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VISTA: Visual Integrated System for Tailored Automation in Math Problem Generation Using LLM

Jeongwoo Lee, Kwangsuk Park, Jihyeon Park

TL;DR

A novel multi-agent framework that leverages Large Language Models (LLMs) to automate the creation of complex mathematical visualizations alongside coherent problem text, demonstrating the immense potential of LLMs in transforming the way educators generate and utilize visual aids in math education.

Abstract

Generating accurate and consistent visual aids is a critical challenge in mathematics education, where visual representations like geometric shapes and functions play a pivotal role in enhancing student comprehension. This paper introduces a novel multi-agent framework that leverages Large Language Models (LLMs) to automate the creation of complex mathematical visualizations alongside coherent problem text. Our approach not only simplifies the generation of precise visual aids but also aligns these aids with the problem's core mathematical concepts, improving both problem creation and assessment. By integrating multiple agents, each responsible for distinct tasks such as numeric calculation, geometry validation, and visualization, our system delivers mathematically accurate and contextually relevant problems with visual aids. Evaluation across Geometry and Function problem types shows that our method significantly outperforms basic LLMs in terms of text coherence, consistency, relevance and similarity, while maintaining the essential geometrical and functional integrity of the original problems. Although some challenges remain in ensuring consistent visual outputs, our framework demonstrates the immense potential of LLMs in transforming the way educators generate and utilize visual aids in math education.

VISTA: Visual Integrated System for Tailored Automation in Math Problem Generation Using LLM

TL;DR

A novel multi-agent framework that leverages Large Language Models (LLMs) to automate the creation of complex mathematical visualizations alongside coherent problem text, demonstrating the immense potential of LLMs in transforming the way educators generate and utilize visual aids in math education.

Abstract

Generating accurate and consistent visual aids is a critical challenge in mathematics education, where visual representations like geometric shapes and functions play a pivotal role in enhancing student comprehension. This paper introduces a novel multi-agent framework that leverages Large Language Models (LLMs) to automate the creation of complex mathematical visualizations alongside coherent problem text. Our approach not only simplifies the generation of precise visual aids but also aligns these aids with the problem's core mathematical concepts, improving both problem creation and assessment. By integrating multiple agents, each responsible for distinct tasks such as numeric calculation, geometry validation, and visualization, our system delivers mathematically accurate and contextually relevant problems with visual aids. Evaluation across Geometry and Function problem types shows that our method significantly outperforms basic LLMs in terms of text coherence, consistency, relevance and similarity, while maintaining the essential geometrical and functional integrity of the original problems. Although some challenges remain in ensuring consistent visual outputs, our framework demonstrates the immense potential of LLMs in transforming the way educators generate and utilize visual aids in math education.

Paper Structure

This paper contains 22 sections, 13 figures, 2 tables.

Table of Contents

  1. Introduction
  2. VISTA
  3. Numeric Calculator.
  4. Geometry Validator.
  5. Function Validator.
  6. Visualizer.
  7. Code Executor and Summarizer.
  8. Math Question Generator.
  9. Evaluation
  10. Datasets
  11. Evaluation Strategy
  12. Results
  13. Geometry
  14. Function
  15. Overall Analysis
  16. ...and 7 more sections

Figures (13)

  • Figure 1: Overview of the multi-agent system for generating math problems and visual aids.
  • Figure 2: Detailed result comparison between our method and baseline on geometry problems. While the bars state mean of the result, the error bars state standard deviation. See appendix A.
  • Figure 3: Detailed result comparison between our method and baseline on function problems.
  • Figure 4: Comparison between application of our method and baseline
  • Figure 5: a sample from comparison between our method(b, 3) and baseline(c, f). while the baseline distort shape or fail to locate critical points, ours follows the geometrical/functional traits from the questions, leads to reproduction of the original images(a,d).
  • ...and 8 more figures