As mentioned in the article "托勒密定理的教学如何设计？" , most instructional materials on Ptolemy's theorem, including lesson plans and study guides, follow a similar structure. They typically begin by introducing the theorem, followed by a rigorous proof, then presenting sample problems, and finally reinforcing the concept with exercises. While this approach seems efficient on the surface, it often overlooks the deeper mathematical insights behind the theorem. It is essential to recognize that every mathematical theorem arises from the need to solve a particular problem—it is not conjured out of thin air. Therefore, a teaching design that lacks the exploration of mathematical thinking and historical context cannot be considered high-quality.
For the teaching design of Ptolemy's Theorem and its extensions, I will focus on two key aspects:
How was Ptolemy's Theorem discovered? What is the logical structure behind its proof?
Attached is a screenshot from my recorded lesson video for reference.
Teaching Design and Question Framework:
