<![CDATA[The integration of artificial intelligence (AI) into mathematics education has demonstrated potential in enhancing students’ conceptual understanding and reasoning abilities, particularly in the context of mathematical proof. Despite these advancements, limited research has investigated the use of AI-based language models such as ChatGPT to support students in learning the logical structure of trigonometric identity proofs, which remain a challenging topic for many learners. To address this gap, this study introduces a novel learning trajectory assisted by ChatGPT aimed at improving students’ abilities in constructing and understanding trigonometric proofs. Employing a validation study design, the research was conducted in three phases: experimental preparation, experimental design, and retrospective analysis. Data were collected through observations, interviews, document analysis, and written tests, and analyzed qualitatively. A total of 50 eleventh-grade students engaged in three learning activities: studying proofs with ChatGPT-generated explanations, interacting directly with ChatGPT to explore proof strategies, and independently solving proof tasks without AI assistance. The findings indicate that ChatGPT effectively supports students in comprehending the logical steps involved in proof construction, enhances their engagement with mathematical reasoning, and promotes deeper understanding of trigonometric identities. These results highlight the potential impact of conversational AI tools in fostering proof-based thinking and enriching mathematics instruction at the secondary education level.]]>
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