Refining Learning Maps with Data Fitting Techniques

Learning maps have been used to represent student knowledge for many years. These maps are usually hand made by experts in a given domain. However, these hand-made maps have not been found to be predictive of student performance. Several methods have been proposed to find bet-ter fitting learning maps. These methods include the Learning Factors Analysis (LFA) model and the Rule-space method. In this thesis we report on the application of one of the proposed operations in the LFA method to a small section of a skill graph and develop a greedy search algorithm for finding better fitting models for this graph. Additionally an investigation of the factors that influence the search for better data fitting models using the proposed algorithm is reported. We also present an empirical study in which PLACEments, an adaptive testing system that employs a skill graph, is modified to test the strength of prerequisite skill links in a given learning map and propose a method for refining learning maps based on those findings. It was found that the proposed greedy search algorithm performs as well as an original skill graph but with a smaller set of skills in the graph. Additionally it was found that, among other factors, the number of unnecessary skills, the number of items in the graph, and the guess and slip rates of the items tagged with skills in the graph have an impact on the search. Further, the size of the evaluation data set impacts the search. The more data there is for the search, the more predictive the learned skill graph. Additionally, PLACEments, an adaptive testing feature of ASSISTments, has been found to be useful for refining skill graphs by detecting the strengths of prerequisite links between skills in a graph