As discussed in Chapter 2, assessment is a process of drawing reasonable inferences about what students know on the basis of evidence derived from observations of what they say, do, or make in selected situations. To this end, the three elements of the assessment triangle—cognition, observation, and interpretation—must be well coordinated. In this chapter, the three elements are defined more specifically, using terminology from the field of measurement: the aspects of cognition and learning that are the targets for the assessment are referred to as the construct or construct variables, observation is referred to as the observation model, and interpretation is discussed in terms of formal statistical methods referred to as measurement models.

The methods and practices of standard test theory constitute a special type of reasoning from evidence. The field of psychometrics has focused on how best to gather, synthesize, and communicate evidence of student understanding in an explicit and formal way. As explained below, psychometric models are based on a probabilistic approach to reasoning. From this perspective, a statistical model is developed to characterize the patterns believed most likely to emerge in the data for students at varying levels of competence. When there are large masses of evidence to be interpreted and/or when the interpretations are complex, the complexity of these models can increase accordingly.

Humans have remarkable abilities to evaluate and summarize information, but remarkable limitations as well. Formal probability-based models for assessment were developed to overcome some of these limitations, especially for assessment purposes that (1) involve high stakes; (2) are not limited to a specific context, such as one classroom; or (3) do not require immediate information. Formal measurement models allow one to draw meaning from quantities of data far more vast than a person can grasp at once and to express the degree of uncertainty associated with one’s conclusions. In other words, a measurement model is a framework for communicating with others how the evidence in observations can be used to inform the inferences one wants to draw about learner characteristics that are embodied in the construct variables. Further, measurement models allow people to avoid reasoning errors that appear to be hard-wired into the human mind, such as biases associated with preconceptions or with the representativeness or recency of information (Kahneman, Slovic, and Tversky, 1982).