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In this paper, student-level indicators of opportunity to learn (OTL) included in the 2012 Programme for International Student Assessment are used to explore the joint relationship of OTL and socioeconomic status (SES) to student mathematics literacy. Using multiple methods, we find consistent evidence that (a) OTL has a significant relationship to student outcomes, (b) a positive relationship exists between SES and OTL, and (c) roughly a third of the SES relationship to literacy is due to its association with OTL. These relationships hold across most countries and both within and between schools within countries. Our findings suggest that in most countries, the organization and policies defining content exposure may exacerbate educational inequalities.

For more than two decades, three components of teacher knowledge have been discussed, namely, content knowledge (CK), pedagogical content knowledge (PCK), and general pedagogical knowledge (GPK). Although there is a growing body of analytic clarification and empirical testing with regard to CK and PCK, especially with a focus on mathematics teachers, hardly any attempt has been made to learn more about teachers’ GPK. In the context of the Teacher Education and Development Study in Mathematics (TEDS-M), Germany, Taiwan, and the United States worked on closing this research gap by conceptualizing a theoretical framework and developing a standardized test of GPK, which was taken by representative samples of future middle school teachers in these countries. Four task-based subdimensions of GPK and three cognitive subdimensions of GPK were distinguished in this test. TEDS-M data are used (a) to test the hypothesis that GPK is not homogenous but multidimensional and (b) to compare the achievement of U.S. future middle school teachers with future middle school teachers from Germany and Taiwan. The data revealed that U.S. future teachers were outperformed by both the other groups. They showed a relative strength in one of the cognitive subdimensions, generating strategies to perform in the classroom, indicating that in particular they had acquired procedural GPK during teacher education.

This article examines the teacher preparation program learning opportunities afforded future lower secondary mathematics teachers and future elementary teachers who may teach mathematics. Data from U.S. participation in the recent international Teacher Education and Development Study in Mathematics are explored against international profiles to address a critical issue oft cited in the teacher education literature: Given the finite time available, what sort of balance is provided for course work across the areas of mathematics content, mathematics pedagogy, and general pedagogy? Results demonstrated major differences for lower secondary preparation programs in both the types of topics or courses covered and the relative emphasis across the three areas in those countries statistically outperforming the United States in comparison to U.S. programs. Similar but less striking differences were noted among elementary programs. These results should provide important empirical evidence relevant to the ongoing policy dialog concerning identifying the specific content of a quality teacher preparation program.

Building on techniques developed for the Third InternationalMathematics and Science Study (TIMSS), we found a very high degree of similarity between CCSSM and the standards of the highest-achieving nations on the 1995 TIMSS. A similar analysis revealed wide variation in the proximity of state standards in effect in 2009 to the CCSSM. Finally, we used regression and analysis of covariance techniques to assess the relationship between the proximity of a state's standards to the CCSSM and performance on the 2009 National Assessment of Educational Progress (NAEP). After adjusting for cut-points on state assessments and controlling for state demographics related to socioeconomic status and poverty, we found that states with standards more like the CCSSM, on average, had higher NAEP scores.

This article examines the range of eighth-grade mathematics learning opportunities in the United States, drawing on data gathered for the Third International Mathematics and Science Study (TIMSS). Sources of variation in the provision of learning opportunities are identified, and patterns in eighth-grade mathematics course offerings are compared across schools. Comparison of students’ learning opportunities includes consideration of the specific course in which they were enrolled, the type of textbook employed for the course, and the proportion of time teachers devoted to teaching specific topics. Analyses revealed a mismatch between the mathematics course title and the textbook employed in the course for nearly 30% of U.S. eighth-grade students. Course-textbook combinations demonstrated significant relationships with the time teachers devoted to specific topics and the international topic difficulty score. Some differences in mathematics learning opportunities were found on the basis of a school’s location (urban, rural, suburban), size, and percentage of minority enrollment. We contend that the significant relationships found were not consistent enough to provide a satisfactory explanation for the observed variation and that individual student differences, which often provide an implicit rationale for tracking, also represent an inadequate explanation for the observed diversity in curricular opportunities. We conclude that recognizing the multiple definitions for students’ classroom mathematics learning experiences is an important step in reform and policy discussions.

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