Domain-specific and domain-general skills in the identification of conceptually-derived arithmetic strategies

Conceptual knowledge of key principles underlying arithmetic is an important precursor to understanding algebra and success in mathematics. One such

principle is associativity, which allows groups of operations to be performed in a different order from that in which they are presented. For example, the problem '6 + 38 - 35' can be solved through an efficient 'shortcut' strategy

of '38 - 35 = 3' and then 3 + 6 = 9'. One issue is that, of all the widely discussed arithmetic principles associativity is the one that individuals have greatest difficulty with, in that they often fail to apply it when solving arithmetic problems. Educators have called for this to change, and for individuals' knowledge and use of arithmetic principles to improve. This thesis contributes to that goal by investigating the cognitive processes involved in using the associativity shortcut, and the ways in which shortcut use can be encouraged.