A Bayesian Network Approach for Modeling the Influence of Contextual Variables on Scientific Problem Solving

A challenge for intelligent tutoring is to develop methodologies for transforming streams of performance data into insights and models about underlying learning mechanisms. Such modeling at different points in time could provide evidence of a student’s changing understanding of a task, and given sufficient detail, could extend our understanding of how gender, prior achievement, classroom practices and other student/contextual characteristics differentially influence performance and participation in complex problem-solving environments. If the models had predictive properties, they could also provide a framework for directing feedback to improve learning. In this paper we describe the causal relationships between students’ problem-solving effectiveness (i.e. reaching a correct solution) and strategy (i.e. approach) and multiple contextual variables including experience, gender, classroom environment, and task difficulty. Performances of the IMMEX problem set Hazmat (n ~ 33,000) were first modeled by Item Response Theory analysis to provide a measure of effectiveness and then by self-organizing artificial neural networks and hidden Markov modeling to provide measures of strategic efficiency. Correlation findings were then used to link the variables into a Bayesian network representation. Sensitivity analysis indicated that whether a problem was solved or not was most likely influenced by findings related to the problem under investigation and the classroom environment while strategic approaches were most influenced by the actions taken, the classroom environment and the number of problems previously performed. Subsequent testing with unknown performances indicated that the strategic approaches were most easily predicted (17% error rate), whereas whether the problem was solved was more difficult (32% error rate).