worksheets, homework, and on report cards—represent summative assessments that are intended to measure the results of learning. After receiving grades, students typically move on to a new topic and work for another set of grades. Feedback is most valuable when students have the opportunity to use it to revise their thinking as they are working on a unit or project. The addition of opportunities for formative assessment increases students’ learning and transfer, and they learn to value opportunities to revise (Barron et al., 1998; Black and William, 1998; Vye et al., 1998b). Opportunities to work collaboratively in groups can also increase the quality of the feedback available to students (Barron, 1991; Bereiter and Scardamalia, 1989; Fuchs et al., 1992; Johnson and Johnson, 1975; Slavin, 1987; Vye et al., 1998a), although many students must be helped to learn how to work collaboratively. New technologies provide opportunities to increase feedback by allowing students, teachers, and content experts to interact both synchronously and asynchronously (see Chapter 9).

A challenge of implementing good assessment practices involves the need to change many teachers’, parents’, and students’ models of what effective learning looks like. Many assessments developed by teachers overly emphasize memory for procedures and facts (Porter et al., 1993). In addition, many standardized tests that are used for accountability still overemphasize memory for isolated facts and procedures, yet teachers are often judged by how well their students do on such tests. One mathematics teacher consistently produced students who scored high on statewide examinations by helping students memorize a number of mathematical procedures (e.g., proofs) that typically appeared on the examinations, but the students did not really understand what they were doing, and often could not answer questions that required an understanding of mathematics (Schoenfeld, 1988).

Appropriately designed assessments can help teachers realize the need to rethink their teaching practices. Many physics teachers have been surprised at their students’ inabilities to answer seemingly obvious (to the expert) questions that assessed their students’ understanding, and this outcome has motivated them to revise their instructional practices (Redish, 1996). Similarly, visually based assessments of “number sense” (see Case and Moss, 1996) have helped teachers discover the need to help their students develop important aspects of mathematical understanding (Bransford et al., 1998). Innovative assessments that reveal students’ understanding of important concepts in science and mathematics have also been developed (Lehrer and Schauble, 1996a, b).



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