Applying Demand Analysis of a Set of test Problems for Developing Adaptive Courses

Knowledge space theory was already applied for building adaptive testing and training systems which contain test and training problems including their prerequisite structure, and which offer explanations and help for solving these problems. Normally, however, lessons prepare students for solving problems. In this paper, we present a method for systematically structuring an adaptive eLearning course containing test problems as well as lessons. This method is based on knowledge space theory extended by component-wise representation of problems and on applying demand analysis. A course developed with such a method can be fed into an adaptive tutoring system, realized, e.g., within the adaptive tutoring system RATH. Theoretical Background This paper is based on an application of the theory of knowledge spaces and its extensions to building an adaptive tutoring system (ATS). An ATS adapts the learning content to the individual learner, e.g. with respect to the learner’s current knowledge. The learner state is assessed through a test or questionnaire, and subsequently learning objects are selected or presented by adapting them to the current learner state which itself may be regularly updated during the learning process. The theory of knowledge spaces [2, 3] is a psychological model for structuring domains of knowledge based on prerequisite relationships. It was developed aiming at the adaptive assessment of knowledge [3, 4]. Later it was also applied to adaptive training in the ALEKS system [3; see also http://www.aleks.com]. However, ALEKS is limited in that it does not offer genuine teaching by presenting lessons but only explanations for training problems. Albert and Held applied methods of demand analysis to obtain knowledge spaces for given domains [1, 5]. In a first step, they searched for components of test problems in a certain area, and attributes for these components. Held, for example, found for elementary probability theory problems on drawing balls from an urn as one component the method of drawing with three attributes from (1) drawing one ball , to (3) drawing multiple balls without replacement [5]. In a second step, the demands (or skills) posed on the learn ers by the different attribute values were investigated. In the aforementioned example, Held identified four demands related to the attributes for the component way of drawing from (a) knowing the Laplace rule for computing probabilities, to (d) knowing that drawing without replacement reduces the number of balls in the urn. For the three attributes and the four demands specified in the example above, Held found the assignments shown in Table 1. Table 1: Demand assignments for attributes of way of drawing