SIMULTANEOUS SYNTHESIS, BEHAVIOR REGULATION AND THE FACTOR STRUCTURE OF ARITHMETICAL PERFORMANCE

This study addresses the issue of the apparent dual nature of arithmetic. There exists a body of correlational and factor analytic research which provides substantial evidence of a computation--problem solving dichotomy in arithmetical performance. This dichotomy is indicated by studies finding low correlations between computation and arithmetic problem solving tests and by studies finding tests of each to load on different factors. However, the apparent dichotomy is not unequivocal since several studies reveal a strong overlap between these two aspects of arithmetic, either by finding appreciable correlations between tests of each, by finding tests of each to load together on oblique factors and/or by finding tests of each to load together on a single factor.;This study analyzes the structure of arithmetic performance in terms of Das, Kirby and Jarman's factor analytic model of cognitive processes which is based on Luria's theory of the anatomical and functional organization of the brain. The model postulates three domain-general factors underlying all cognitive activity: simultaneous synthesis (occipital and parietal lobes), successive synthesis (temporal lobes) and behavior regulation (frontal lobes). The approach taken here examines the relationship between performance on computation tests and performance on quantitative ability and arithmetic problem solving tests by comparing the patterns of factor loadings they each have on a set of reference factors. Since arithmetic tests will load together for a variety of reasons, including having content, format and one or more underlying factors in common, it was felt that a clearer pattern of differences would emerge if each arithmetic test was analyzed separately with the reference factors.;The results indicate that performance on tests of quantitative ability and arithmetic word problem solving are primarily related to the simultaneous synthesis factor while performance on a computation test is primarily related to the behavior regulation factor. Performance was also interpreted with respect to the different types of domain-specific knowledge necessary for successful performance on the problem solving and computation tests. The results support a dual nature interpretation of arithmetical performance.