Difficulties Of Function Concept And Design Research On Teaching

The result of "The ten difficult concepts in mathematic education of senior high school survey" which conducted by Songjiang District, Shanghai, in 2012 shows that the function concept is one of the most difficult concepts recognized both by teacher and students. Based on the result, this paper further study the difficulties and teaching design of function concept. The study includes the problem that what is the function concept cognition of students and where the misunderstanding exist on the basis of knowledge learned in their junior middle school. In the mean time, this article also analyzes the difficult point of function concept during class from the perspective of math teachers who is investigated by the author. Finally, the paper, in solving the difficulties of function concept, carries out a teaching design of function concept through the discussion and survey of teachers.In this paper, the investigation of 127 senior high school freshman’s understanding on the function concept learned in junior middle school, finds that only a small number of students can describe the correct definition. And the misunderstanding can be summarized as follows:1. Believing that the function is the equation with two unknown numbers; 2. Believing that the image of function has some rule to follow; 3. Believing that piecewise function is multiple functions; 4. Believing that a function must be a specific function.The results of teacher questionnaire and interview shows that the majority of teachers would like to choose definition and symbols of function as the teaching difficulties during the class. In addition, they prefer to choose "everyone", "the only" and "corresponding" as the key words in concept of function.Through the analysis of the concept of function, analysis of the various countries of the function concept teaching, and the questionnaire and interviews of teachers, the author of this paper carries out the teaching strategy of function concept. The strategy should focus on analyzing the concept of function as well as the multiple examples. Through the analysis of function concept, let student experience the "action", "program" and "object" in the theory of APOS, and ultimately form a complete "image" of function concept. The author cooperating with a teacher from study group practiced this teaching strategy twice, and for each time, the students were tested and discussions were conducted after class, which carries out the completion of final teaching design.