Smart Algebraic Approach to Analysis of Learning Outcomes

Abstract

One of the problematic issues of education is a comparative analysis of the results achieved by students in the learning process. The results may vary, for example, in breadth, in depth of knowledge, different areas of mathematics can be mastered by the same student at completely different levels, etc. The proposed smart algebraic approach that uses a probabilistic approach, semantic networks, and marked graphs for the analysis of learning outcomes allows you to measure learning outcomes, taking into account the structure of the knowledge system, rank of students according to their level of knowledge, evaluate their strengths and weaknesses, identify gaps among students in knowledge, and create recommendations on the teaching methodology. Smart algebraic model of learning outcomes analysis uses algebraic formalization of systems and probabilistic estimation methods.