Development of an Interactive User Interface for Teaching and Analysing the Pebble Game

Abstract

The Pebble Game, widely utilised within mathematical and computational research, acts as a vital tool for operationalising complex principles derived from finite model theory. This game provides a robust framework for exploring the interplay between formal languages and finite structures, addressing core issues in computational complexity. Increasing interest in finite model theory reflects its profound impact on the advancement of theoretical knowledge and its application in resolving practical challenges. This study explores the design and implementation of a user interface for the Pebble Game, which aims to demystify and enhance the understanding of complex concepts in graph theory and computational logic. The project integrates a Q-learning algorithm to simulate strategic gameplay, providing an automated and adaptable opponent. We designed the user interface (UI) to improve the game's accessibility and engagement, particularly for learners from diverse educational backgrounds. Our research focused on analysing the total rewards generated by the AI across multiple gaming sessions, a critical metric for assessing the adopted techniques' efficacy. The results demonstrated the AI's capacity for knowledge acquisition and gradual improvement in gameplay, underscoring the utility of reinforcement learning in educational tools. The results indicate that the improved Pebble Game interface not only helps achieve the educational goals of simplifying complicated theoretical concepts but also offers a strong foundation for future enhancements, such as integrating user feedback and refining the AI's learning algorithms. This study contributes significantly to the broader field of educational technology by illustrating how the synergy between interactive design and artificial intelligence can boost learning outcomes. Based on the study's results, we suggest implementing a user feedback mechanism to continuously refine the user interface, along with customising the game's difficulty level based on each user's progress. Lastly, we recommend conducting long-term studies to evaluate the game's impact on academic achievement over time.