Numerical cognition: On the convergence of componential and psychometric models

Abstract

The relationship between the elementary operations underlying the processing of numerical information and performance on psychometrically derived ability measures defining the Numerical Facility, Perceptual Speed, General Reasoning, and Memory Span factors was examined for a sample of 112 Air Force recruits. The process variables were derived based on a componential model for arithmetic and an additional measure that indexed the ability to allocate attention while executing arithmetical operations in working memory. All numerical facility, general reasoning, and memory-span tests required the processing of numbers, but only the numerical facility and general reasoning measures required arithmetic. Analyses of the pattern of relationship between the process variables and the ability measures indicated that the rate of executing the operations of arithmetic fact retrieval and carrying contributed to individual differences on the measures defining both the Numerical Facility and General Reasoning factors, but was unrelated to performance on the memory-span tests. Moreover, the attentional allocation aspect of working-memory capacity directly contributed to individual differences on only the general reasoning and memory-span measures. The results demonstrated a pattern of convergent and discriminant relationships for parameters reflecting the processing of numerical information and performance on theoretically similar and subtly dissimilar ability measures. Implications for the representation of individual differences in human abilities were discussed.