Diagnostic support of an intelligent tutor system for teaching skills to solve algebraic equations

Although all advantages of a standard approach to teaching students new skills, we are increasingly faced with problems such as the inability to pay an equal amount of attention to many students, to work through and unambiguously highlight all possible problems and mistakes, to close knowledge gaps. Also, all these difficulties are becoming even more urgent given the current state of affairs in the world and the global transition to an online learning format. As a possible solution to the problem, one can consider the creation of independent intelligent systems capable of taking on a part of the load of teachers and automatically participating in the process of teaching students. The subject of research in this article is the process of analyzing the steps for solving algebraic equations using the Lobachevsky-Graeffe-Dandelen method. The goal is to model the process of solving algebraic equations and to identify all possible steps, difficulties and problems in solving such problems. Objective: development of a system capable of monitoring the execution of all necessary steps for a given solution, identifying and classifying possible student mistakes in the process of mastering the skill and work them out. In the process of the task, the following results were obtained: one possible solution for learning to solve an n-degree algebraic equation using the Lobachevsky-Greffe-Dandelen method has been described. On the basis of the signal-parametric approach to diagnostics of faults in dynamic systems the mathematical diagnostic models are created which allow detecting classes of errors by comparing the results of Student's calculations and the results of system calculations. The features and possible difficulties of application of the proposed diagnostic models are presented. An intelligent self-contained tutor system was developed and integrated into the work at practical classes on "Theory of Automatic Control" by 3rd year students of the National Aerospace University.