| The study attempted to clarify the structure of mathematical abilities. Forty-eight factor-analytic studies were selected and their results conceptually synthesized. The factors were compared in six families: General, Numerical, Reasoning, Spatial, Verbal, and Mathematical.; Eleven data sets were reanalyzed from: Barakat (1951), Campbell (1956), Kline (1959), Mitchell (1938), Very (1967), Weiss (1955), Werdelin (1958), and Wrigley (1958). In each reanalysis, principal factor analysis was followed by graphical rotation to oblique simple structure. Higher-order analyses followed the same procedure. The structure was orthogonalized by the Schmid-Leiman procedure. The results were compared to each other and to the original results. Percents of total variance accounted for by factors were used to examine the association of each family with mathematical abilities.; A partial hierarchical structure of mathematical abilities appeared across the original and reanalyzed results. Reasoning abilities were closely associated with mathematics achievement. Numerical and spatial abilities were associated with certain aspects of mathematics achievement. Verbal abilities were minimally associated with mathematics achievement. There was evidence for a kind of mathematical factor. Fluid- and crystallized-intelligence abilities were closely associated with mathematics achievement. Evidence for the automatization of responses was found that extended to certain algebraic skills and revealed sex differences. Some algebraic factors appeared to split according to the cognitive processes involved in the tasks. Factors in the Numerical and Spatial families accounted for about 7% and 5% of the variance in mathematical abilities as measured by the test batteries in the reanalyses. The percents of variance accounted for by the Reasoning, Verbal, or Mathematical families were less definite. Fluid- and crystallized-intelligence-like factors each accounted for about 9% of the variance. Higher-order factors together accounted for about 25% of the variance, as did first-order factors together. Collectively, the factors in the reanalyses accounted for about 50% of the variance, most of which represented the relationship of mathematical abilities to general cognitive abilities. The diversity among the studies that prevented a statistical synthesis of the results strengthened the generality of the finding concerning structure. |
