Students' Understanding And Misconception Of Arcsin Function Concept

The author participated in the subject research ?Ten top difficulty concepts of senior high school mathematical? which hosted by the super teacher Mr RuanXiaoMing in songjiang district of Shanghai. Premenstrual survey had found that the arcsin function concept is just located in the eighth of the ten difficult concepts. In this background, the author futher investigated "high school students' understanding of the concept of arcsin function and error analysis". The paper focused on the difficulty of the concept of arcsin function, students' understanding of the concept, and the error types when students solve the questions related to arcsine function. Based on literature analysis, questionnaire investigation, penci-paper tests and interviews. And the following conclusions:(1) The teaching difficulty of arcsin function concept including:the necessity of arcsin function, the symbol explanation of arcsin function and the particularity of the three elements of arcsin function regulation. Learning difficulties:understanding of the symbol, the range and limit of angle, transformation of "angle" and "value",said angle with arcsin function value.(2)Literal representative turned out to be dominant in students' concept representative of arcsin function, then symbolic representation and finally graphic representation. Also, the students' understanding of each representation level is different. In addition, the paper examined the students' understanding of three elements of arcsine function concept, and found that students' understanding of range selection principles of arcsine function mainly from the "function"?"geometric feature"?"actual demand".(3) Students error types in solving questions related to arcsin function for problem solving mainly include:the informative errors?the strategic errosr and the careless errors, while rarely appear logical errors. At the same time, a certain type of error is also associated with other types of error.