MS EXCEL TEMPLATES FOR MODELING PROBLEMS ON INTEGRATION OF RATIONAL FUNCTIONS - Radchenko, Serhiy; Astafieva, Mariia; Mazur, Anatoly (Physical and Mathematical Education, 2026)
Formulation of the Problem. In teaching mathematical analysis, regardless of the educational organization, training exercises play an essential role in developing and improving students’ practical skills and abilities. In particular, when studying the integration of rational functions, there is a need for a large number of similar tasks that are methodologically correct, computationally moderate, and focused on the formation of appropriate algorithmic skills. Practice shows that an arbitrary choice of numerical parameters in such tasks often leads to cumbersome calculations involving fractional or irrational expressions, which does not correspond to the didactic purpose of training exercises. This determines the relevance of developing formalized approaches to task modeling that meet predefined didactic requirements.Materials and Methods. To address the stated problem, an analysis of theoretical and practical results of Ukrainian and international researchers and practitioners concerning the design of mathematical tasks was conducted. MS Excel was used to create task templates, followed by formatting the problem statements and solutions using the LaTeX typesetting system.Results. A set of templates for the automated generation of collections of training tasks with controlled complexity and predefined methodological characteristics has been developed. It is shown that the use of such templates enables the avoidance of incorrect or didactically undesirable variants, increases the effectiveness of students’ independent work, and significantly simplifies the preparation of instructional materials. Conclusion. The development of templates in the MS Excel environment for modeling tasks on the integration of rational functions is an effective tool for creating educational content aimed at students’ independent practice. The proposed approach combines mathematical correctness, methodological appropriateness, and technological accessibility, making it suitable for teaching mathematical analysis.
Keywords: templates for modeling mathematical tasks; MS Excel environment; MS Excel; LaTeX; mathematical analysis; integration of rational functions