ALGORITHMIC SUPPORT FOR REVERSE GENERATION OF TRIGONOMETRIC TASKS USING OBJECT-ORIENTED MODELING - Bodnaruk, Svitlana; Rybchynskyi, Nazarii (Physical and Mathematical Education, 2026)
Formulation of the problem. The article presents the results of developing and implementing an algorithmic system to automate the preparation of trigonometry didactic materials. The core research idea is based on a transition from the traditional mechanical selection of problems to a model of reverse equation construction. The proposed approach implies that the software algorithm generates a mathematical condition based on a predetermined set of answers (roots), enabling the teacher to instantly create a vast number of variable tasks of the same complexity level to ensure a personalized learning trajectory. Materials and methods. The system’s technical implementation is implemented in Python using the SymPy symbolic computation library. The paper details the developed class architecture, covering various types of trigonometric equations, from basic ones to homogeneous equations and those solved by the variable-substitution method. A crucial technical characteristic of the algorithm is the automatic verification of the domain of permissible values and the filtering of extraneous roots during problem condition synthesis, which guarantees the absolute mathematical accuracy of each generated task. Results. The described system is effective not only for rapid knowledge assessment but also for organizing students’ independent work in distance and blended learning formats. The availability of automatically generated step-by-step solutions allows students to independently master algorithms for solving complex problems, minimizing knowledge gaps without constant teacher intervention. The effectiveness of the proposed methodology was verified during practical testing at a lyceum in the Chernivtsi region. Analysis of the experimental results showed that the systematic use of personalized tasks enabled students to better master trigonometric transformations, and the average academic performance in the experimental groups increased by 15–20%. Conclusions. The authors demonstrate that implementing these digital tools significantly reduces teachers’ workload, freeing up time for creative pedagogical activities and individualized work with students. The conclusions identify opportunities to scale the reverse algorithm to other topics in the algebra and mathematical analysis course.