matter of the assessment and the grade level; it also has varied from one assessment to the next within the same subject area. The First International Mathematics Study (FIMS) placed the 174 items used across the different age populations assessed into one of 14 topics, ranging from basic arithmetic to calculus (Thorndike, 1967, p. 105). The content dimension was primary, and considerable effort went into defining the topics and obtaining items for them. Despite the emphasis on content, some reviewers of the FIMS results (e.g., Freudenthal, 1975) were sharply critical of the assessments for what was seen as an overemphasis on psychometrics and a lack of involvement of subject-matter experts who were familiar with curricula and teaching practices in the participating countries.

In the Second International Mathematics Study (SIMS), the main emphasis continued to be placed on content categories, but there was substantially greater involvement of mathematics educators and much greater salience was given to the mathematics curricula of the participating countries. SIMS maintained links to FIMS by including a sizable fraction of items from FIMS, but used a different set of topical categories. SIMS had 133 content categories under five broad topics (arithmetic, algebra, geometry, probability and statistics, and measurement) for the eighth-grade population and 150 content categories under nine broad topics for the twelfth-grade population (Romberg, 1985, p. 9). Other international studies have divided the content domain using fewer broad topic areas.

A rather different approach was taken in the International Assessment of Educational Progress (IAEP) studies conducted by the Educational Testing Service (Lapointe, Askew, & Mead, 1992; Lapointe, Mead, & Askew 1992), using frameworks more in keeping with the ones developed for NAEP. In mathematics for 9- and 13-year-olds, the IAEP framework had five broad content categories. Those content categories were crossed with three cognitive process categories to yield a framework with the 15 cells shown in Table 2-1. The broad categories used by IAEP stand in sharp contrast to the fine-grained breakdown in SIMS.

The TIMSS assessments also were based on tables of specifications with characteristics that had some similarity to the frameworks used in the IAEP studies, but had greater specificity of content. For example, the eighth-grade science assessment had eight broad content areas (earth sciences; life sciences; physical sciences; science; technology and mathematics; environmental issues; nature of science; and science and other disciplines). Those categories were crossed with five cognitive process categories called performance expectations in the TIMSS reports (understanding; theorizing, analyzing, and solving problems; using tools, routine procedures, and science processes; investigating the natural world; and communicating) (Beaton et al., 1996a, p. A-6). Finer breakdowns of



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