Student-generated metaphors about mathematics can provide insights into students' attitudes, beliefs, identities, and experiences, but expert human assessment through thematic coding of these semantically complex metaphor responses is labor-intensive and difficult to scale. This study examines whether Low-Rank Adaptation (LoRA)-based supervised fine-tuning of Large Language Models (LLMs) can improve their performance on codebook-guided coding tasks for student mathematics metaphors. We utilized a human-coded corpus of 2,265 Grade 6-8 responses to food- and animal-based metaphor prompts and evaluated LLMs on two tasks: valence-intensity coding of students' affective orientations toward mathematics and thematic coding of their metaphorical framings of mathematics. Two open-weight LLMs, DeepSeek-R1 1.5B and Mistral 7B, were evaluated before and after fine-tuning and compared with two proprietary LLMs, GPT-4o mini and GPT-5 mini. Results show that fine-tuning substantially improved the performance and run-to-run reliability of the open-weight LLMs across both tasks relative to their base versions, making the fine-tuned LLMs competitive with and often outperforming the proprietary LLMs. These findings suggest the potential of fine-tuned open-weight LLMs for scalable and automated AI-assisted measurement of students' metaphor responses with competitive performance while maintaining local controllability and privacy-conscious deployment.

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