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.

This article demonstrates the usefulness of analysis of covariance structure procedures for estimating variance components under more general assumptions than are provided in the typical mixed-model analysis of variance. A seq uence of eight models is presented based on varying degrees of restrictive assumptions. Maximum likelihood procedures are employed in the estimation of the parameters of the models. The procedures are applied to simulated data and to an empirical example which shows the necessity of the more general assumptions.

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I n the last few years, we have been inundated with repetitions of a new schooling myth. From the report on Equality of Educational Opportunity (Coleman et al., 1966) and the most recent reanalyses of its data (Mosteller and Moynihan, 1972) to the Jencks et al book onInequality (1972), we have been flooded with reports of the lack of effect of schooling. These reports have discouraged professional educators and comforted those who would reduce the resources allocated to education. Moreover, recent teachers' strikes, response to the "energy" crisis, and budget cutbacks passed on as shorter school years and increased class sizes, all have decreased the amount of schooling and instruction for many pupils in this country. These curtailments did not produce any enraged outcry or concerted action from those who for so long have promoted quality and equality of education. It seems that those concerned have silently joined the chorus performing De Nihilo Nihil. What they do not realize is that they play a part in a new American tragedy.Schooling does have effects and racher than asking if there are any efects of schooling, we should be asking how much of an effect schooling has. If we take a more appropriate stance towards assessing school effects and a fresh look at the above studies, then we not only must conclude that schooling has large effects on pupils' achievements but also must take immediate steps to insure equality and quality of education. The drawbacks that currently result from cutting the amount of schooling are alarming, as we will show. Quantity of SchoolingIt is unwarranted to say that schooling has no effect. Certainly, some children would learn to read even if they did not attend school, and certainly, the school is not effective in teaching reading to some children. However, this does not mean that children do not acquire appreciably better reading skills by attending school. Some children learn to read who would not learn to read if they did not attend school. Some children who would have learned to read anyway, read much more capably because of their schooling. The level of discussion, however, still has not risen above the question: "Does schooling have an effect?" It is the degree of schooling effect that is important for educa-tional policy. For example, if it were found, after a large concentration of resources in reading instruction, that only small gains in levels of competency were attained, then we might be dissatisfied with the return on our investment in this area. In this case, we would perhaps want to understand why there was such a small effect so that we could modify the conditions of our investment, i.e., change the conditions of instruction or perhaps, we might wish to reduce our investment in this area, either so we could improve the yield of the system in another area, where we could produce more valued outcomes with the same amount of resources or invest our resources in non-educational endeavours. To facilitate such educational decision making, we must be able to assess the exten...

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The California Learning Assessment System 1993 OTL Study allowed examination of the extent to which California public school mathematics teachers had been exposed to the practices consistent with those advocated in the California Curriculum Frameworks; the extent to which those teachers implemented these practices in their classrooms; and their impact on student performance in mathematics. The findings support the conclusion that curriculum and instruction that require higher level skills benefit students’ achievements. The data are the best available measures of California students’ learning of higher level skills, and provide consistent information for discussion and debate among educators about reform strategies.