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In order to show how the teacher spreads the international Chinese language and Chinese culture for the foreign audience group through the classroom teaching behavior, and to shape the communication mechanism of the national image of China, with the help of the classical theory models of communication, this paper analyzed the role of international Chinese education in the transmission of China’s national image. The conclusion shows that international Chinese education is an effective way to build China’s image. It can not only show China’s image objectively and truly, but also offset the negative noise.

Taking the idea of “reflective and critical optimization thinking”, this article first examines “the outlook on development of big mathematics” in International Mathematics Day in 2003 from the perspective of the history of mathematics. Then according to the requirements of mathematical core literacy and mathematical beauty, a deep analysis is conducted on the limitations of the teaching methods in the Turing mathematics and statistics series “Terence Tao Analysis”. The case study shows that (1) the sets, relations, functions and operations present a concentric circle relationship of layer-by-layer proper subsets; (2) rejecting mathematical notation damages the beauty of simplicity and learning efficiency; and (3) forcing the first mapping function to be a surjection unnecessarily limits the wider range of applications that composite functions can have, and it lacks the unified beauty of mathematical definitions. Finally, itemized strategies and suggestions for improvement and optimization are proposed.