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In this paper we review generalizability (G) theory, a theory of the multifaceted errors of a behavioral measurement. The review was undertaken at the request of Philip Levy, then editor of the Journal.His idea was that the review would commemorate the first article on G theory, which the Journal published in 1963 (Cronbach, Rajaratnam, & Gleser, 1963). For these and personal reasons, we undertook the review. The review does not cover the period 1963-1972 because that has already been done by Cronbach, Gleser, Nanda, and Rajaratnam (1972).In Section 1 we sketch out generalizability theory for those who are not familiar with it. In doing so, we summarize the notation used in the review. Section 2 reviews theoretical contributions. While it primarily reflects what has been published, we take up some new topics and identify others in need of treatment. Section 3 presents an application of the theory in some detail. This application illustrates basic concepts in the theory (Section 1) as well as recent theoretical contributions (Section 2

This study investigated the relationship between policies related to the recruitment, selection, preparation, and certification of new teachers and (a) the quality of future teachers as measured by their mathematics content and pedagogy content knowledge and (b) student achievement in mathematics at the national level. The study used data collected for the Teacher Education and Development Study in Mathematics, which compared the ways in which 17 countries prepared teachers of mathematics for the primary and secondary levels. A consistent positive association was found between the strength of a country’s quality assurance arrangements and future teachers’ knowledge of mathematics and mathematics pedagogy. Countries with strong policies for assuring the quality of new teachers were also found to be among the strongest performers on international tests of mathematics achievement.