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Most of us have very imperfect control over our attention. Our minds slip away from duty before we realize that they are gone. Part of being a good student is learning to be aware of that state of ones own mind and the degree of one's own understanding. The good student may be one who often says that he does not understand, simply because he keeps a constant check on his understanding. The poor student, who does not, so to speak, watch himself trying to understand, does not know most of the time whether he understands or not. Thus the problem is not to get students to ask us what they don't
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see now that I was wrong about Emily's task. The task for her was not to spell "microscopic," or write a word backwards, or balance a weight The thought in her mind must have been something like this: "These teachers want me to do something. I haven't got the faintest idea what it is, or why in the world they want me to do it. But I’ll do something, and then maybe they'll let me alone."
I find myself coming to realize that what hampers their thinking, what drives them into these narrow and defensive strategies, is a feeling that they must please the grownups at all costs.
For children, the central business of school is not learning, whatever this vague word means; it is getting these daily tasks done, or at least out of the way, with a minimum of effort and unpleasantness.
It is not the teacher's proper task to be constantly testing and checking the understanding of the learner. That's the learner's task, and only the learner can do it. The teacher's job is to answer questions when learners ask them, or to try to help learners understand better when they ask for that help.
They have not learned how to learn from a mistake, or even that learning from mistakes is possible. If they say, "Is the number between 5,000 and 10,000?" and I say yes, they cheer; if I say no, they groan, even though they get exactly the same amount of information in either case.
The point I now want to make is that "success," as much as "failure," are adult ideas which we impose on children. The two ideas go together, are opposite sides of the same coin. It is nonsense to think that we can give children a love of "succeeding" without at the same time giving them an equal dread of "failing."
Children who undertake to do things, like my five-year-old friend Vita who is beginning the very serious study of the violin, do not think in terms of success and failure but of effort and adventure. It is only when pleasing adults become important that the sharp line between success and failure appears.
But most homework, when it is not pure busywork to fill up the children's time, is designed to convince the teacher, not the children, that they know something. And so it rarely does good, and usually does harm.
Left alone, children made very prudent choices about what kind of risks they would run--for being adventurous, of course they wanted to run some risks.
The scared fighter may be the best fighter, but the scared learner is always a poor learner.
Children who depend heavily on adult approval may decide that, if they can't have total success, their next-best bet is to have total failure.
What I tell a child may seem to contradict his common sense, the common usage of English, and even other things I have told him; but he must bow to superior force and accept it whether it makes sense or not.
We don't have to make human beings smart. They are born smart. All we have to do is stop doing the things that made them stupid.
when Learning happens, the school and teachers take the credit; when it doesn't, the students get the blame. The
may help to have in our minds a picture of what we mean by understanding. I feel I understand something if I can do some, at least, of the following: (1) state it in my own words; (2) give examples of it; (3) recognize it in various guises and circumstances; (4) see connections between it and other facts or ideas; (5) make use of it in various ways; (6) foresee some of its consequences; (7) state its opposite or converse. This list is only a beginning; but it may help us in the future to find out what our students really know as opposed to what they can give the appearance of knowing, their
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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, com- pare with, and fit in with each other. It
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.
The only answer that really sticks in a child's mind is the answer to a question that he asked or might ask of himself.
if we think we have to "teach" children what the schools call "basic arithmetic facts," e.g., that 3 + 4 = 7 and 5 x 4 = 20, a better way to do it is by having them discover for themselves, by experiment, as these two girls were doing, some of the basic properties of numbers. The statement that 3 + 2 = 5 is best understood, not as a statement about addition which someone invented and which can be learned only be being memorized, but as a statement about one property of the number 5. This property, that a group of five objects may be split up into a group of three objects and another of two
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In mathematics certainly, and very probably in all subjects, knowledge which is not genuinely discovered by children will very likely prove useless and will be soon forgotten.
Children cannot learn much from cookbooks, even the best cookbooks. A child learns, at any moment, not by using the procedure that seems best to us, but the one that seems best to him; by fitting into his structure of ideas and relationships, his mental model of reality, not the piece we think comes next, but the one he thinks comes next.
child must discover for himself that if, for example, 2 X 75 = 150, then 2 x 74 must equal 150 - 2, or 148. Until he does, no amount of talk will enable him to make that step, far less make use of this understanding to see that since 3 X 50 = 150, 3 X 49 must equal 150 -- 3, or 147.
few good principles to keep in mind: (1) Children do not need to be "taught" in order to learn; they will learn a great deal, and probably learn best, without being taught. (2) Children are enormously interested in our adult world and what we do there. (3) Children learn best when the things they learn are embedded in a context of real Life, are part of what George Dennison, in The Lives of Children, called "the continuum of experience." (4) Children learn best when their learning is connected with an immediate and serious purpose.
any case, I hold to my first point, that the best way to expose children to the world of numbers is to let them see those numbers at work in adult life. HOW SCHOOLS FAIL
It is as true now as it was then that no matter what tests show, very little of what is taught in school is learned, very little of what is learned is remembered, and very little of what is remembered is used. The things we learn, remember, and use are the things we seek out or meet in the daily, serious, non-school parts of our lives.
the schools could only learn to recognize, to value, and to foster courage in children, a great many of their most serious problems, not just of learning, but also of discipline, would be well on the road toward a solution. But there are few signs that this is about to happen.
Most children learn more, even more schoolwork, when they are out of school than when they are in. As
For all our talk and good intentions, there is much more stick than carrot in school, and while this remains so, children are going to adopt a strategy aimed above all else at staying out of trouble. How can we foster a joyous, alert, wholehearted participation in life if we build all our schooling around the holiness of getting "right answers"?
The true test of intelligence is not how much we know how to do, but how we behave when we don't know what to do.
about. It is a rare child who, anywhere in his growing up, meets even one older person with whom he can talk openly about what most interests him, concerns him, and worries him.
