Chapter 2

THE DYNAMIC OF ARITHMETIC - RICHARD DALLAWAY


MEMORY FOR ARITHMETIC FACTS

There are a number of ways to find the answer to "6x7". Strategies might include counting a row of six 7s, recalling the answer to 6x6 and adding on another 6, using a calculator, or pure recall. Children tend to use a number of strategies, but as they become older they tend to rely on recall alone (Siegler 1988).

This chapter investigates adults' recall of multiplication facts. Although adults do use other strategies, recall seems to be most frequently used, and it is also the strategy that has been the subject of many detailed experiments. First, a review is presented of the typical reaction times (RTs) and errors of adults recalling multiplication facts. A number of models have been proposed to account for the phenomena, and these are reviewed in section 2.2. A new connectionist model of fact recall, based on McClelland's (1979, 1988) "cascade" equations, is described in chapter 3.

  • Phenomena
  • The production task
  • Neuropsychological constraints
  • Rule based processing
  • Summary
  • Previous models
  • Distributions of associations
  • Network interference
  • Previous connectionist models
  • Brain-stae-in-a-box
  • Backpropagation
  • interactive activation
  • Mean field theory
  • Summary

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