Cognitive assessment in a computer-based coaching environment in higher education : diagnostic assessment of development of knowledge and problem-solving skill in statistics

Diagnostic cognitive assessment (DCA) was explored using Bayesian networks and evidence-centred design (ECD) in a statistics learning domain (ANOVA). The assessment environment simulates problem solving activities that occurred in a web-based statistics learning environment. The assessment model is composed of assessment constructs, and evidence models. Assessment constructs correspond to components of knowledge and procedural skill in a cognitive domain model and are represented as explanatory variables in the assessment model. Explanatory variables represent specific aspects of student's performance of assessment problems. Bayesian networks are used to connect the explanatory variables to the evidence variables. These links enable the network to propagate evidential information to explanatory model variables in the assessment model. The purpose of DCA is to infer cognitive components of knowledge and skill that have been mastered by a student. These inferences are realized probabilistically using the Bayesian network to estimate the likelihood that a student has mastered specific components of knowledge or skill based on observations of features of the student's performance of an assessment task.The objective of this study was to develop a Bayesian assessment model that implements DCA in a specific domain of statistics, and evaluate it in relation to its potential to achieve the objectives of DCA. This study applied a method for model development to the ANOVA score model domain to attain the objectives of the study. The results documented: (a) the process of model development in a specific domain; (b) the properties of the Bayesian assessment model; (c) the performance of the network in tracing students' progress towards mastery by using the model to successfully update the posterior probabilities; (d) the use of estimates of log odds ratios of likelihood of mastery as a measure of "progress toward mastery;" (e) the robustness of diagnostic inferences based on the network; and (f) the use of the Bayesian assessment model for diagnostic assessment with a sample of 20 students who completed the assessment tasks. The results indicated that the Bayesian assessment network provided valid diagnostic information about specific cognitive components, and was able to track development towards achieving mastery of learning goals