During the 20year period between the conduct of the First IEA Mathematics Study in 1964 (see Husen, 1967), and the present day when data from the Second IEA Mathematics Study are being analyzed, there have been significant advances in both the conceptual and methodological approaches to the investigation of the determinants of mathematics achievement. The first study employed a tacitly assumed input-output model and screened a very large number of variables that were associated with factors which could potentially influence mathematics achievement. This long list of variables was sieved by a process of stepwise regression, with the increment in the explained variance of the criterion measure, achievement in mathematics, being used as the basis for the selection of variables for inclusion in the fina regression equation.