ABSTRACT
Some who wish to teach mathematics to young children have the wrong kind of understanding of their subject. It is not that they know too little, though they may, but rather that their knowledge is not of an appropriate kind. The psychologist Richard Skemp coined a distinction between two sorts of understanding. Some have understood Skemp to be extolling the virtues of relational understanding at the expense of instrumental understanding. Chunking was never supposed to be a practical skill that might be used in the supermarket. The term 'triangle' is defined in terms of certain properties of 2D plane shapes. Research into adult mathematics carried out around the time of the Cockcroft Report in 1982 showed that many intelligent educated adults lacked mastery of, for instance, the long division algorithm. The intended learning outcome is a sophisticated one – that pupils begin to learn that mathematical 'truths' depend in part on the definitions given to the relevant terms and symbols.
