Characterizing master fringes in competence-based knowledge space theory for personalized learning applications

Abstract

This paper proposes a general method to directly compute the outer (inner) master fringe of the knowledge state based on the top or bottom of the equivalence class of competence state, and a general method for personalized learning guidance (reinforcement learning recommendation) based on competences and the master fringe. Two characterization theorems are mainly given: one characterizes the top (bottom) of competence states using skill functions; the other characterizes the outer (inner) master fringe of knowledge states using problem functions. As applications of two characterization theorems, the first is to provide a new method to directly obtain the corresponding competence state’s top or bottom from the knowledge state. The second application is to integrate skills into the competence-based master fringe, which takes into account the influence of students’ latent competences, resulting in more precise values.