Divergent-Convergent Thinking in Large Language Models for Creative Problem Generation

TL;DR

This paper introduces CreativeDC, a two-phase prompting technique for large language models that enhances diversity and novelty in generated educational problems by explicitly separating creative exploration from finalization.

Contribution

CreativeDC is a novel two-phase prompting method inspired by creativity theories, significantly improving diversity and novelty in LLM-generated problems while maintaining utility.

Findings

CreativeDC achieves higher diversity and novelty than baseline methods.

It maintains high utility in generated problems.

Scaling analysis shows increased effective problem diversity with more samples.

Abstract

Large language models (LLMs) have significant potential for generating educational questions and problems, enabling educators to create large-scale learning materials. However, LLMs are fundamentally limited by the ``Artificial Hivemind'' effect, where they generate similar responses within the same model and produce homogeneous outputs across different models. As a consequence, students may be exposed to overly similar and repetitive LLM-generated problems, which harms diversity of thought. Drawing inspiration from Wallas's theory of creativity and Guilford's framework of divergent-convergent thinking, we propose CreativeDC, a two-phase prompting method that explicitly scaffolds the LLM's reasoning into distinct phases. By decoupling creative exploration from constraint satisfaction, our method enables LLMs to explore a broader space of ideas before committing to a final problem. We evaluate CreativeDC for creative problem generation using a comprehensive set of metrics that capture diversity, novelty, and utility. The results show that CreativeDC achieves significantly higher diversity and novelty compared to baselines while maintaining high utility. Moreover, scaling analysis shows that CreativeDC generates a larger effective number of distinct problems as more are sampled, increasing at a faster rate than baseline methods.