| The present study investigates the nature of mathematical ability. This is accomplished by using Kyllonen and Christal's (1989) framework, which distinguishes between mediator and enabler variables, for identifying pervasive sources of variance in cognitive tasks. The findings indicate that several well established findings in the mental and verbal ability domains are also applicable to the mathematics domain. More specifically, students high in mathematical ability performed significantly better than those low in ability on measures of mediator (i.e., speed of processing, working memory capacity) and enabler variables (i.e., knowledge base characteristics). It also appears that the mediator and enabler variables most related to mathematics achievement are general mental ability, language achievement, automatization of basic arithmetic facts, and memory capacity. Together, these variables account for 70.20 percent of the variance in mathematics achievement. As expected, general mental ability is the main predictor, accounting for slightly more than half of the variance predicted by the variables that contributed significantly to {dollar}Rsp2{dollar}. Together, however, the other variables predict about as much variance in mathematics achievement as general mental ability. This suggests their importance in mathematics achievement. In sum, the framework used in this study encompasses a wider range of variables than those used in the past, because elementary processes related to the acquisition of knowledge and the knowledge one has already acquired are examined in relation to cognitive ability. Traditionally, researchers have focused on either the more elementary aspects of task performance or the more complex knowledge base components. The use of both may explain why such a high percentage of variance was accounted for by the various measures. Thus, future studies should explore the relationship between mathematical ability and other types of elementary processes, in order to get a fuller picture of the variables that influence mathematical performance. |
