A production task evaluation of individual differences in mental addition skill development: internal and external validation of chronometric models.

A production task paradigm for obtaining reaction times to mental addition stimuli was used for internal and external validation of chronometric models of mental addition processing. The first analysis explored the internal validity of extant chronometric models and found that three models, (a) a tabular memory network retrieval strategy (PRODUCT), (b) a nontabular memory network retrieval strategy (ERROR RATE), and (c) a computational strategy (MIN), were able to encompass individual differences in strategy choice for 155 individuals from Grades 2 to 8 and 111 college students. Patterns of convergent and discriminant validity for these models were also demonstrated. The second analysis explored the external validity of relations among (a) two traditionally measured factor analytic dimensions of ability, Numerical Facility and Perceptual Speed; (b) two information processing dimensions presumed to underlie mental addition. Addition Efficiency and Speediness; and (c) a digit-span measure of Short-Term Memory. We specified a series of two-group (grade school and college) structural equation models to represent the relations among all measures and showed that individual differences in the apparently calculative processes that underlie the traditionally defined ability dimension of Numerical Facility are highly related to individual differences in Addition Efficiency and Speediness of information processing.