Senior Middle School Students' Understanding About The Composite Functions

The composite function is an important component of the knowledge of functions and one of the key and difficult topics in high school mathematics teaching. This paper is a report of an empirical study on students' understanding about the inverse function with both questionnaire survey and interview.Based upon the analysis of the results of the survey, the following conclusions are arrived at:(1) Most students reach the levels of pre-structure and uni-structure and their understanding of the composite functions stay at the stage of operation. They prefer the operation over the structure.(2) Students' image of the concept of composite functions is affected by that of function concept, the latter being the basis of the former.(3) Students do better in identifying conditions of the composition of two functions, establishing a composite function, finding the zeros of a composite function, finding the analytical expression of the exterior function and finding the derivative of a composite function than finding the domain and the monotonous intervals of a composite functionTo improve the students' understanding of the concept of a composite function, mathematics teachers should update the teaching notions, attach importance to comprehension-oriented teaching and properly apply technology in mathematics teaching.