that schoolchildren learn progressively more complicated (and more accurate) schemas for dealing with a variety of situations, such as balance-scale problems (Siegler, 1976) (see Boxes 2–1, 2–2, and 2–3 in Chapter 2) and simple addition (Siegler and Crowley, 1991). Marshall (1995) developed a computer-aided instruction program that reinforces correct schematic problem solving in elementary arithmetic. Finally, Lopez, Atran, Coley, and Medin (1997) showed that different cultures differentially encourage certain types of schemas. In reasoning about animals, American college students tend to resort to taxonomic schemas, in which animals are related by dint of possessing common features (and indirectly, having certain genetic relationships). In contrast, the Itzaj Maya, a jungle-dwelling group in Guatemala, are more likely to reason by emphasizing ecological relationships. It is not that the Americans are unaware of ecological relations or the Maya are unaware of feature possession. Rather, each group has adopted its own schema for generalizing from an observed characteristic of one animal to a presumed characteristic of another. In each case, however, the schema has particular value for the individuals operating within a given culture.
Extensive research shows that the ways students represent the information given in a mathematics or science problem or in a text that they read depends on the organization of their existing knowledge. As learning occurs, increasingly well-structured and qualitatively different organizations of knowledge develop. These structures enable individuals to build a representation or mental model that guides problem solution and further learning, avoid trial-and-error solution strategies, and formulate analogies and draw inferences that readily result in new learning and effective problem solving (Glaser and Baxter, 1999). The impact of schematic knowledge is powerfully demonstrated by research on the nature of expertise as described below.
Although we have discussed aspects of cognition at a rather general level thus far, it is possible to draw implications for assessment practice. Most of these implications relate to which memory system one might need to engage to accomplish different purposes, as well as the care needed to disentangle the mutual effects and interactions of the two systems.
For example, it can be argued that estimates of what people have stored in long-term memory and how they have organized that information are likely to be more important than estimates of working memory capacity in most instances of educational assessment. The latter estimates may be useful in two circumstances: first, when the focus of concern is a person’s capacity to deal with new and rapidly occurring situations, and second, when one is assessing individuals below the normal range and is interested in a potential indicator of the limits of a person’s academic learning proficiency. However,