The present study investigated the extent to which mental attentional capacity (M-capacity), inhibition, updating, and shifting contribute to children's ability to solve multiplication word problems. Task analyses were conducted to estimate the mental-attentional demands ( M-demand) of various kinds of multiplication word problems (i.e., scalar, array, combinatorial, and proportion). One hundred and fifty-five children in grades 3 through 6 (i.e., 8 to 13 year-olds) completed a reading comprehension test and were given a battery of M-capacity, inhibition, shifting, and updating measures. In addition, children completed a multiplication task consisting of word problems at two levels of difficulty: basic (i.e., one-step) problems and complex (i.e., multi-step) problems. Results generally supported the hypothesis that children would not be able to solve a problem when the task's estimated M-demand exceeded the child's M-capacity. Structural equation modeling showed updating mediated the relationship between multiplication performance (i.e., basic and complex multiplication problems, controlling for reading comprehension abilities) and latent factors M-capacity and inhibition. Age was found to play a more important role in predicting performance on basic problems than updating did. The reverse was found for complex problems, in which updating accounted for more of the variance when compared to age. Shifting was not a significant predictor in either model, likely because ability to shift was not needed to solve many of the math items. The implications of proposing executive function updating as a mediator between chronological age, core cognitive abilities, and mathematical cognition are discussed.Age was found to play a more important role in predicting performance on basic problems than updating did. The reverse was found for complex problems, in which updating accounted for more of the variance when compared to age.
|Title||:||The Development of Mathematical Reasoning: Role of M-capacity, Inhibition, Updating, and Shifting|
|Publisher||:||ProQuest - 2008|