Middle School Students' Understanding Of The Concept Of Function

The firm foundation of the development of function, which is the base of modern math, has promoted the development of the entire math field. The transition from constant math to variable math begins from the concept of function, which is a requisite for middle school students throughout the world. It is abstract and hard for the beginners, who may have difficulty with cognition and understanding because of their comprehensive faculty. the concept of function is an important and difficult point in teaching, to which enough attention should be paid.This article deals with the following problems through surveys and interviews: (1) How do students in Senior 1 understand function? (2) What are students' common problems in understanding the concept of function? (3) What are the main causes of the difficulties in studying function?The results of studies show that students' ideas about functions are mostly function images (mainly the images of beeline and parabola), the symbol "y=f(x)", linear functions, quadratic functions, etc. Few students connect it with the standard definition of mapping or the characters of function.To students' mind, the function is not only its standard definition but some transmutations. When judging functions, they sometimes don't use the standards as they are taught or the concepts of the transmutations. They have their own spontaneous standards. With the development of their math abilities and the adoption of its standard definition, the proportion of correct judgment of functions increases.Some common problems for Senior 1 students in understanding functions are as follows:1. Some students' ideas about functions are not correct or overall, which are in conflict with the definition in the text book.2. Students have their individual tendency when expressing functions. Most of the examples they have are limited to some images and algebraic expressions.3. Many students believe that the existence of formulae is necessary for the function, and there must be an image for a function.4. There are difficulties understanding constant functions.5. The images of function drawn by students are sometimes affected by linear images. Of those who can draw the non-linear images, the proportion of the students with stronger abilities is bigger than that of the students with weaker abilities.