New Delhi, July 8 -- Last week in a school, I watched a teacher run an 'activity' on fractions. About 20 children folded paper into halves and quarters with evident enjoyment. There was movement, colour, buzz-all signs of a progressive classroom.

At the end of the class, I asked a few children what a fraction was. They looked at the folded paper in their hands and then at me and had nothing to say. The activity had happened; the learning had not.

The teacher was not at fault. He was sincerely doing what he had been told was good teaching. The fault lay in an intellectual error that has influenced school education for two decades. It is worth naming because we are still living with its consequences.

The error concerns constructivism. As...