# Interpretable Math Word Problem Solution Generation Via Step-by-step Planning

arXiv: https://arxiv.org/abs/2306.00784 · HTML: https://mlsanity.com/paper/2306.00784/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 66 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 30 of 41)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [CTRL: A Conditional Transformer Language Model for Controllable Generation](https://mlsanity.com/paper/1909.05858/) (2019)
- [BARTScore: Evaluating Generated Text as Text Generation](https://mlsanity.com/paper/2106.11520/) (2021)
- [GPT Understands, Too](https://mlsanity.com/paper/2103.10385/) (2021)
- [DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts](https://mlsanity.com/paper/2105.03023/) (2021)
- [GeDi: Generative Discriminator Guided Sequence Generation](https://mlsanity.com/paper/2009.06367/) (2020)
- [Factual Probing Is [MASK]: Learning vs. Learning to Recall](https://mlsanity.com/paper/2104.05240/) (2021)
- [WARP: Word-level Adversarial ReProgramming](https://mlsanity.com/paper/2101.00121/) (2021)
- [Text and Patterns: For Effective Chain of Thought, It Takes Two to Tango](https://mlsanity.com/paper/2209.07686/) (2022)
- [A Distributional Approach to Controlled Text Generation](https://mlsanity.com/paper/2012.11635/) (2020)
- [When to Make Exceptions: Exploring Language Models as Accounts of Human Moral Judgment](https://mlsanity.com/paper/2210.01478/) (2022)
- [Generate & Rank: A Multi-task Framework for Math Word Problems](https://mlsanity.com/paper/2109.03034/) (2021)
- [Translating a Math Word Problem to an Expression Tree](https://mlsanity.com/paper/1811.05632/) (2018)
- [Pre-Training Transformers as Energy-Based Cloze Models](https://mlsanity.com/paper/2012.08561/) (2020)
- [Energy-Based Reranking: Improving Neural Machine Translation Using Energy-Based Models](https://mlsanity.com/paper/2009.13267/) (2020)
- [Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction](https://mlsanity.com/paper/2203.10316/) (2022)

## Built on by (most cited first, 17 of 17)

- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [Evaluating Mathematical Reasoning Beyond Accuracy](https://mlsanity.com/paper/2404.05692/) (2024)
- [Guiding Language Model Reasoning with Planning Tokens](https://mlsanity.com/paper/2310.05707/) (2023)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [Large Language Models for Planning: A Comprehensive and Systematic Survey](https://mlsanity.com/paper/2505.19683/) (2025)
- [Mathematical Language Models: A Survey](https://mlsanity.com/paper/2312.07622/) (2023)
- [Self-Refine Instruction-Tuning for Aligning Reasoning in Language Models](https://mlsanity.com/paper/2405.00402/) (2024)
- [Exploring Automated Distractor Generation for Math Multiple-choice Questions via Large Language Models](https://mlsanity.com/paper/2404.02124/) (2024)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [Chain-of-Thought Reasoning is a Policy Improvement Operator](https://mlsanity.com/paper/2309.08589/) (2023)
- [PersonaMath: Boosting Mathematical Reasoning via Persona-Driven Data Augmentation](https://mlsanity.com/paper/2410.01504/) (2024)
- [An Expression Tree Decoding Strategy for Mathematical Equation Generation](https://mlsanity.com/paper/2310.09619/) (2023)
- [Mathematical Computation and Reasoning Errors by Large Language Models](https://mlsanity.com/paper/2508.09932/) (2025)
- [Towards Goal-oriented Prompt Engineering for Large Language Models: A Survey](https://mlsanity.com/paper/2401.14043/) (2024)
- [Plan, Verify and Fill: A Structured Parallel Decoding Approach for Diffusion Language Models](https://mlsanity.com/paper/2601.12247/) (2026)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)

## Abstract (arXiv)

Solutions to math word problems (MWPs) with step-by-step explanations are valuable, especially in education, to help students better comprehend problem-solving strategies. Most existing approaches only focus on obtaining the final correct answer. A few recent approaches leverage intermediate solution steps to improve final answer correctness but often cannot generate coherent steps with a clear solution strategy. Contrary to existing work, we focus on improving the correctness and coherence of the intermediate solutions steps. We propose a step-by-step planning approach for intermediate solution generation, which strategically plans the generation of the next solution step based on the MWP and the previous solution steps. Our approach first plans the next step by predicting the necessary math operation needed to proceed, given history steps, then generates the next step, token-by-token, by prompting a language model with the predicted math operation. Experiments on the GSM8K dataset demonstrate that our approach improves the accuracy and interpretability of the solution on both automatic metrics and human evaluation.