Drawing from my decade-long experience as a math teacher, I've observed that the introduction of geometric proof often marks a fresh beginning for middle school students. Interestingly, students who are good at algebra may not necessarily excel in geometry, while those under performers in elementry school may surprisingly develop a fondness for geometry. In contrast to school algebra, geometry presents distinct cognitive challenges mainly involving spatial reasoning and deductive reasoning. The process of solving high-cognitive geometric questions often mirrors the thinking patterns mathematicians experience. During the process of problem solving, intuition is considered of great importance to mathematicians (Burton, 1999). Similarly, intuition also plays a pivotal role in solving challenging geometric problems, especially when the application of auxiliary lines is essential.
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