This work will continue ongoing research concerning the construction of a theory and the related computer algorithms for the efficient assessment of knowledge. The key concept of the theory is that a knowledge structure, that is, a basic set of Q of questions or problems in a given domain of information, equipped with a distinguished family of subsets called the knowledge states. The interpretation of these concepts is that the knowledge state of a student is the set of all those problems in the basic set Q that the student is capable of solving. A probabilistic version of these concepts has been developed, permitting an analysis of the data with standard statistical techniques. The knowledge assessment routines were developed in the framework of Markov chains theory. The focus of this work will be the application of the theory in one particular case, namely, the Regents Competency Test in Mathematics of June, 1987. Other aspects of the research include investigation of a number of technical questions regarding the combination of distinct knowledge structures and practical adaptation and implementation of knowledge assessment procedures.
