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Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective

Zhenya Huang, Jiayu Liu, Xin Lin, Zhiyuan Ma, Shangzi Xue, Tong Xiao, Qi Liu, Yee Whye Teh, Enhong Chen

TL;DR

The paper analyzes math word problem solving through five human cognitive abilities: Problem Understanding, Logical Organization, Associative Memory, Critical Thinking, and Knowledge Learning. It surveys neural-network solvers and large language model (LLM) approaches, detailing methods that instantiate each cognitive capability and how these methods fare on common benchmarks. A unified re-evaluation across five MWP datasets highlights the relative strengths of tree/DAG-based reasoning, memory augmentation, and tool-enabled computation, with LLMs often outperforming traditional NN-based models. Beyond MWPs, the work surveys geometry problem solving and automatic theorem proving to illustrate how cognitive-style reasoning can scale to broader mathematical tasks, and it releases a public repository for reproducibility. The findings suggest that enhancing higher-order cognitive abilities and tool integration in both small models and LLMs is key to advancing robust mathematical reasoning in AI.

Abstract

Math word problem (MWP) serves as a fundamental research topic in artificial intelligence (AI) dating back to 1960s. This research aims to advance the reasoning abilities of AI by mirroring the human-like cognitive intelligence. The mainstream technological paradigm has evolved from the early rule-based methods, to deep learning models, and is rapidly advancing towards large language models. However, the field still lacks a systematic taxonomy for the MWP survey along with a discussion of current development trends. Therefore, in this paper, we aim to comprehensively review related research in MWP solving through the lens of human cognition, to demonstrate how recent AI models are advancing in simulating human cognitive abilities. Specifically, we summarize 5 crucial cognitive abilities for MWP solving, including Problem Understanding, Logical Organization, Associative Memory, Critical Thinking, and Knowledge Learning. Focused on these abilities, we review two mainstream MWP models in recent 10 years: neural network solvers, and LLM based solvers, and discuss the core human-like abilities they demonstrated in their intricate problem-solving process. Moreover, we rerun all the representative MWP solvers and supplement their performance on 5 mainstream benchmarks for a unified comparison. To the best of our knowledge, this survey first comprehensively analyzes the influential MWP research of the past decade from the perspective of human reasoning cognition and provides an integrative overall comparison across existing approaches. We hope it can inspire further research in AI reasoning. Our repository is released on https://github.com/Ljyustc/FoI-MWP.

Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective

TL;DR

The paper analyzes math word problem solving through five human cognitive abilities: Problem Understanding, Logical Organization, Associative Memory, Critical Thinking, and Knowledge Learning. It surveys neural-network solvers and large language model (LLM) approaches, detailing methods that instantiate each cognitive capability and how these methods fare on common benchmarks. A unified re-evaluation across five MWP datasets highlights the relative strengths of tree/DAG-based reasoning, memory augmentation, and tool-enabled computation, with LLMs often outperforming traditional NN-based models. Beyond MWPs, the work surveys geometry problem solving and automatic theorem proving to illustrate how cognitive-style reasoning can scale to broader mathematical tasks, and it releases a public repository for reproducibility. The findings suggest that enhancing higher-order cognitive abilities and tool integration in both small models and LLMs is key to advancing robust mathematical reasoning in AI.

Abstract

Math word problem (MWP) serves as a fundamental research topic in artificial intelligence (AI) dating back to 1960s. This research aims to advance the reasoning abilities of AI by mirroring the human-like cognitive intelligence. The mainstream technological paradigm has evolved from the early rule-based methods, to deep learning models, and is rapidly advancing towards large language models. However, the field still lacks a systematic taxonomy for the MWP survey along with a discussion of current development trends. Therefore, in this paper, we aim to comprehensively review related research in MWP solving through the lens of human cognition, to demonstrate how recent AI models are advancing in simulating human cognitive abilities. Specifically, we summarize 5 crucial cognitive abilities for MWP solving, including Problem Understanding, Logical Organization, Associative Memory, Critical Thinking, and Knowledge Learning. Focused on these abilities, we review two mainstream MWP models in recent 10 years: neural network solvers, and LLM based solvers, and discuss the core human-like abilities they demonstrated in their intricate problem-solving process. Moreover, we rerun all the representative MWP solvers and supplement their performance on 5 mainstream benchmarks for a unified comparison. To the best of our knowledge, this survey first comprehensively analyzes the influential MWP research of the past decade from the perspective of human reasoning cognition and provides an integrative overall comparison across existing approaches. We hope it can inspire further research in AI reasoning. Our repository is released on https://github.com/Ljyustc/FoI-MWP.
Paper Structure (27 sections, 3 equations, 4 figures, 4 tables)

This paper contains 27 sections, 3 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Task Definition
  3. Neural Network Solvers
  4. Ability 1: Problem Understanding
  5. Ability 2: Logical Organization
  6. Ability 3: Associative Memory
  7. Ability 4: Critical thinking
  8. Ability 5: Knowledge Learning
  9. Large Language Models
  10. General LLM-based Reasoning Methods
  11. Logical Organization
  12. Associative Memory
  13. Critical thinking
  14. Tool Integration
  15. Specialized LLM-based Reasoning Methods
  16. ...and 12 more sections

Figures (4)

  • Figure 1: Taxonomy of Methods Based on Human Cognitive Abilities.
  • Figure 2: Comparison between Tree-based and DAG-based methods.
  • Figure 3: Comparison of Different Reasoning Structures and Tool Integration Methods in LLM-based Approaches: From Sequential Reasoning (CoT) to Tree/Graph Structures (ToT/GoT) and Programming Language Integration (PoT/PAL).
  • Figure 4: Examples of three Mathematical Tasks beyond MWP.