Quotes from Mindstorms

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.

It is this double relationship -- both abstract and sensory -- that gives the gear the power ot carry powerful mathematics into the mind ... I fell in love with the gears ... Something very personal happened, and one cannot assume that it would be repeated for other children in exactly the same form ... What the gears cannot do the computer might. The computer is the Proteus of machines. Its essence is it universality, its power to simulate ... This book is the result of my own attempts over the past decade to turn computers into instruments flexible enough so that many children can each create for themselves something like what the gears were for me.

Difficulty with school math is often 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 artistic," "musical" or "not musical," "profound" or "superficial," "intelligent" or "dumb."

Learning to be a master programmer is learning to become highly skilled at isolating and correcting "bugs", the parts that keep the program from working. The question to ask about the program is not whether it is right or wrong, but if it is fixable. If this way of looking at intellectual products were genearlized to how the larger culture thinks about knowledge and its acquisition, we all might be less intimidated by our fears of "being wrong".

• QWERTY Phenomenon: "There is a tendency for the first usable, but still primitive, product of a new technology to dig itself in."

In our culture, fear of learning is no less endemic (although more frequently disguised) than fear of mathematics. Children begin their lives as eager and competent learners. They have to learn to have trouble with learning in general and mathematics in particular. In both senses of "math" [mathematics & learning] there is a shift from mathophile to mathophobe, from lover of mathematics and of learning to a person fearful of both.

Principles of Appropriable mathematics

1. 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.

2. Power Principle:

   It must empower the learner to perform personally meaningful projects that could not be done without it.

3. Principle of Cultural Resonance

   The topic must make sense in terms of a larger social context ... it will not truly make sense to children unless it is accepted by adults too.

First, relate what is new and to be learned to something you already know. Second, take what is new and make it your own: Make something new with it, play with it, build with it.

Unorthodox theories of young children are not deficiencies or cognitive gaps, they serve as ways of flexing cognitive muscles, of developing and working through the necessary skills needed for more orthodox theorizing.

The cultural assimilation of the computer presence will give rise to a computer literacy. This phrase is often taken as meaning knowing how to program, or knowing about the varied uses made of computers. But true computer literacy is not just knowing how to make use of comuters and computational ideas. It is knowing when it is appropriate to do so.

The important question is not whether the brain or the computer is discrete but whether knowledge is modularizable.

In earlier chapters it was suggested that how we think about knowledge affects how we think about ourselves. In particular, our image of knowledge as divided up into different kinds leads us to a view of people as divided up according to what their aptitudes are. This in turn leads to a balkanization of our culture.

It was not made. It happened. This must be true too of any new successful forms of associations for learning that might emerge out of the mathetic computer culture. Powerful new social forms must have their roots in the culture, not be the creatures of bureaucrats.