According to some educational theories, it is not a good thing to be wrong, and it is an important part of the teacher’s functional to keep his pupil from error, planning every step of way so that they avoid pitfalls. There are no doubt certain types of learning situation where mistakes are better avoided. On the other hand, it is also quite clear that error can play a highly constructive role in the development of thinking, and it is not well established that the advent of error can be a sign of progress.
Many examples can be given, but the following example is in some ways particularly interesting. Children were given a task which involved balancing a set of blocks across a narrow beam (see diagram below). Sometimes the blocks had their weight evenly spread along their length, so that the center of gravity and their geometric center coincided, but sometimes they were more heavily weighted at one end. When the weight of the block was not symmetrically distributed, the difference between the ends was sometimes obvious, because one was bigger than the other. However, sometimes the blocks were weighted at one end with metal which was hidden inside them, and in this case the difference was invisible.
On this task, the youngest subjects were often successful in situations where older one failed, and still older ones succeeded. What seemed to happen was that the very young children were guided almost entirely by the ‘feel’ of the blocks: they had no kind of theory. They took each block in turn and simply balanced it. But primitive theories soon appeared on the scene. The children began to try to operate systematically and according to rules. It should be moted that there was no intervention from teachers-the children evolved the rules spontaneously.
Of course, it often happened that the children did not state the rules that they were using though remarks like ‘Things balance in the middle’ were recorded by researchers/ Even without such explicit formulations, however, the existence of rules can be inferred from observations of behavior, just as the operation of some grammatical rules is inferred from the speech of children, long before they can themselves give any account of what these rules are.
This is the kind of thing that was observed to happen. The children at the intermediate stages would lift an asymmetrically weighted block and, apparently ignoring the ‘feel’, would place it down across the bar at the midpoint of its length, it would fall off. They would then try again, doing exactly the same thing-and of course, it would fall again. But sometimes the ‘midpoint’ rule would work, because for some blocks the weight was equally distributed. This partial success seemed to be enough to keep the theory alive for some time. It was as if the child had to consolidate his first theory with counterexamples. And then the modified theory would tend to grow up alongside the original one, instead of ousting it suddenly.
It is not surprising if, when rules are first devised for devised for dealing with a complex system, they should be inadequate and oversimplified, so that their application leads to error in certain cases. What is of interest is the manner in which the inadequate rules are replaced by better ones and the errors transcended.
In the case we have been considering, the situation was such that the child could clearly see that his theory was wrong. Sometimes it is not so obvious-and being wrong without knowing it is clearly not of much value. So if we are going to try to put the occurrence of error to good use in education, we must ask how we can make children aware of their errors- how we can help to bring them to the critical realization that they are wrong.
There is a very famous historical example of this being done by a great teacher. In this dialogue Meno, the Greek philosopher Plato describes how his teacher Socrates gave a slave boy a lesson in geometry. The boy came to the lesson with the belief that to double the area of a square, you have to double the length of its sides. However, this is mathematically incorrect.
Socrates proceeded, by careful questioning, to lead they boy into self-contradiction. The boy then acknowledged that his original belief was wrong, and that he did not know how long the sides of the new square would have to be if the area was to be doubled. Socrates concluded that the boy was now in a stronger position than before, despite not knowing the answer to the original question, because he was aware of his error. Socrates went on to argue that as long as people think they know something, there is clearly no hope of change, for they are satisfied with their state. But they cannot be satisfied with being ignorant. They will want to get themselves out of this state.
The former of these two assertions can scarcely be challenged. But when about the latter? Will they want to get themselves out of it? Or will they merely be discouraged and give up? What makes us want to learn?