A REVIEW AND CLASSIFICATION OF ONLINE TOOLS FOR SUPPORTING MATHEMATICAL MODELING IN EDUCATION

Abstract

The article provides a review and classification of modern online services used to support mathematical modeling processes in educational settings. The relevance of using online calculators is substantiated in the context of the digital transformation of education and the implementation of a competency-based approach to teaching mathematics. More than twenty online services have been systematized according to their functional capabilities, user orientation (students, teachers, university students, researchers), and modeling potential. Four main groups of services are identified: for engineering and scientific modeling; for use in general secondary and higher education institutions; mobile assistants (including photo calculators); and self-learning services with explanations. For each group, a specific tool is highlighted and an example of its use in education is provided: Maple – as an environment for creating mathematical models and 3D visualizations of complex objects; Desmos – as an interactive function graphing tool and instrument for exploratory learning; Photomath – as a mobile assistant capable of recognizing problems and providing step-by-step explanations; MathDF – as a step-by-step calculator for studying matrices, complex numbers, integrals, and equations. Examples of tasks, illustrations, and usage scenarios are provided for classroom application, considering modern teaching approaches such as project-based learning and STEM orientation. The article concludes with the rationale for the gradual integration of digital services into school and higher education as a means of developing mathematical competence, critical thinking, and digital literacy among students. It outlines the prospects for developing methodological recommendations for educators with sample exercises adapted to curricula of various levels, and identifies opportunities for integrating digital tools into teacher professional development systems. The importance of aligning technological infrastructure with pedagogical appropriateness and a sustainable digital education strategy in Ukraine is emphasized.

Keywords: mathematical modeling, online calculators, digital educational tools, computer-based learning, MathDF, Photomath, Maple, Desmos, function graphing, mobile applications, step-by-step solutions, STEM, project-based learning, mathematical competencies, digital transformation in education, mathematical visualization, analytical tools.