Xinming Yang

Xinming Yang, Jun Li

Personalized tutoring, teacher training, and education research need access to \emph{targeted} synthetic misconceptions, but privacy and IRB constraints make labelled corpora of real student errors scarce. LLMs could in principle generate synthetic errors at scale, but producing an arbitrary wrong answer is easy for a modern LLM while producing one that matches a specified cognitive failure mode is much harder. We present a framework that generates errors targeted to a five-class taxonomy adapted from the revised Bloom's taxonomy, evaluated on questions from the TheoremQA dataset. A Generation Agent (GA) drafts a candidate erroneous solution conditioned on a target class, and an Examination Agent (EA) judges whether the draft is incorrect and class-consistent. The framework yields a reusable recipe for building class-stratified synthetic error datasets where authentic student corpora are unavailable. As a secondary diagnostic, targeted error generation is substantially harder than free-form incorrect-answer generation, and answer-grounding contributes more than expanded examples or external textbook content.

Xinming Yang, Haasil Pujara, Jun Li

While Large Language Models (LLMs) are often used as virtual tutors in computer science (CS) education, this approach can foster passive learning and over-reliance. This paper presents a novel pedagogical paradigm that inverts this model: students act as instructors who must teach an LLM to solve problems. To facilitate this, we developed strategies for designing questions with engineered knowledge gaps that only a student can bridge, and we introduce Socrates, a system for deploying this method with minimal overhead. We evaluated our approach in an undergraduate course and found that this active-learning method led to statistically significant improvements in student performance compared to historical cohorts. Our work demonstrates a practical, cost-effective framework for using LLMs to deepen student engagement and mastery.