Silver, Alacaci, and Stylianou (2000) have demonstrated some limitations of scoring methods used by the National Assessment of Educational Progress (NAEP) for capturing the complexities of learning. They reanalyzed a sample of written responses to an NAEP item that asked students to compare two geometric figures and found important differences in the quality of the reasoning demonstrated: some students showed surface-level reasoning (paying attention to the appearance of the figures), others showed analytic reasoning (paying attention to geometric features), and still others demonstrated more sophisticated reasoning (looking at class membership). Despite these qualitative differences, however, the NAEP report simply indicated that 11 percent of students gave satisfactory or better responses—defined as providing at least two reasons why the shapes were alike or different—while revealing little about the nature of the students’ understanding. Whereas the current simple NAEP scoring strategy makes it relatively easy to control variation among raters who are scoring students’ responses, much other information that could have educational value is lost. Needed are enhanced scoring procedures for large-scale assessments that capture more of the complexity of student thinking while still maintaining reliability. When the scoring strategy is based on a strong theory of learning, the interpretation model can exploit the extra information the theory provides to produce a more complex and rich interpretation, such as those presented in Chapter 4.

Task Sets and Assembly of an Assessment Instrument

An assessment should be more than a collection of items that work well individually. The utility of assessment information can be enhanced by carefully selecting tasks and combining the information from those tasks to provide evidence about the nature of student understanding. Sets of tasks should be constructed and selected to discriminate among different levels and kinds of understanding that are identified in the model of learning. To illustrate this point simply, it takes more than one item or a collection of unrelated items to diagnose a procedural error in subtraction. If a student answers three of five separate subtraction questions incorrectly, one can infer only that the student is using some faulty process(es), but a carefully crafted collection of items can be designed to pinpoint the limited concepts or flawed rules the student is using.

In Box 5–6, a typical collection of items designed to work independently to assess a student’s general understanding of subtraction is contrasted with a set of tasks designed to work together to diagnose the common types of subtraction errors presented earlier in Box 5–2. As this example shows, significantly more useful information is gained in the latter case that can be used to provide the student with feedback and determine next steps for instruction. (A similar example of how sets of items can be used to diagnose

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