Using three themes, this chapter reviews broad categories of formal measurement models and the principles of reasoning from evidence that underlie them:

  • Formal measurement models are a particular form of reasoning from evidence. They provide explicit, formal rules for how to integrate the many pieces of information that may be relevant to a particular inference. Effectively, they are statistical examples of ways to articulate the relationships between the cognition and observation elements of the assessment triangle described in Chapter 2. The current array of psychometric models and methods is the result of an evolutionary progression shaped, in part, by changes in the kinds of inferences teachers and policy makers want to draw, the ways people have thought about learning and schooling, and the technologies that have been available for gathering and using test data.

  • Work on measurement models has progressed from (1) developing models that are intended to measure general proficiency and/or to rank examinees (referred to here as standard models); to (2) adding enhancements to a standard psychometric model to make it more consistent with changing conceptions of learning, cognition, and curricular emphasis; to (3) incorporating cognitive elements, including a model of learning and curriculum directly into psychometric models as parameters; to (4) creating a family of models that are adaptable to a broad range of contexts. Each model and adaptation has its particular uses, strengths, and limitations.

  • Measurement models now exist that can address specific aspects of cognition. An example is the choice of problem-solving strategies and the strategy changes that occur from person to person, from task to task for an individual, and within a task for an individual. Developments in statistical methods have made it possible to create and work with models more flexibly than in the past, opening the door to a wider array of assessment data and uses. To do so, however, requires closer attention to the interplay between the statistical and cognitive aspects of assessment than has been customary.

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