I am reading in the literature of Constructivism, and will post my observations and interesting quotations from the pioneers from time to time to stimulate discussion. It is a curious fact, and one that seems quite important to me, that I come to understand my own thinking about a subject much better when I have to explain it to someone else.
The following is the best example I have so far seen of Piaget's approach to Genetic Epistemology and to Constructivism. Genetic Epistemology suggests that to understand the nature of knowledge, we must understand the process by which knowledge has come about. Since we cannot study prehistoric humans, our best source is to study the origins of ideas in children. This study requires an understanding of human psychology, and also the current state and historical development of logic, mathematics, and the progress of science. Such interdisciplinary study has not been popular, in part because so few people have enough knowledge, and because people in different disciplines have great difficulty communicating with others. http://www.marxists.org/reference/subject/philosophy/works/fr/piaget.htm Jean Piaget (1968) Genetic Epistemology Source: Genetic Epistemology, a series of lectures delivered by Piaget at Columbia University, Published by Columbia Univesity Press, translated by Eleanor Duckworth. First lecture reproduced here. "This example, one we have studied quite thoroughly with many children, was first suggested to me by a mathematician friend who quoted it as the point of departure of his interest in mathematics. When he was a small child, he was counting pebbles one day; he lined them up in a row, counted them from left to right, and got ten. Then, just for fun, he counted them from right to left to see what number he would get, and was astonished that he got ten again. He put the pebbles in a circle and counted them, and once again there were ten. He went around the circle in the other way and got ten again. And no matter how he put the pebbles down, when he counted them, the number came to ten. He discovered here what is known in mathematics as commutativity, that is, the sum is independent of the order. But how did he discover this? Is this commutativity a property of the pebbles? It is true that the pebbles, as it were, let him arrange them in various ways; he could not have done the same thing with drops of water. So in this sense there was a physical aspect to his knowledge. But the order was not in the pebbles; it was he, the subject, who put the pebbles in a line and then in a circle. Moreover, the sum was not in the pebbles themselves; it was he who united them. The knowledge that this future mathematician discovered that day was drawn, then, not from the physical properties of the pebbles, but from the actions that he carried out on the pebbles. This knowledge is what I call logical mathematical knowledge and not physical knowledge." This states the importance of such ideas, and calls attention to the need for research. The research itself is a long, arduous, and contentious process, with a vast literature, as is all scientific observation, experiment, and theory-building, with many false leads and backtracks. It has not simply given us a body of definite knowledge in the way that we can say elementary physics does. It is more like the parts of physics out near the frontiers, where the variety of models of reality under consideration changes from year to year. But some lessons can be, and have been drawn from all of this, of which more another time. For the moment is it enough to have a powerful example of integrated thought, action, and discovery. This child did not only discover what we may call the Law of Conservation of Pebble Number. He discovered the existence of laws amenable to experiment and rational thought, but not dependent on the particular objects used in the discovery. In short, he discovered mathematics itself. Most children don't do this in this way, and of course, most don't become mathematicians as a result. What do children discover? How? What do they become as a result? These questions amply repay any amount of attention and effort aimed at the continued creation of ever-more-accurate understanding, because they allow us to explain ourselves better to ourselves and to others, a conversation that has always been rewarding, but never more so than now. Please let me know if this makes sufficient sense to you, and what else might need explaining. Also if you have been taught some quite different view of the nature of knowledge, or simply find this one obviously false, as some do. -- Edward Cherlin End Poverty at a Profit by teaching children business http://www.EarthTreasury.org/ "The best way to predict the future is to invent it."--Alan Kay _______________________________________________ Olpc-open mailing list [email protected] http://lists.laptop.org/listinfo/olpc-open
