Sequential mastery detection and Bayesian learning promotion under cognitive diagnosis models

Abstract

E-learning assessments are becoming a common educational medium to instruct fine-grained skills in modern pedagogy. To accentuate the advantages of e-learning assessments, it is vital to automate the process of instruction and advancement in accordance with the learning progress of each individual. Though building computerized assessments can adopt some established developments from the computerized adaptive testing (CAT) literature, the guidelines to facilitate computerized adaptive learning assessments that aim for didactic outcomes are yet underdeveloped.

In order to empower the automated process of instruction in an e-learning setting, statistical tools that detect mastery and promote learning were developed. First, we consider the use of sequential change-detection methods under the cognitive diagnosis models. To that end, we introduce the change-detection methods that involve different set of information. We further introduce a model for the didactic value of items that readily leads to a sequential learning enhancement and learning detection procedure. Bayesian measurements of one-step-ahead posterior probability of mastery and expected sum of attributes are utilized together with a simple model for learning for use in item selection, and stopping rules are developed for detection of learning that control for the rate of false discovery. Simulation studies showed that the delays of mastery detection can be minimized and the mastery acquisition can be hastened with statistical methods introduced.