via John Holt's How Children Fail:
Knowledge, learning, understanding, are not linear. They are not little bits of facts lined up in rows or piled up one on top of another. A field of knowledge, whether it be math, English, history, science, music, or whatever, is a territory, and knowing it is not just a matter of knowing all the items in the territory, but of knowing how they relate to, compare with, and fit in with each other. It is the difference between being able to say that a room in your house has so many tables, so many chairs, so many lamps, and being able to close your eyes and see that this chair goes here and that table there. It is the difference between knowing the names of all the streets in a city and being able to get from any place, by any desired route, to any other place.
I believe this now more strongly than ever, and it seems to me as important as any other idea set forth in this book.
Why do we talk and write about the world and our knowledge of it as if they were linear? Because that is the nature of talk. Words come out in single file, one at a time; there's no other way to talk or write. So in order to talk about it, we cut the real, undivided world into little pieces, and make these into strings of talk, like beads on a necklace. But we must not be fooled; these strings of talk are not what the world is like. Our learning is not real, not complete, not accurate, above all not useful, unless we take these word strings and somehow convert them in our minds into a likeness of the world, a working mental model of the universe, as we know it. Only when we have made such a model, and when there is at least a rough correspondence between that model and reality, can it be said of us that we have learned something.
What happens in school is that children take in these word strings and store them, undigested, in their minds, so that they can spit them back out on demand. But these words do not change anything, fit with anything, relate to anything. They are as empty of meaning as parrot speech is to a parrot. How can we make school a place where real learning goes on, and not just word swallowing?
I now realize that when we keep trying to find out what our students understand we are more likely than not to destroy whatever understanding they may have. Not until people get very secure in their knowledge and very skillful in talking about it--which rules out almost all young children--is there much point in asking them to talk about what they know, and how they know they know it. The closest we can come to finding out what children really know---and it's not very close - is to watch what they do when they are free to do what interests them most.