Mathematical competencies in primary school: Structure and relation to psychometrical intelligence

The present article addresses the question whether different mathematical content areas and cognitive operations can be separated in statistical analyses. Samples of n = 10 328 and n = 6 638 primary school students (grades 3 and 4) worked on a large item pool of math items measuring skills in five content areas (numbers, space and shape, patterns and structure, measurement, data representation and probability) and six cognitive dimensions, i.e., mathematical routines, problem solving, communication, reasoning, modeling, and mathematical illustration. Multidimensional analyses revealed that a model with five factors representing the different content areas fits the empirical data best. Reliabilities of the content scales were high and correlations with other tests of mathematical competencies underline the validity of the item pool. Further analyses clearly show that mathematics items and items measuring general cognitive abilities form distinct factors. Based on these findings we discuss the question which constructs scholastic achievement tests measure.