Algebraic Word Problem Solving System Based on Qualia Structure

Project Overview

This project (2022-2023) is supported by the Outstanding Doctoral Dissertation Incubation Program of Central China Normal University. It focuses on research into methods for solving algebraic word problems based on qualia structure and the integration of commonsense knowledge. The project aims to connect concepts and contexts by combining qualia structure with syntax-semantics models, expanding the application of machine solvers in intelligent tutoring systems.

Research Background

Traditional neural solvers use end-to-end models to convert problem text into mathematical expressions, but lack the ability to extract quantitative relationships in complex scenarios. This project proposes a qualia role-based entity-dependency graph (EDG) to represent and extract quantity relations for solving Chinese algebraic word problems.

Core Innovations

1. Qualia Structure Integration

• Qualia Role Theory: Applies qualia structure (formal, constitutive, telic, agentive roles) to analyze mathematical objects.
• Concept-Context Connection: Establishes semantic links between mathematical concepts and real-world contexts.
• Commonsense Knowledge Fusion: Effectively integrates commonsense knowledge into the problem-solving process.

2. Entity-Dependency Graph (EDG)

• Graph Structure Representation: Uses graph structures to represent dependency relations among mathematical objects.
• Quantity Relation Extraction: Extracts implicit quantity relations from qualia roles.
• Algorithm Design: Develops dedicated algorithms for EDG generation and quantity relation extraction.

3. Chinese Language Processing

• Chinese-Specific Features: Addresses unique linguistic features of Chinese algebraic word problems.
• Language Understanding: Enhances understanding of Chinese mathematical expressions.
• Cultural Adaptation: Considers the cultural context of Chinese mathematics education.

Technical Architecture

System Components

1. Problem Text Analysis Module
   • Natural Language Processing
   • Entity Recognition and Classification
   • Semantic Role Labeling
2. Qualia Structure Analysis Module
   • Qualia Role Identification
   • Conceptual Relationship Modeling
   • Commonsense Reasoning
3. EDG Construction Module
   • Entity Dependency Modeling
   • Graph Generation
   • Quantity Relation Extraction
4. Solver Engine
   • Mathematical Expression Generation
   • Equation Solving
   • Result Verification

Research Outcomes

Academic Contributions

• SCI Journal Paper: Published in Computer Modeling in Engineering and Sciences
• Conference Papers: Multiple EI-indexed conference papers
• Algorithmic Innovation: Proposed a novel framework for algebraic word problem solving

Technical Breakthroughs

• Accuracy Improvement: Significantly improved solution accuracy compared to traditional methods
• Interpretability Enhancement: Provided better interpretability of the solving process
• Application Expansion: Broadened the applicability of automatic solvers

Application Prospects

Intelligent Tutoring Systems

• Personalized Learning: Provides personalized math problems based on student profiles
• Error Diagnosis: Intelligently identifies student errors and offers targeted guidance
• Learning Path Planning: Plans optimal learning paths based on student abilities

Educational Technology Platforms

• Automatic Problem Generation: Intelligently generates math word problems of varying difficulty
• Intelligent Grading: Automatically evaluates the correctness of student answers
• Learning Analytics: Deeply analyzes student learning behaviors and cognitive processes

Project Impact

The research outcomes of this project have made significant academic contributions and provided technical support for practical educational applications. By integrating qualia structure theory with modern AI technology, the project opens new directions for the development of intelligent tutoring systems.

Future Development

Technical Expansion

• Multilingual Support: Extend to math word problems in other languages
• Complex Problem Handling: Address more complex types of math problems
• Real-Time Interaction: Develop real-time human-computer interactive solvers

Application Extension

• Interdisciplinary Applications: Extend methods to other subjects such as physics and chemistry
• Industrial Applications: Promote the industrialization of the technology
• International Collaboration: Conduct international collaborative research projects

This project represents an important exploration in the field of intelligent education, laying a solid theoretical and technical foundation for the future development of educational technology.