Diagnosing the depth of understanding using cognitive diagnostic models and their application to a regular test: Examining the applicability of cognitive diagnostic models with a Q-matrix specified through qualitative and quantitative procedures

Abstract

Schoolteachers have engaged in their daily teaching practices to achieve the global education goal of deepening students’ understanding. If they can classify students based on the depth of students’ understanding, they can effectively provide students with classroom instructions and learning strategies tailored to students’ specific needs. Such a classification can be achieved by a class of discrete latent variable models called a cognitive diagnostic model, which aims to evaluate students’ mastery states of some cognitive abilities and perform clustering based on the estimated mastery states. To apply this model to regular classroom tests, we specified a Q-matrix –which is required for data analysis with this model and determines which cognitive abilities are necessary to answer testitems– considering the depth of understanding with schoolteachers and using a Q-matrix estimation method. A discussion with schoolteachers indicated the potential usefulness of the estimated mastery states to grasp the tendency of students’ understanding in the classroom intuitively and easily.