 |
I am convinced that the best learning takes place when the learner takes charge... ,(p. 25)
Studying one's own learning process--as the example of croissant making also shows--can be a powerful method of enhancing learning. (p. 32)
I want to suggest that fluency in its own right is an important and insufficiently recognized area of competence. (p. 48)
School's hierarchical organization is intimately tied to its view of education and in particular to its commitment to hierarchical ways of thinking about knowledge itself. What one will consider to be the proper place for School on the heterarchy-hierarchy scale of organizational forms depends on the location of one's theory of knowledge on the heterarchy-hierarchy scale of epistemologies. (pp. 61-62)
Teachers who give so much autonomy to their students are thereby declaring their belief in a radically different theory of knowledge, one that entails far more work for them as well as their students. (p. 63)
What would happen if children who can't do math grew up in Mathland, a place that is to math what France is to French? (p. 64)
...participants thought of themselves as teachers-in-training rather than as learners. Their awareness of being teachers was preventing them from giving themselves over fully to experiencing what they were doing as intellectually exciting and joyful in its own right, for what it could bring them as private individuals. The major obstacle in the way of teachers becoming learners is inhibition about learning. (p. 72)
One moral of the story is that we might all do better if we dared classify ourselves as "developing." (p. 75)
From a feminist stance she sees women as the essential agents of change in education; but the same women have themselves internalized a model of women in a nonaggressive role of accepting authority and as teachers doubly so. (p. 80)
There are many books and courses on the art of constructivist teaching, which talk about the art of setting up situations in which the learner will "construct knowledge;" but I do not know any books on what I would assume to be the more difficult art of actually constructing the knowledge. The how-to-do-it literature in the constructivist subculture is almost as strongly biased to the teacher side as it is in the instructionist subculture. (p. 83)
... to illustrate the gap in our language and my proposal for filling it, consider the following sentence: When I learned French I acquired ___ knowledge about the language, ___ knowledge about the people, and ___ knowledge about learning. Linguistic and cultural would fill in the first two blanks with no problems; but the reader will be hard put to think up a word to fill in the third blank. My candidate is mathetic ... for a course on the art of learning, as in: "Mathetics (by whatever name it will come to be known) is even more important than mathematics as an area of study for children." (p. 84)
Give yourself time is an absurdly obvious principle that falls equally under heuristics and mathetics. (p. 89)
The simple moral is that learning explodes when you stay with it: A full year had passed before the effect in my mind reached a critical level for an exponential explosion of growth. The more complex moral is that some domains of knowledge, such as plants, are especially rich in connections and particularly prone to give rise to explosions of learning. (pp. 103-104)
...they [the children] become producers instead of consumers of educational software. (p. 107)
Designing Lego-Logo was a small but instructive step toward knowing how to provide material that will serve well as a technological infrastructure for suitable learning environments. (p. 123)
The fact that many children make a similar discovery without the computer increases rather than diminishes my enthusiasm for the episode for Dawn. (p. 127)
The kind of knowledge children most need is the knowledge that will help them get more knowledge ... which is why we need to develop a large range of mathematically rich activities or "microworlds." ... It is obvious that as a society we in the United States (and most places in the world) are mathematical under achievers. It is also obvious that instruction in mathematics is on the average rather poor. But it does not follow that the only route to better performance is the improvement of instruction. Another route goes via offering children truly interesting microworlds in which they can use mathematics as Brian did, or think about it as Debbie did, or play with it as Dawn did. If children really want to learn something, and have the opportunity to learn it in use, they do so even if the teaching is poor. For example many learn difficult video games with no professional teaching at all! (pp. 139-140)
But while School's self-serving lesson has pervaded world culture, what is most remarkable is that we all have personal experience and personal knowledge that go against it. ... the most important principle of mathetics may be the incitement to revolt against accepted wisdom that comes from knowing you can learn without being taught and often learn best when taught least. (p. 141)
Constructionism also has the connotation of "construction set," starting with sets in the literal sense, such as Lego, and extending to include programming languages considered as "sets" from which programs can be made, and kitchens as "sets" from which not only cakes but recipes and forms of mathematics-in-use are constructed. One of my central mathetic tenets is that the construction that takes place "in the head" often happens especially felicitously when it is supported by construction of a more public sort "in the world" -- a sand castle or a cake, a Lego house or a corporation, a computer program, a poem, or a theory of the universe. Part of what I mean by "in the world" is that the product can be shown, discussed, examined, probed, and admired. It is out there...Thus, constructionism, my personal reconstruction of constructivism, has as its main feature the fact that it looks more closely than other educational -isms at the idea of mental construction. It attaches special importance to the role of constructions in the world as a support for those in the head, thereby becoming less of a purely mentalist doctrine. It also takes the idea of constructing in the head more seriously by recognizing more than one kind of construction (some of them as far removed from simple building as cultivating a garden), and by asking questions about the methods and the materials used. How can one become an expert at constructing knowledge? What skills are required? And are these skills the same for different kinds of knowledge? (pp. 142-143)
The entire point of all the examples I have given is that the computers serve best when they allow everything to change. (p. 149)
Most of his [Piaget's] followers in education set out to hasten (or at least consolidate) the passage of the child beyond concrete operations. My strategy is to strengthen and perpetuate the typical concrete process even at my age. Rather than pushing children to think like adults, we might do better to remember that they are great learners and to try harder to be more like them. (p. 155)
Everything I have said in this book converges to suggest that this would produce rich intellectual environments in which not only children and teachers but also new ideas about learning would develop together. It is only in such an ecology of mutations and hybridizations of ways of learning that a truly new mathetic culture could emerge. (p. 217)
|