Chronic Noncorrespondence Between Elementary Math Curricula and Arithmetic Tests
Test of academic achievement are administered routinely as an estimate of student learning. In turn, estimates of student learning are used in making a number of educational decisions, including classification, placement, program planning, program evaluation, and grading. Inferences about learning, however, are accurate only to the extent that students have had an opportunity to learn the material tested. Thus, it is implicit that the content of assessment must bear a close correspondence to the content of instruction (Armbruster, Stevens, & Rosenshine, 1977, p. 2). For this reason, attainment and achievement are usually distinguished. "Attainment is what an individual has learned, regardless or where it has been learned. Achievement is what has been learned as a result of instruction in the schools" (Salvia & Ysseldyke, 1985, p. 9).
This need for tests to correspond to curriculum is in direct conflict with the needs of test publishers to market profitable products. Commercially prepared standardized tests are designed for broad appeal; they are intended to reflect the typical curricula offered to the majority of students, i.e., nonhandicapped students in the middle instructional tracks. The correspondence between test and curricular content is a particularly thorny issue for special educators because the curricula adopted for most exceptional students (and especially handicapped students) often differ systematically from the curricula offered nonexceptional students. Even when mainstreaming is a goal for handicapped students, one would anticipate curricular differences.
In the last decade, several researchers have examined curriculum-test correspondence in reading and mathematics. Armbruster et al. (1977) compared content coverage and emphasis of three third-grade reading curricula and two standardized test. They concluded that the tests were similar in emphasis on reading comprehension, but that the curricula differed widely in their emphases: "Only a small percentage of the skills emphasized in the curricula have counterparts on the standardized test" (p. 38). Jenkins and Pany (1978a) also examined reading tests and curricula in a paper that appeared in the Journal of Reading Behavior. They discussed a portion of that research in Exceptional Children (1978b), where they compared first- and second-grade books from five reading series with five word-recognition sub-tests. They found that the correspondence between tests and curricula varied widely and that the assumption of representatives of curricular content on achievement tests was not supported.
Leinhardt and Seeward (1981) examined correspondence between curriculum and test by evaluating first- and third-graders' opportunity to learn what was covered on the reading and math subtests of a standardized achievement battery. They used two different methods, instruction-based measurement and curriculum-based measurement. In instruction-based measurement, opportunity to learn was based on curricular materials and teacher-reported activities. In curriculum-based measurement, opportunity to learn was based only on curricular materials. Their results were summarized by Airasian and Madaus (1983, p. 113):
1) Correlations between measures of instructional overlap are moderate, indicating some, but not total redundancy in the information obtained from the two estimates; 2) the mean curriculum-based-test overlap measure is lower than the instruction-based overlap measure because the former does not encompass instruction covered by textbooks; 3) both overlap estimates tend to be stable; 4) overlap measure contribute significantly to the prediction of post-test scores on the test and curriculum under study.
The Institute for Research on Teaching conducted a series of studies to address the correspondence of mathematics curricula and tests. …