THE PRINCIPLE OF INSTRUMENTAL RELEVANCE OF AI IN MATHEMATICS EDUCATION

Abstract

Abstract. The rapid integration of artificial intelligence technologies into mathematics education necessitates a scientific justification for their use in designing personalized learning paths. This paper aims to assess the effectiveness of different AI tools within a personalized digital learning environment for mathematics. The research design employed a comparative study in a natural educational setting, using questionnaires, analysis of students' digital footprints, statistical processing (Student's t-test, ANOVA, Tukey's test, Cohen's d), and thematic analysis of open-ended responses. The study involved 168 students working with 32 interactive mathematical modules on the "Academic Resilience" platform. The findings indicate that the effectiveness of AI tools is contingent on the type of mathematical content. The most significant pedagogical effect was observed for a combination of graphical environments and AI assistants in tasks requiring both visualization and analytical reasoning. For algorithmic topics, a dialog-based AI assistant proved to be the most effective. These results support the consideration of AI technologies as a tool for adaptive modeling of individual educational trajectories in mathematics education.