Beyond Correctness: Evaluating and Improving LLM Feedback in Statistical Education

Large language models (LLMs) have been proposed as scalable tools to address the gap between the importance of individualized written feedback and the practical challenges of providing it at scale. However, concerns persist regarding the accuracy, depth, and pedagogical value of their feedback responses. The present study investigates the extent to which LLMs can generate feedback that aligns with educational theory and compares techniques to improve their performance. Using mock in-class exam data from two consecutive years of an introductory statistics course at LMU Munich, we evaluated GPT-generated feedback against an established but expanded pedagogical framework. Four enhancement methods were compared in a highly standardized setting, making meaningful comparisons possible: Using a state-of-the-art model, zero-shot prompting, few-shot prompting, and supervised fine-tuning using Low-Rank Adaptation (LoRA). Results show that while all LLM setups reliably provided correctness judgments and explanations, their ability to deliver contextual feedback and suggestions on how students can monitor and regulate their own learning remained limited. Among the tested methods, zero-shot prompting achieved the strongest balance between quality and cost, while fine-tuning required substantially more resources without yielding clear advantages. For educators, this suggests that carefully designed prompts can substantially improve the usefulness of LLM feedback, making it a promising tool, particularly in large introductory courses where students would otherwise receive little or no written feedback.