The present study demonstrates the utility of a multidimensional representation of student mathematics achievement. Third in a series of studies using the math test item level data from the NELS:88 longitudinal study, it carries the analyses through the 12th grade. Full information factor analysis was employed to investigate the structure of math achievement, create meaningful achievement scales, and explore their relationships with student background, academic program, and instructional variables. The findings support a basic distinction between Mathematical Reasoning (MR) and Mathematical Knowledge (MK) for two of the three administered test forms (low and middle levels), replicating previous findings for the 8th- and 10th-grade data. A more complex structure for the high test form reflected variation in problem-solving strategies as well as in content. Regression analyses suggested differential patterns of relationships between student, program, and instructional variables for math achievement subscores. These patterns were also compared with results for the unidimensional total score. Discussion emphasizes implications for score interpretations, both normative and criterion-referenced, within the context of a validity argument.
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