Students' Understanding Of Inverse Function Concept

Learning Mathematics well depends on students' understanding, "Mathematics understanding" should receive universal concerns from mathematics educational circle. "Inverse function" is an important part of function knowledge, and it is also stress and difficulty in the teaching of function. We examine "students' understanding of inverse function", looking for some valuable findings for our mathematics' teaching. In this research, we'll examine students' understanding on the definition of inverse function concept , the relations of inverse function and its primary function, as well as the existence property of inverse function, by questionnaire investigation and individual interview to 156 students in Grade 1, Grade 2, Grade 3 in senior high school. These are some conclusions hereinafter:(1) The levels of students' understanding on the definition of inverse function concept are different, and the students achieving the level of pre-structure, uni-structure, multi-structure and relation are 32.9%, 27%, 28.3% and 11.8% separately. Students' understandings present diversity, and the understanding on the point of view from "correspondence", "change", "operation", "symbol", "symmetry", "examples" occupies 25.5%, 21.4%, 15.0%, 8.5%, 7.3%, 1.7% separately in all the understandings. Senior 2 students' understanding is the most comprehensive, senior 3 students' in the next place, and senior 1 students' is the last.(2) Students' understanding on the relations of inverse function and its primary function doesn't turn up trumps. Their recognition is rather limited and shows various mistakes. Students understand different relations in different degrees. They do best in the interchanging of domain and range, better in symmetry of the two figures concerning v = x, and worst in the switching of formal symbols. Difference among the three grades varies along with different relations.(3) Students' understanding on the existence property of inverse function is better relatively, but methods they use to judge whether a function have inverse function or not are simplex relatively. Students do the best in judging the function presented with graph forms, they do better in judging the function presented with analysis formula forms, and they do worst in judging the function presented with table forms. Among grades, senior 3 do the best, and senior 2 do better than senior 1 in understanding on the existence property of inverse function.To improve the students' understanding of inverse function concept, we mathematics educators should update the concept of teaching, pay important attention to students' understanding and apply modern educational technology in mathematics teaching properly, and refine the assessment manners of students' learning positively.