  High-quality conversational datasets are crucial for the successful
development of Intelligent Tutoring Systems (ITS) that utilize a Large Language
Model (LLM) backend. Synthetic student-teacher dialogues, generated using
advanced GPT-4 models, are a common strategy for creating these datasets.
However, subjects like physics that entail complex calculations pose a
challenge. While GPT-4 presents impressive language processing capabilities,
its limitations in fundamental mathematical reasoning curtail its efficacy for
such subjects. To tackle this limitation, we introduce in this paper an
innovative stateful prompt design. Our design orchestrates a mock conversation
where both student and tutorbot roles are simulated by GPT-4. Each student
response triggers an internal monologue, or `code soliloquy' in the
GPT-tutorbot, which assesses whether its subsequent response would necessitate
calculations. If a calculation is deemed necessary, it scripts the relevant
Python code and uses the Python output to construct a response to the student.
Our approach notably enhances the quality of synthetic conversation datasets,
especially for subjects that are calculation-intensive. Our preliminary Subject
Matter Expert evaluations reveal that our Higgs model, a fine-tuned LLaMA
model, effectively uses Python for computations, which significantly enhances
the accuracy and computational reliability of Higgs' responses. Code, models,
and datasets is available at https://github.com/luffycodes/Tutorbot-Spock-Phys.
