The wise teacher puts the 2 + 2 = 5 student with those who think the answer is different and let them discuss the issue. Children often correct themselves autonomously as they try to explain their reasoning to someone else. In the process of explaining, they have to decenter -- that is, to try to coordinate their points of view with those of others. In doing so, they often recognize their own mistakes.

An even better way of teaching arithmetic in lst grade is to eliminate all formal instruction and to introduce instead such games as "Double War": In this game, a player compares the sum of his or her two cards with the sum of the opponent's two cards, and the player whose sum is greater takes all fur cards. It is not necessary to teach children sums, because they can figure out for themselves the result of each addition. Moreover, in a game they can exchange points of view and correct one another. This method of learning is more active and more conducive to the development of autonomy than are workbooks. My current research indicates that children cannot help but remember sums, if they play such games often enough. Autonomy as the aim of education

the time has come to stop being satisfied with conservative changes and to plan a Copernican revolution in education

The part of the shaded circle that does not overlap the other circle stands form the implicit and explicit, intended and unintended, heteronomous goals of education today. This education requires of students a great deal of memorization, so that they can pass one examination after another. Those of us who succeeded in school did so by memorizing an enormous number of "right" answers -- without understanding or caring about them. We all remember the relief we felt at being free to forget the things we had memorized, as soon as the test was over. We did the memorizing mostly because we were obedient conformists in a system that reinforce our heteronomy.

Studies by McKinnon and Renner and Schwebel

(Note: renner was Leyden's teacher)

demonstrate the outcomes of this kind of education. These researchers investigated the ability of college freshman to think logically at the formal operational level. The freshmen had performed well enough in elementary had HS to gained entrance to a university. Yet McKinnon and Renner found only 25% of them were capable of solid logical thinking at the formal level. A mere 20% of Schwebel's subjects were capable of such thinking.

In the Piaget folder (G-2) for the 5660 class, there is a complete copy of Renner's depressing data.

In the moral realm, too, the schools reinforce children's heteronomy and unwittingly prevent students from developing autonomy. To enforce rules and standards that have been set by adults, the school use grades, gold stars, the detention hall, merits and demerits, and awards. In Fig. 2 - the part of the circle labeled "autonomy" that does not overlay with the other circle thus stand for intellectual and moral autonomy.

The intersection between the two circles stands for things taught in school that are useful to the development of autonomy ( even though the goal of such instruction is conformity ). Such skills as reading and writing, calculating, comprehending maps and charts, and placing events in history are examples of learnings that help us adapt to our environment. If autonomy is the aim of education, educators must try to increase the are of overlap between the two circles.

Teaching for Autonomy

If an individual opposes "the goals of most educators and the public," other people sometimes assume that this individual opposes the teaching of academic subjects. I have nothing against academic subjects; in fact, I strongly favor them. But I think that we can increase the area of overlap between the two circles by teaching such subjects in ways that foster the development of autonomy in children.

Let me use an illustration an afternoon that I spend observing a 6th grade class. I do not know enough about the teaching of grammar to judge the desirability of teaching youngsters to diagram sentences, but this example allows me to discuss the importance of thinking that is stimulated by social interaction. The class was divided into 6 groups of four or five students each. When I arrived after lunch, the teacher wrote a rather tricky sentence on the board and gave the small groups 20 minutes to diagram it. A representative of each group places a diagram on the board when the allotted time was up. Two of the six diagrams were immediately erased, because they were duplications. Individual students then offered well-reasoned arguments favoring or opposing one or another of the remaining four diagrams. The authors of a diagram under attack defended it vigorously, and the intense debate continued until recess time. By then everyone had agreed that two of the four diagrams were inadequate and had to be erased.

When the children returned form recess, the teacher asked if they wanted the answer. Some said, "Yes." But others answered, "No, because you'll give us the wrong answer just to see if you can trick us." The teacher admitted that he had intended to do just that. So the arguments and conterarguments continued, and the class finally agreed on the superiority of one diagram.

This class spent an entire afternoon on one sentence. But my impression was that the children thought so hard about each well- articulated argument that they were thoroughly convinced of the superiority of the final diagram. Many pupils offered wrong ideas along the way, but the teacher encouraged them to defend their opinions until they themselves were convinced that their opinions were wrong. According to the theory of constructivism, children learn by modifying old ideas, not by accumulating new ones. A debate about the superiority of one idea or another is good, because it encourages children to think critically by putting different ideas into relationship with one another. It also allows students to modify old ideas autonomously when they are convinced that new ideas are better.

This 6th grader teacher taught academic content and simultaneously tried to foster the development of intellectual and moral autonomy. Children can develop intellectual autonomy only when all ideas, including wrong ones, are respected. Children can develop moral autonomy only when their ideas are given serious consideration in the process of making decisions. It is also important to note that children mobilize their intelligence and the totality of their knowledge when they have to take a stand and confronted opposing opinions.

Thus teaching methods that encourage children to coordinate viewpoints are far more effective than traditional methods that aim only at getting students to give "right answers."

Another research confirms the importance that Piaget attributed to social interactions. Piaget argued that exchanging points of view is indispensable for children's moral development. He later went on to say that these exchanges are equally necessary for the development of logic in children. Using Piaget's statement as a hypothesis, and taking into account the research of others, the effects of social interaction on childrenŐs cognitive development has been studied. She concluded that, when children confront the ideas of other children for a brief interval as 10 minutes, higher levels of logical reasoning are often the outcome. Moreover, she found that children could generalize these higher levels of reasoning to areas not covered in the experiment.

These experiments are similar in one important way to the situations I described earlier, involving the teaching of 6th grade grammar and of lst grade arithmetic. In each case, children were stimulated to think by having them confront the ideas of their peers. Clearly, social life in the classroom affects childrens' intellectual development. Exchanging points of view also contributes positively to children's social, affective, moral and political development.

A few more examples of the teaching of academic content will show that each subject must be taught differently when the teacher's broad aim is the development of autonomy. In history, biographies of famous people enable children to view historical facts from the perspectives of individuals. It is easier to construct history by approaching facts through subjective viewpoints than through memorizing dates and reading or listening to "objective" interpretations. Certain questions are almost always appropriate: "What do you think of ...." "Does everybody agree with ....?" "Is there anyone who has a different opinion?" In school, children are almost never asked what they honestly think, and they are seldom given two different interpretations of the same event. By asking children what they think of one interpretation or another, teachers can stimulate thinking. Such discussions lead both to intellectual autonomy and to better comprehension of content, because children can actively relate ideas and simultaneously evaluate their classmates' various perspectives.

In literature, teachers can ask their students for different interpretations of a poem or for personal reactions to a novel. Again, the important thing is to encourage students to compare and evaluate the reactions of their peers. In science teachers can suggest projects aimed at producing certain effects (such as making of cars for a soapbox derby). To produce a successful soapbox racer, children have to understand the relevance of such factors as friction, center of gravity, and size of wheels.

These examples do not mean that Piaget's theory implies simply a different way of teaching the same stuff. Autonomy as the aim of education implies a kind of schooling that is very different from the conformist education's practiced around the world today. Piaget's conceptualization of the aim of education is unique, in that it is rooted in a scientific theory of how human beings acquire moral values and knowledge. Others have had ideas similar to this but they base their objectives and methods on personal opinions rather than on scientific theories.

The details of Piaget's theory continue to be modified, but constructivism --- the fundamental concept in his theory has never been disproved. The idea that children acquire moral values and knowledge by construction from within -- by putting things into relationships -- still stands, as does the idea that social interactions are essential for this construction to take place. Moreover, according to Piaget, honest exchanges of points of view are bound to lead, in the long run, to autonomy.

Of the intellectual aspect of autonomy - Piaget said -- cooperation alone leads to autonomy. With regard to logic, cooperation is at first a source of criticism; thanks to the mutual control which it introduces; it suppresses both the spontaneously conviction that characterizes egocentrism and the blind faith in adult authority. Thus, discussion gives rise to reflection and objective verification. But through this very fact cooperation --- leads to the recognition of the principles of logic in so far as these normative laws are necessary to common search for truth.

On the moral aspect of autonomy, Piaget said.

Moral autonomy appears when the mind regards as necessary an ideal that is independent of all external pressure. Now, apart form our relations to other people, there can be no moral necessity -- autonomy --- appears only with reciprocity, when mutual respect is strong enough to make the individual feel from within the desire to treat others as he himself would wish to be treated.

My conviction about the importance of is based partly on the fact that most adults who attend traditional schools came out underdeveloped, considering their potential. Piaget note that if we examine "normal adult individuals who are representative of the honest, human average, the truly logical personas who are masters of their reasoning power are as rare as the truly moral men who exercise their conscious with all of the strength."

Educators today are trying to solve a variety of problems -- including low test scores, violence and apathy in the schools, truancy, alcoholism, drug abuse, teenage, pregnancies and vandalism -- as if these were separate problems. The solutions that educators have turned to include high-pressure instruction and tests to raise academic achievement; exclusion from school to stop physical violence; reliance on police and truancy officers; programs to teacher students about sex, alcohol, and drugs; and special budgets to replace broken windows with opaque, unbreakable materials. Piaget's theory of autonomy suggests instead not a search for more ? Band-Aids, but a fundamental reexamination of educational objectives.

Autonomy as the aim of education is, in once sense, a new idea that could education. In another sense, it is simply a re-emphasis of human values and who write about the educational implications of Piaget's theory will soon become convinced that the significance of this theory lies not in the development state he identifies, but in the importance he attached to constructivism and autonomy. I am personally outraged to see the legal power of taxation and compulsory education used to hamper the development of human potential. I am also scandalized by the fact that the educational establishment of ever country I know is characterized by two factors: ignorance and power. Educators are ignorant of post-behaviorist scientific theory. Those educators who control the education's enterprise are also ignorant of children: the higher an educator advances in the hierarchy, they more he or she become isolated from children and classrooms.

There is something and archaic about all the so called innovation in education. However, the time has come to stop being satisfied with these conservative changes and to plan instead of Copernican revolution in education. By shifting the focus of our thinking always from what we do to children to how children develop, we can begin -- socially, intellectually, and morally -- to allow and encourage them to construct their own ideas. Children respect the rules that they make of themselves. They also work hard to achieve the goals that they set for themselves. I call on educators to heed more carefully Piaget's own words about the radical reform implied by his theory.