Learning XYZ as a second language

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Teaching English, Chinese, or any language as a second language must obey the rule that the students learn the fastest when they understand a certain amount of materials, either spoken or written. Without scientific study, I place the "certain amount" at roughly 75%, beyond which the students find it boring, and below which they find it too challenging to be interesting. A local high school in the town is academically reputed in all subjects, including the foreign language. The Advanced Chinese class is taught by teachers from Taiwan, who are excellent in the Chinese language and less than desired in English. As the class is taught in mostly Chinese, almost all students are Chinese-descent so as to be able to follow the teacher's instructions; basically, students not hearing Chinese in everyday life have a hard time to survive. Another high school not far away is not as competitive, and the Chinese class is taught by one whose mother toungue is English. The class is full of white and black students fully engaged and sufficiently but not overly challenged. A similar case is given by a friend of mine, who opened a foreign language school in southern China in the 1990's. Initially, the students demanded foreign teachers, who were fairly expensive back then. Recently, my friend said, some of her students "became more realistic" and preferred Chinese teachers, because they "felt they learned more" this way.

In a nutshell, other things being approximately equal, the determining factor for the fastest progress, and as a side effect, personal interest, is the percentage of the language that can be understood. The graph of the learning speed vs. difficulty (measured in this percentage) may be a bell-shaped curve centered around 75%. Now, all I wish is a proof from a controlled study by psychologists or pedagogists!

P.S. There's one unique aspect in teaching Chinese as a second language. Traditionally, the students are required to memorize the characters completely so they can write them manually. As everyone knows, the Chinese writing system is not spelling-based and so poses the greatest difficulty to all students. With the advent of computer technology and acceptance of the unofficial standard of input, pinyin, one no longer needs to completely memorize a character to "write" it; he only needs to recognize the one out of multiple given by the IME, Input Method Editor. (A classical example is "嚏" as in "喷嚏", "sneeze", which few Beijing University students can write with free hand.) This has made significant impact on all the people around the world using the Chinese language, businessmen, workers, students, and teachers themselves. Unfortunately, some teachers in some schools still require the students to write the characters in hand, wasting their energy otherwise available to study more characters, more sentence structures, or more culture topics.