chapter  4
34 Pages

Knowledge Space Generated From a Q Matrix

Both an error analysis and a task analysis are tremendously laborious and time-consuming. Tatsuoka (1991) developed a new technique utilizing Boolean algebra to generate a list of item response patterns corresponding to psychologically meaningful knowledge states. However, if we have identified 17 attributes for a domain of our interest, then the profiles of mastery or nonmastery on the 17 attributes have the combination of 217 = 131,072 patterns, which is a very large number. We need some clever techniques to deal with the combinatorial computational problems for handling enormously large numbers of knowledge states, and to classify a student response into one of these knowledge states. The traditional statistical decision theory (Kendall & Stuart, 1973; M. Tatsuoka, 1990) handles only a small number of classification groups.