bined to report less detailed summary information for students, parents, and teachers. The model should, in turn, be compatible with a coarse-grained model of learning used as a basis for an end-of-year summative assessment.

To be sure, there will always be school subjects for which models of cognition and learning have not yet been developed. Policies about what topics should be taught and emphasized in school change, and theories of how people learn particular content will evolve over time as understanding of human cognition advances. In such situations, the assessment developer may choose to start from scratch with a cognitive analysis of the domain. But when resources do not allow for that, basic principles of cognition and learning described in Chapter 3—such as the importance of how people organize knowledge, represent problems, and monitor their own learning— can inform the translation of curriculum into instruction and assessment. The principle that learning must start with what students currently understand and know about a topic and build from there will always hold.

Some existing assessments have been built on the types of models of learning described above. The following examples have been chosen to illustrate the variation in theories that underlie assessments for different purposes. First, we use the example of intelligent tutoring systems (used to illustrate a number of points in this volume). Existing intelligent tutoring systems are built on detailed cognitive theories of expert problem solving (Anderson, Boyle, Corbett, and Lewis, 1990; VanLehn and Martin, 1998). The tutors use assessment constantly to (1) provide continuous, individualized feedback to learners as they work problems; (2) offer help when appropriate or when requested by the learner; and (3) select and present appropriate next activities for learning. The second example describes a classroom assessment approach that teachers can use for diagnosing qualitatively different states of student understanding in physics. An important point of this report is that a model of learning can take different forms and encompass different research perspectives. Thus the third example illustrates a model of learning that focuses on the situative and participatory aspects of learning mathematics. The fourth example demonstrates how models of learning can be used as the basis for large-scale as well as classroom assessments.

Underlying Models of Cognition and Learning: Examples
PAT Algebra Tutor

John Anderson’s ACT-R research group has developed intelligent tutoring systems for algebra and geometry that are being used successfully in a number of classrooms (Koedinger, Anderson, Hadley, and Mark, 1997). The cognitive models of learning at the core of their systems are based on the group’s more general theory of human cognition, ACT-R, which has many

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