# Design of Chain-of-Thought in Math Problem Solving

**Authors:** Zhanming Jie, Trung Quoc Luong, Xinbo Zhang, Xiaoran Jin, Hang Li  
**arXiv:** [2309.11054](https://arxiv.org/abs/2309.11054)  
**Date:** 2023-09-20  
**Summary page:** https://www.summarizepaper.com/en/paper/2309.11054v2/

## Key points

- Chain-of-Thought (CoT) design for math problem solving
- Categorized into three types: non-describing program, self-describing program, and comment-describing program
- Self-describing programs outperform other CoT types and even surpass GPT-3.5-turbo in few-shot prompting capabilities
- Program CoTs are more effective than natural language CoTs for math problem solving tasks
- Self-describing and comment-describing programs outperform non-describing programs, with self-describing programs showing superior performance
- Using Python for program CoTs yields better results than using Wolfram Language
- Datasets and code used in the study are publicly available for further research

## Summary

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In this study, we explore the design of Chain-of-Thought (CoT) for math problem solving, categorizing program CoTs into three types: non-describing program, self-describing program, and comment-describing program. Through extensive experiments on GSM8K, MATHQA, and SVAMP datasets, we discover that the self-describing program consistently outperforms other types of CoTs and even surpasses the few-shot prompting capabilities of GPT-3.5-turbo. Our findings suggest that utilizing program CoTs is more effective than relying on natural language CoTs for math problem solving tasks. Additionally, we observe that both self-describing and comment-describing programs outperform non-describing programs, with self-describing programs showing superior performance compared to comment-describing ones. Furthermore, our research indicates that using Python for program CoTs yields better results than using Wolfram Language. These experimental insights provide valuable guidance for future developments in CoT designs for math problem solving tasks. The datasets and code used in our study are publicly available to facilitate further research in this area.