Geometric proof competencies encompass understanding the development of deductive reasoning and logical thinking in students, particularly in the context of mathematical proofs. It also involves exploring how students understand and apply geometric concepts such as definitions, postulates, theorems in the construction of proofs. This study investigated the geometric proof competencies among Grade 8 students, with a focus on understanding their proficiency levels, the challenges they face, and the implications for teaching strategies. Utilizing the Van Hiele Theory of Geometric Thought with five levels: Level 0 (Visualization), Level 1 (Analysis), Level 2 (Informal deduction), Level 3 (Formal deduction), and Level 4 (Rigor), the research presents an in-depth analysis of students' abilities in proving triangle congruence, asserting statements on triangle congruence, and applying these concepts in constructing geometric figures such as perpendicular lines and angle bisectors. The findings revealed a predominant concentration of students at the lower levels of geometric reasoning, highlighting a critical gap in higher-order proof competencies essential for advanced mathematical understanding. Through structured interviews and assessment tasks, the study uncovered key challenges hindering student progress, including Low Conceptual Understanding in Geometric Proof and Lack of Independent Problem-Solving. These insights lead to the development of a video learning guide aimed at bridging these gaps, offering a comprehensive guide that aligns with the Van Hiele levels to foster deeper geometric understanding and reasoning. The study concluded with actionable recommendations for educators, curriculum developers, and policy makers, emphasizing the importance of targeted instructional strategies and resources to enhance students' geometric proof competencies. This research contributed significantly to the field of Mathematics education by identifying specific learning barriers and proposing pedagogical interventions to support effective geometry teaching and learning.
Lilian Manalo (2025) studied this question.