Abstract:This paper advances a teaching design of the theorem for interior angle sum of a triangle based on "four understandings". Experimental operation: "intuitive understanding"for acquiring a perceptual understanding and savoring the mathematics abstractness;Theorem proving:"deep understanding" for guiding students to explore the interior angle sum theorem of a triangle and understand the rationalist spirit of mathematics;Reflective proof: "reflective understanding" for inspecting and analyzing different approaches to prove triangle interior angle sum theorem and understanding of the essence of different methods;Historical review: "cultural understanding" for reviewing the process of theorem discovery and recreation,appreciating mathematical culture.