Expert Comment

The virtues of intelligent ignorance

Eleanor Duckworth

In most classrooms, it is the quick right answer that is appreciated. Knowledge of the answer ahead of time is, on the whole, more valued than ways of figuring it out.

Similarly, most tests of intellectual ability seek to establish what children have already mastered. True, intelligence tests require that certain things be figured out, but figuring out doesn’t count. No tester will ever know and no score will ever reveal whether the right answer was a triumph of imagination and intellectual daring, or whether the child knew the right answer all along. In addition, the more time a child spends on figuring things out in a test, the less time there is for filling in the right answers; that is, the more time a student allocates to actually think to get the right answers in an intelligence test, the less impressive the results.

However it is pertinent to focus attention to what is involved when the right answer is not already known.

I once observed a class of ten-year-olds while they learned about pendulums. In the class, was a boy named Alec who would be any teacher’s joy. He was full of ideas, articulate about them, and thoughtful and industrious about following them through.

After a number of weeks of working with pendulums, the class watched some film loops in which a pendulum dropped sand as it moved, thus leaving a record of its travels. One question the students considered was, that as a pendulum swings back and forth, does it slow down at each end of its swing, or does it maintain the same speed and simply change direction? Alec, who was a mathematician by inclination, finding merit more readily in deduction than in experience, quickly maintained that the pendulum did not slow down at the ends "because there’s no reason for it to". The other children tended to agree, because the first opinion had come from Alec. The teacher withheld comment but continued playing the loop from which the sand fell into a row of straws.

After a while, one child commented, "I don’t get it. Why isn’t it all along the straws then?" i.e distributed equally. There was silence again as they continued their watch. Another child said, "There’s more sand at the ends — it piles up at the ends." Other remarks included: "How come it isn’t higher in the middle because it goes back and forth over the middle?" "It probably goes fast over the middle and slows down at the ends." "Besides, how can it stop without slowing down?"

Gradually, the comments added up. At last one child dared to commit himself: "It has to be slowing at the ends." And one by one, each child committed himself to an opinion that was contrary to Alec’s. Alec, who was accustomed to hold on to his convictions took a long time to be persuaded by their reasoning. But finally he changed his mind.

It was quite plain that the class had displayed the virtues of courage, caution, confidence, and risk. The courage to submit an idea to someone else’s scrutiny is a virtue in itself, unrelated to the rightness of the idea. Alec’s deduction was wrong, but it was his customary willingness to propose it and defend it that paved the way for a more accurate deduction. The other children were right, but they would never have arrived at that right answer if they had not taken the risk — both within themselves and in public — to question Alec’s reasoning.

In this example, a problem was set for the children, and we assessed what was involved in trying to resolve it. Another whole domain of virtues not even mentioned is that of sitting alone, noticing something new, wondering about it, framing a question for oneself to answer, and sensing some contradiction in one’s own ideas — in other words, all of those virtues that are involved when no one else is present to stimulate thoughts or act as prompter.

The outcome of this observation exercise is that virtues involved in not knowing are the ones that count in the long run. What students do about what they don’t know, will in the final analysis determine what they will ultimately know.

For teachers, it’s important to acknowledge that it is possible to help children develop these virtues. Providing occasions such as the one described here, accepting surprise, puzzlement, excitement, patience, caution, honest attempts, and wrong outcomes as legitimate and important elements of learning, leads to their further development. And helping children to come honestly to terms with their own ideas is not difficult to do. There was nothing particularly subtle in the role of the teacher in this example.

It would make a significant difference to the cause of intelligent thought in general, and to the number of right answers that are ultimately known, if teachers are encouraged to focus on the virtues of intelligent ignorance, so that these virtues would get as much attention in classrooms as the virtue of knowing the right answer.