| This dissertation describes the development of two central components of a computerized knowledge assessment system.;The first component, the knowledge structure, captures the cognitive organization of a set of items and forms the core of the assessment system. According to Falmagne and Doignon's Knowledge Space Theory, the knowledge state of a subject is represented by a particular subset of items that the subject is capable of solving. The collection of all feasible states forms the knowledge structure. A knowledge structure which is also closed under union is called a knowledge space.;The empirical construction of a knowledge structure for ten high school mathematics items is explained in detail. The construction began with an application of Koppen's QUERY routine, a computerized procedure designed to systematically question an expert and elicit the unique knowledge space consistent with the expert's responses. The resulting knowledge spaces for five experts/teachers were merged to create a combination knowledge structure. This initial structure was extensively refined by applying a probabilistic model to a large reference sample of students, (N = 60,000), using likelihood ratio techniques. The probability distribution on the refined structure as well as item parameters for careless error and guessing were estimated, and provided a foundation for the second component under investigation, the assessment routine.;In the stochastic knowledge assessment procedures developed by Falmagne and Doignon, the knowledge state of a student is efficiently identified through a sequence of appropriately chosen items. A probability distribution on the knowledge structure, updated on each trial, provides the basis for selecting maximally informative items.;Various assessment routines were implemented. Parameters of these routines were calibrated with respect to their accuracy in assessing students (N = 1000). The assessment performances of five experts' knowledge structures, the refined structure and a Guttman-scale based structure were evaluated. The experts' structures demonstrated significant individual differences in assessment accuracy. The most important result for practical applications was the development of a technique through which the a priori probability distribution on a knowledge structure was estimated by assessing the reference sample of students. The obtained distributions yielded the best assessment results overall. |
