Large Language Models (LLM) are transforming Intelligent Tutoring Systems (ITS) via more natural explanations, multi-turn dialogue, and more adaptive support for students. Yet their effectiveness depends on rigorous benchmarking to ensure reliability, fairness, and pedagogical soundness. Such benchmarking relies on detailed student data, especially data that accurately reflect the actual distribution of wrong answers and misconceptions. A robust dataset of domain-specific wrong answers and misconceptions is critical for the ITS research community. Such a dataset enables training and testing of LLM-based ITS designed to correct misconceived student responses and guide students appropriately. Unfortunately, in advanced areas such as Theoretical Computer Science (TCS), such data are scarce, costly to collect, and limited by privacy concerns.

To address this problem, we propose a synthetic data generation technique grounded in real-world data. Our method works as follows: we curate a set of human-generated (question, answer, misconception) tuples to seed an LLM with the goal of generating a corpus of incorrect answers that resemble the kinds of mistakes students make while solving undergraduate-level math and algorithmic problems. We then prompt the LLM to generate a synthetic dataset with similar distribution of mistakes. Once such a technique has been validated on a math topic, we can easily transfer it over to others. Our goal is to lay the groundwork for scalable benchmarks that enable rigorous evaluation and broader adoption of LLM-based tutoring systems in the most conceptually demanding areas of computer science education, namely, theoretical computer science.