Large Language Models: A tool for solving mathematical problems in high school

Abstract

Mathematics learning resources have evolved from static textbooks to collaborative online forums and conversational artificial intelligence (AI) tools. This evolution reflects students’ ongoing demand for clarity, adaptability, and accessible support. While traditional textbooks offered privacy, they limited flexibility. Online forums, such as Yahoo! Answers, Math Stack Exchange, and Mathematika.bg, enabled collaborative problem-solving, but they required public participation. Large language models (LLMs), including ChatGPT, now offer private, adaptive "comfort mode" interactions, combining the autonomy of self-study with the responsiveness of a personal tutor. The potential of LLMs to support mathematics education in Bulgaria is examined through a dual approach in this study: (1) eleven models solving problems from the Bulgarian National External Assessment (NEA) for 10th grade are empirically evaluated, and (2) practicing mathematics teachers enrolled in a Master program are qualitatively observed. Model performance was evaluated based on accuracy, methodological alignment with the national curriculum, and linguistic appropriateness. The findings indicate that, although several models, such as Mistral (22B) and DeepSeek R1, achieved perfect accuracy, they often used solution strategies that deviated from national standards. Locally fine-tuned models (e.g., BgGPT) demonstrated stronger curriculum alignment and the use of precise Bulgarian mathematical terminology. Teacher feedback revealed recognition of AI's potential for personalized student support, as well as caution toward integration, reflecting a preference to retain creative and methodological control. The study concludes that three conditions are necessary for successful AI integration in mathematics education: mathematical accuracy, adherence to curriculum-specific methods, and linguistically precise explanations. Large language models (LLMs) can complement, but not replace, the teacher's role when deliberately embedded in the continuum of educational resources, from books to forums to conversational AI.

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