Exploring students' understanding of Pascal's Mystic Hexagon Theorem within projective geometry

Abstract

This study investigates Blaise Pascal's contribution to mathematics, focusing on the Mystic Hexagon Theorem, and evaluates the understanding of Mathematics Education students at Padang State University (Class of 2021). A qualitative approach was employed, combining a systematic literature review and semi-structured interviews with 10 students selected from five classes. Student responses were analyzed and categorized into four levels: Expert, Medium, Low, and Unknowing. The findings reveal that only two students could successfully prove Pascal's Mystic Hexagon Theorem with clear and logical steps. At the same time, the remaining participants struggled to identify key concepts or complete the solution process. This outcome indicates students' significant lack of understanding of historical mathematical theories, highlighting an educational gap in integrating historical contexts into modern curricula. The study implies that incorporating historical mathematical theories, such as Pascal's contributions, into classroom instruction can improve students' problem-solving abilities, critical thinking, and geometric reasoning. Additionally, exposure to mathematical history fosters deeper appreciation and motivation, connecting abstract concepts to their historical evolution. Bridging this gap through history-based learning strategies can make mathematics more engaging and meaningful, enabling students to develop more substantial foundational knowledge and practical skills.