Interactive Game-Based Learning of Pythagorean Theorem Proofs through 2D Geometric Structures

Abstract

This research explores the development of an interactive educational game application aimed at illustrating the Pythagorean Theorem through 2D plane figures and their associated geometric properties. The visual proof employs positional movements (translation) and rotations, strategically positioning plane figures and animating the step-by-step process from initial positions to the proof position. The selection of figures and properties depends on the proof method, incorporating angles in right-angled triangles, straight-line angles, and area substitution. The application showcases four Pythagorean Theorem proof methods: Zhou Bi Suan Jing, Henry Perigal, Garfield Trapezoid, and The Brides Chair. Developed using Unity, supported by Adobe Illustrator and Visual Studio in C#, it underwent testing on middle school students with a pretest-posttest control group method. Results analysis revealed significant average differences, indicating the application’s substantial impact on students’ theorem comprehension. Further examination of completion durations identified the Henry Perigal proof as the fastest, implying the ease of understanding area-based proofs over those involving analytic equations. This aligns with the perceptual simplicity of the Henry Perigal method compared to others. The study contributes an innovative educational approach, demonstrating the potential for effective theorem instruction through interactive applications.