Skill Maps, Labels and Filters

Abstract

So far, cognitive interpretations of our mathematical concepts have been limited to the use of mildly evocative words such as ‘knowledge state’, ‘learning path’ or ‘gradation.’ This makes sense since, as suggested by our Examples in 1.4.1, 1.4.2 and 1.4.3, many of our results are potentially applicable to widely different fields. It must be realized, however, that our basic concepts are consistent with traditional explanatory features of psychometric theory, such as ‘skills’ or ‘latent trait’ (cf. Lord and Novick, 1974; Weiss, 1983; Wainer and Messick, 1983; Wainer, Dorans, Eignor, Flaugher, Green, Mislevy, Steinberg, and Thissen, 2000). Some possible relationships between knowledge states and skills, and other features of the items, are explored in this chapter.