This paper presents a novel exploration into the regressive side effects of training Large Language Models (LLMs) to mimic student misconceptions for personalized education. We highlight the problem that as LLMs are trained to more accurately mimic student misconceptions, there is a compromise in the factual integrity and reasoning ability of the models. Our work involved training an LLM on a student-tutor dialogue dataset to predict student responses. The results demonstrated a decrease in the model's performance across multiple benchmark datasets, including the ARC reasoning challenge and TruthfulQA, which evaluates the truthfulness of model's generated responses. Furthermore, the HaluEval Dial dataset, used for hallucination detection, and MemoTrap, a memory-based task dataset, also reported a decline in the model accuracy. To combat these side effects, we introduced a "hallucination token" technique. This token, appended at the beginning of each student response during training, instructs the model to switch between mimicking student misconceptions and providing factually accurate responses. Despite the significant improvement across all datasets, the technique does not completely restore the LLM's baseline performance, indicating the need for further research in this area. This paper contributes to the ongoing discussion on the use of LLMs for student modeling, emphasizing the need for a balance between personalized education and factual accuracy.