Analysis Of The Difficulties Of Periodic Function Concept And Design Research On Teaching

The result of "The ten difficult concepts in mathematic education of senior high school survey" which was conducted by Songjiang District, Shanghai, shows that in all the mathematical concepts of high school, "the periodic function concept’ has been listed as one of the most difficult ten mathematical concepts by teachers and students. The author together with the group members, has further difficulty analysis and research on instructional design for the difficult concept of "periodic function" in order to provide help for the current periodic function concept teaching and explore a solution to break through the difficulties. Based on the literature research, the author compiled a test volume, carried out a questionnaire survey and interviewed 30 special grade or senior teachers, found out the difficulties existed in periodic function and the teaching strategies to solve these difficulties, and made teaching design research to solve these difficulties in two parallel classes of grade one of two rounds.The survey result shows that from teachers’perspective, when students study the periodic function concept, the following understanding obstacles and difficulties are existed:1.Having difficulties when understanding "arbitrary"^ "existence" and other key words in the concept; 2. Can’t be separated from the trigonometric function model; 3. Having difficulties in using formula f(x+T)=f(x); 4. Recognition of image features is not in place.The existence of the wrong understanding is as followed:1. There must be a minimum positive period of a periodic function; 2. The domain of the definition of a periodic function can be a bounded set; 3. The T that satisfies f(x+T)= f(x) is the periodic; 4. There is only one periodic of a periodic function; 5. Only trigonometric functions are periodic functions; 6. It is considered that the image characteristic of the periodic function is "repetition" or "regular".According to the research results of the teaching design, the teaching strategies of periodic function concept are as followed:1. In the teaching of the concept of periodic function, using a large number of positive cases, counterexamples to explain many key points of the periodic function concept, and changing abstraction to concrete, can help students understand the concept.2. By using the combination of image and formula method, can enable students to understand the periodic function from multiple perspectives.