An Investigation Into The Grade 9 Students' Understanding Of The Function In Changzhou

The thickly resistance of the history development of the function concept, which decide the function concept and promote the whole mathematics to develop, is the important basic of mathematics. Function is the most important basal concept. Function not is one special important mathematics knowledge, but also mathematics ideas. Function idea is a means and method to solve many practical issues, and it's also regarded as an effective mathematical model to depict realism world. However, as a result of the complexity of function concept, It become a difficulty to junior high school teaching.This paper includes two research methods—questionnaire investigation and visiting based on previous study. The main research includes several aspects as follow:1. How do students describe and understand the function after learning all contents of function in junior high school phase?2.Examine junior high school students' capability of understanding of expression for function(analytic method, tabulation method, graphical method).3. Examine junior high school students understanding of essence characteristic of function concept.4. Examine junior high school students to synthesize application level for function.Research' s result:1. Students have all kinds of understandings for function concept, but only very few students find out that when the independent variable is fixed, the dependent variable has the only number. Students have more examples just of linear function and quadratic function, and they are mainly analysis formulas.2. Students of grade 9 understand inconsistently for function expressed with three methods.3. Students of grade 9 don' t have a clear understanding for the substantive characteristics of function concept, so they can' t understand the relationship between independent variable "X" and dependent variable "Y" . Very few students put forward that when the independent variable is fixed, the dependent variable has the only number that when they judge whether an example is a function or not.4. Students of grade 9 are competent for function better.Suggestions about function concept:1. Deepen the understanding of substantive characteristics of function concept.2. Practice the transition of the three forms of function more.