Accumulative memory: Developmental perspectives

The contrast between learning and cognitive development rests not so much on their different time signatures as on the extent to which numerous localised changes in a knowledge base come to be co-ordinated as a whole. The child acquiring the notations and algorithms of arithmetic is not just on course towards making fewer errors and solving problems more quickly, he or she is also beginning to co-ordinate a set of component skills into a larger, integrated system. Addition and subtraction can be learned in isolation but they can also be understood as inverse operations within a larger representational system. If this progressive reorganisation does not occur, then a child may be able to provide the correct answers to particular problems but the necessity behind these answers will be missed—that they really could not be otherwise. Murray (1987 , p.43) puts the point succinctly: It is not just that 15 from 91 is 76, true as that is, but that it has to be 76, that it cannot be anything else however notated. Moreover, if it were anything else an entire mental system of other known things would have to be changed. The development of necessity requires the invention of a system in which otherwise separate events are connected together on some common dimension.