Paper 39: An Automated Graphing System for Mathematical Pedagogy

Teachers use a variety of in-classroom technological tools in day-to-day instruction. The variety and complexity of operating these tools imposes a cognitive and time-overload, that teachers would rather spend with students. Pedagogical tool orchestration systems, based on generative AI, hold the promise of untethering teachers by enabling simple language-based operation of tools. Graphs are an essential tool in the classroom, allowing students to visualize and interact with mathematical concepts. In this paper, we present an automated graphing system for mathematical pedagogy. The system consists of an LLM and a mathematical solver used in conjunction with a math graphing tool to produce accurate visualizations from simple natural language commands. Our goal is to allow teachers to easily invoke math graphing tools through natural language, which is not possible through the use of a solver or an LLM alone. For benchmarking purposes, we create a dataset of graphing problems based on Common Core standards. We also develop an autoevaluator to easily evaluate the outputs of our system by comparing them to ground-truth expressions. Our results demonstrate the potential of tool usage with LLMs, as we show that incorporating a solver into the system results in significantly improved performance.