Richard G. Wolfe

The Identification and Description of Student Growth in Mathematics Achievement

Publisher Summary This chapter describes the identification and description of student growth in mathematics achievement. Achievement tests used in international educational surveys are inevitably compromised because national curricula vary significantly in content, and emphasis. In some systems, notably the United States, there is substantial curriculum variation within the system. An initial focus of the SIMS project was to describe and report the curriculum variation. A book on the curriculum analysis includes the mathematics items. Final selection of items for the international testing was determined by ensuring that for each system, its most important Population A content areas were included, and that over all systems, more items were used for content areas that were important in a majority of school systems. In each school system, a complex sample was drawn, starting with basic stratification of schools according to jurisdictional or geographical categories. The general pattern was to sample schools within stratum with probabilities proportional to size, or estimated size.

Robust Analysis of a Nonlinear Model for Multilevel Educational Survey Data

A statistical model is proposed that describes the determination of an educational outcome variable as a nonlinear function of explanatory variables defined at different levels of a survey data hierarchy, say students and classes. The model hypothesizes that the student-level explanatory variables form a composite such that the intercept and slope in the regression of the outcome on the composite vary across classes systematically as functions of class-level variables and aggregates. A method is described for estimating the parameters of the model using robust techniques. The theoretical and practical derivation of the model is discussed, and an example is given.

Factor Structure of the Strengths and Difficulties Questionnaire in a Canadian Elementary School Sample.

The Strengths and Difficulties Questionnaire (SDQ) is a 25-item screening measure for emotional and behavioral problems in children and adolescents aged 4 to 16. Structural equation modeling was used to test the five-factor structure of teacher and parent ratings on the British version of the SDQ in a community sample of 501 Canadian children aged 6 to 9 years. The five-factor model fit the data well for both teacher and parent ratings. In addition, the SDQ demonstrated acceptable reliability based on internal consistency coefficients and inter-rater agreement. The findings provide preliminary support for the reliability and validity of the British version of the parent and teacher SDQ in a sample of early elementary school Canadian children.

Understanding Patterns of Student Growth

Publisher Summary This chapter elaborates patterns of student growth. In many systems, the mathematics instruction at the Population A level is undifferentiated and unstreamed; that is, all students take the same mathematics course, and are not grouped by ability or previous mathematics achievement. By looking at the components of the pretest score variance, one can learn about whether things actually happen that way. In some systems, such as Japan, they evidently do, and there is virtually no classroom, or school variance in the pretest scores. A notable exception is the United States, where there is enormous between-classroom, within-school variance at the beginning of the school year, and where, in effect, there are four different mathematics courses being offered, and these can be termed remedial, regular, enriched, and algebra. This classification was developed by examining the teachers reports of streaming, the time allocations to topics, and the textbooks reported to be in use.

Translating Policy into Practice

The opportunities to learn experienced by students in classrooms around the world are the result of both cultural forces that permeate the society of which the educational system is a part, and of specific educational policies. Though mindful of the many forces affecting the results of their efforts, decision makers in educational systems are continuously confronted with the question of which educational opportunities are to be provided to which students, within constraints that are social, cultural, economic and political. Definition of these opportunities and the provisions for delivering them to students result from social and political processes of decision- making that vary from nation to nation. Resulting instruments — statements of content standards — detailing goals are necessarily also varied. However, all nations confront two fundamental challenges.

Textbook Expectations for Performance

Textbooks not only put forward the content students are to learn but they also advocate what students should be able to do with that content. Textbook developers do not intend to simply convey information, but to encourage behaviors on the part of students. This book is about the structure and pedagogy of textbooks by which they do so. Chapters 2, 3 and 4 examine aspects of structure while this chapter has more direct implications for pedagogy and style.

Physical Features of Textbooks

Textbooks around the world differ greatly in size, length, and other structural features. They also vary in the types of chapters and units they contain and in the ways they are laid out. There are also notable differences in sequencing and complexity as one examines closely the presentation of the mathematics and science topics.

A Holistic View of Textbooks

In the preceding chapters, we have examined a set of characteristics that describe textbook structure and pedagogy to help understand how textbooks from across the world vary on these dimensions. Previous work has established that these same books differ in their content profiles. The hypothesis here is that form and style are potentially important in that they can influence the degree to which the content profile is taught by teachers and learned by students.

Textbooks and Educational Opportunity

Attending school dominates the lives of most children around the world. Much evidence indicates that their specific schooling experiences vary considerably from country to country. There is evidence that they even vary among schools and among classrooms in the same country. However, within this variety there are parts of the school setting so common as to be virtually universal. Textbooks are one such element. Perhaps only students and teachers themselves are a more ubiquitous element of schooling than textbooks. As such a central facet of schooling, understanding textbooks is essential to understanding the learning opportunities provided in educational systems around the world.