# A Theoretical Review on Solving Algebra Problems

arXiv: https://arxiv.org/abs/2411.00031 · HTML: https://mlsanity.com/paper/2411.00031/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 73 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 19 of 19)

- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification](https://mlsanity.com/paper/2308.07921/) (2023)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Solving Math Word Problems via Cooperative Reasoning induced Language Models](https://mlsanity.com/paper/2210.16257/) (2022)
- [Translating a Math Word Problem to an Expression Tree](https://mlsanity.com/paper/1811.05632/) (2018)
- [Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction](https://mlsanity.com/paper/2203.10316/) (2022)
- [PALM: Pre-training an Autoencoding&Autoregressive Language Model for Context-conditioned Generation](https://mlsanity.com/paper/2004.07159/) (2020)
- [Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks](https://mlsanity.com/paper/2107.01431/) (2021)
- [Mapping to Declarative Knowledge for Word Problem Solving](https://mlsanity.com/paper/1712.09391/) (2017)
- [MWP-BERT: Numeracy-Augmented Pre-training for Math Word Problem Solving](https://mlsanity.com/paper/2107.13435/) (2021)
- [The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers](https://mlsanity.com/paper/1808.07290/) (2018)
- [Graph-to-Tree Neural Networks for Learning Structured Input-Output Translation with Applications to Semantic Parsing and Math Word Problem](https://mlsanity.com/paper/2004.13781/) (2020)
- [Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems](https://mlsanity.com/paper/2110.08464/) (2021)
- [Towards Tractable Mathematical Reasoning: Challenges, Strategies, and Opportunities for Solving Math Word Problems](https://mlsanity.com/paper/2111.05364/) (2021)
- [Sequence to General Tree: Knowledge-Guided Geometry Word Problem Solving](https://mlsanity.com/paper/2106.00990/) (2021)
- [Equation Parsing: Mapping Sentences to Grounded Equations](https://mlsanity.com/paper/1609.08824/) (2016)
- [Generalizing Math Word Problem Solvers via Solution Diversification](https://mlsanity.com/paper/2212.00833/) (2022)
- [Theory and Practice of Algorithm Engineering](https://mlsanity.com/paper/2107.10675/) (2021)

## Abstract (arXiv)

Solving algebra problems (APs) continues to attract significant research interest as evidenced by the large number of algorithms and theories proposed over the past decade. Despite these important research contributions, however, the body of work remains incomplete in terms of theoretical justification and scope. The current contribution intends to fill the gap by developing a review framework that aims to lay a theoretical base, create an evaluation scheme, and extend the scope of the investigation. This paper first develops the State Transform Theory (STT), which emphasizes that the problem-solving algorithms are structured according to states and transforms unlike the understanding that underlies traditional surveys which merely emphasize the progress of transforms. The STT, thus, lays the theoretical basis for a new framework for reviewing algorithms. This new construct accommodates the relation-centric algorithms for solving both word and diagrammatic algebra problems. The latter not only highlights the necessity of introducing new states but also allows revelation of contributions of individual algorithms obscured in prior reviews without this approach.