An Investigation into the Challenges and Strategies of Secondary Students' Geometric Thought Processes through the Lens of Van Hiele's Theory

This paper delves into the intricacies of the Van Hiele Theory, which posits a developmental framework for understanding how students think geometrically. The study examines the challenges secondary students face in advancing their geometric cognitive levels, particularly in transitioning from informal to formal deduction. It highlights the prevalence of students at Level 2 (Informal Deduction) and identifies a significant gap in their ability to progress to Level 3 (Formal Deduction). The paper proposes targeted strategies for facilitating this critical leap, emphasizing the need for rigorous natural reasoning, symbolization of geometric reasoning, a deep understanding of logical thinking components, and optimization of the geometric cognitive structure. Through these strategies, the paper aims to equip educators with the tools necessary to enhance students' geometric thinking and foster a robust understanding of mathematical proofs. The findings underscore the importance of a structured approach to geometric instruction that aligns with the cognitive stages of students, ultimately aiming to improve students' logical reasoning capabilities and success in mathematics.