Automatic control: The natural approach for a quantitative-based personalized education

This paper proposes an engineering-oriented framework that casts the problem of learning as an automatic control problem, and that can ultimately be used to design education activities that autonomously adapt to individual students' abilities, prerequisites, learning goals and other restrictions. The framework leverages on quantitative descriptions of knowledge flows within university programs in terms of Knowledge Components Matrices (KCMs) and Knowledge Flow Graphs (KFGs), that serve as the basis for developing the aforementioned automated approach to personalized education. Essentially, the manuscript proposes to: 1) combine these descriptions with results from exams and assessments to statistically estimate the learning status of a student; 2) combine these descriptions with data-driven approaches to derive models of how knowledge ladders logically and in time; 3) use these two ingredients to automatically design suitable and personalized study activities for a student, given his/her current knowledge status and desired learning outcome. We describe all steps (modelling of the knowledge flows, estimating the current learning status, and derivation of suitable learning activities to close the loop) with formal and control-oriented notation. The paper serves thus the purpose of showing how methods from the field of system theory and control engineering are naturally useful for the implementation of quantitative-based personalized education.