency becomes identity and learn- ing is transformed from the early child's free exploration of the world to a chore beset by insecurities and self-imposed restrictions
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The metaphor of imitating the way the child learns to talk has been constantly with us in this work and has led to a vision of education and of education research very dif- ferent from the traditional ones. For people in the teaching profes- sions, the word "education" tends to evoke "teaching," particularly classroom teaching. The goal of education research tends therefore to be focused on how to improve classroom teaching. But if, as I have stressed here, the model of successful learning is the way a child learns to talk, a process that takes place without deliberate and organized teaching, the goal set is very different.
I see the classroom as an artificial and inefficient learning environment that society has been forced to invent because its informal environments fail in certain essential learning domains, such as writing or grammar or school math.
Thus this book is really about how a culture, a way of thinking, an idea comes to inhabit a young mind. I am suspicious of thinking about such problems too abstractly, and I shall write here with par- ticular restricted focus. I shall in fact concentrate on those ways of thinking that I know best.
But I think that the kind of pleasure I take in mathematics should be part of a general vision of what education should be about.
My interest is in the process of invention of "objects-to-think-with," objects in which there is an intersection of cultural presence, embedded knowledge, and the possibility for personal identification.
The examples are infinitely varied, but in each the child is learning how to exercise control over an exceptionally rich and sophisticated "micro-world."