CONCEPTUAL FOUNDATIONS OF DESIGNING INTELLIGENT KNOWLEDGE ASSESSMENT SYSTEMS FOR MATHEMATICAL DISCIPLINES IN DISTANCE FORMAT

Abstract

This paper proposes a novel approach to designing intelligent knowledge assessment systems for students in the discipline of «Integral Calculus» within a distance learning framework. Unlike the majority of existing knowledge control systems, which rely on static databases of predefined tasks and answers, the developed system eliminates such fixed repositories to enhance flexibility, personalization, and objectivity in evaluation. Instead, task conditions are dynamically generated based on predefined rules incorporating random numbers, ensuring each assignment is unique and tailored to individual learner needs. The generation process begins with selecting from four main categories of integrals: basic integration formulas, substitution methods, integration by parts, and integrals involving quadratic trinomials. Each category includes subclasses or templates where parameters—such as coefficients, exponents, and integration limits—are randomly assigned within specified constraints. The generated function undergoes correctness checks before presentation to the user via a web-based interface. A key distinguishing feature is the response format: users provide the analytical antiderivative rather than a numerical result. The system evaluates answers by computing the definite integral using numerical (Simpson's method) and analytical (Newton-Leibniz theorem) approaches. Simpson's rule approximates the integral using step size and function values. The Newton-Leibniz method uses the antiderivative to compute the difference at limits, ignoring the constant. The student's input is parsed, and its value is compared to the etalon. Implemented as a scalable web application, the system offers real-time feedback and analytics. It addresses limitations of traditional tools like Moodle or Khan Academy by providing unlimited variability and objective grading.