search reveals that children’s difficulties are derived from underlying conceptual representation issues that transcend linguistic differences (Verschaffel, Greer, and DeCorte, 2000).

Differences among learners should not be ignored. Thus a third key feature of a model of learning is that it should convey a variety of typical ways in which children come to understand the subject matter of interest. Children are exposed to different content depending on the curriculum and family environment they encounter, and this affects what they learn (see Chapter 3). When developing models of learning, one starting point for capturing such differences is to study a group of learners that reflects the diversity of the population to be instructed and assessed in terms of such factors as age, culture, socioeconomic status, gender, and region.

Fourth, starting with a theory of how people learn the subject matter of interest, the designers of an assessment will need to select a slice or subset of the larger theory of cognition and learning as the assessment targets. That is, any given model of learning underlying an assessment will capture some, but not all, aspects of what is known about how students think and learn in the domain. That selection should depend on the purpose for the assessment. For instance, the purpose of an intelligent tutor is to determine the precise topic or skill area in which a student is struggling at the moment so that the student can be directed to further help. To develop this kind of assessment, a detailed description of how people at different levels of expertise use correct and incorrect rules during problem solving is often needed (such as that illustrated by the model of cognition underlying the Anderson tutor, described below). More typical classroom assessments, such as quizzes administered by teachers to a class several times each week or month, provide individual students with feedback about their learning and areas for improvement. They help the teacher identify the extent of mastery and appropriate next steps for instruction. To design such assessments, an extraction from the theory that is not quite so detailed, but closer to the level at which concepts are discussed in classroom discourse, is most helpful. The model of cognition and learning underlying a classroom assessment might focus on common preconceptions or incomplete understandings that students tend to have and that the teacher can identify and build on (as illustrated by the Facets example described below). If the purpose for the assessment is to provide summative information following a larger chunk of instruction, as is the case with statewide achievement tests, a coarser-grained model of learning that focuses on the development of central conceptual structures in the subject domain may suffice.

Finally, a model of learning will ideally lend itself to being aggregated in a principled way so that it can be used for different assessment purposes. For example, a fine-grained description of cognition underlying an intelligent tutoring system should be structured so the information can be com-

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