methods of assessment that can enhance the processes of learning and teaching.

Without question, important work remains to be done to develop models for areas of the curriculum as it now exists and as it will change with the advent of powerful technology-based learning environments (see Chapter 7). In most domains, including many parts of the science and mathematics curricula, research has not produced descriptions as detailed or robust as some of the examples mentioned in this chapter and elsewhere throughout this report. More extensive research should eventually produce models of progression in learning in many domains beyond mathematics and science. Ultimately, it may be necessary to develop as many models as there are disciplines in the curriculum or domains within a discipline.

METHODS OF OBSERVATION AND INFERENCE

We close this presentation of advances in the sciences of thinking and learning with a discussion of some of the methods of observation and inference that underlie our current understanding of cognition. We describe these methods for two reasons. The first is to illustrate the types of scientific methods on which the findings in this chapter are based. The second is to suggest connections between methods of educational assessment and the methods used by cognitive researchers to uncover students’ content knowledge and cognitive processes.

To accomplish the goal of understanding cognition and learning, cognitive scientists have developed a variety of methods and tools for evaluating people’s knowledge structures and mental processes as they reason and solve problems and for studying what infants and young children know and can do. These methods are linked to a general approach of theory development and testing identical in its overall logic to our earlier discussion in Chapter 2 of the three elements of the assessment triangle—cognition, observation, and interpretation—and their interrelationships. For instance, many detailed studies of human cognition begin with the development of a theoretical model (or models) of the knowledge structures and cognitive processes that characterize people at different levels of competence. Researchers then design tasks for people to perform in order to test the model, carefully selecting those tasks that maximize the possibility of discriminating among competing models or hypotheses. Data from observations of individuals performing various tasks are then evaluated using a logical and/or statistical scheme to determine how well the evidence fits a given model.

This method of reasoning from data about underlying cognitive processes and knowledge structures has been applied to both simple and complex performances. As illustrated earlier in Box 3–4, it is possible to obtain a highly accurate and detailed picture of how children are approaching prob-



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