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Reform in mathematics education calls for a closer tie between instruction and assessment. This study developed performance assessments from hands-on instructional activities and examined their reliability and validity for obtaining individual achievement data in large-scale surveys. The major source of unreliability was the tasks, not the raters. Many tasks are needed to get a dependable measure of a student's mathematics achievement. With respect to validity, results suggested that the performance assessments measure different aspects of mathematics achievement than do traditional multiple-choice tests. Moreover, the performance assessments, but not the multiple-choice test, distinguished the performance of students in hands-on and traditional curricula with the former scoring higher, on average, than the latter. Ethnic group comparisons indicated that Anglos scored higher, on average, than Latinos on all achievement measures. The magnitude of the difference varied by the curricular experience of the student. For students in traditional curricula, qualitative analysis indicates that Anglo and Latino students approached the problems similarly, made the same types of errors, and employed the same strategies in solving the mathematics problems.

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