Discussion And Research About The Concept Of Function Teaching Under The New Curriculum Standard

New curriculum standard has been implemented for about ten years. Under the guidance of the newteaching concept, corresponding changes are found in contents, requirements, arrangements of teachingmaterials. How about the changes in teaching methods and what’s the status of function concept andrelevant contents for students to flexibly use them are unknown. According to the requirements of"curriculum standard", function study runs through the whole period of high school mathematics.Function in high school is the core of high school mathematics, at the same time it is the base of advancedmathematics. However, grasping the concept of function is the base and key to well learn function. Butbecause function concept is rather abstract, students who are new to high school are difficult to describe thevariable quantity by set point and to master the mathematic thoughts and methods contained in functionteaching, such as classification discussion, symbolic-graphic combination, the equivalent transformation,the functional equation thought and so on. However, due to limited time of classroom teaching in highschool, function classroom teaching in high school should be finished teaching tasks in given time asefficient and qualified as possible. Learning function concept well is the precondition of learning functionrelated contents, so the author has spread the study of function teaching based on the study of functionconcept teaching.After reading a large number of literature and materials, first, the writer summarized the developmenthistory of function concept and then analyzed the changes of function contents and requirements offunction teaching in New Curriculum Standard. Also the theoretical base of function concept and basictheory of practical teaching in high school were analyzed respectively from teaching methods and contents.Meanwhile the survey about the relevant contents of logarithmic function and inverse function byquestionnaire selected teachers and students in two different high schools. But the survey showed therewere a series of difficulties in teaching function for teachers based on the requirements of new curriculumreform, difficulties include the understanding and application of function concept for students, more oldteaching methods were still adopted by teachers etc. And the questionnaire about students also reflectedtheir weakness in application of function. Aiming at these phenomena, the author has designed the function concept teaching case after careful analysis. In the case design, first of all, the teacher encourages thestudents to discuss the textbook examples to cultivate their ability of cooperation and communication;Secondly, the author emphatically introduces the thoughts of model, students may feel more difficult toestablish the mathematical model, so when introducing the concept of function, the author will guide thestudents to strengthen their understanding of mathematical model of thought at the same time; Thirdly, theauthor makes full use of the information technology to support this lesson, such as the multimediaanimation artillery firing and the Geometer’s Sketchpad to draw the function’s image.Paper conclusions:(1) Teachers should include the process of function concept formed when teachingthem function, that is " the foundation lies in exploration of roots”, thus students will deepen theirunderstanding of function concept.(2) Teachers should link mathematics with actual life in teachingprocess so as to inspire more interests of students to learn mathematics as well as its practicality.(3)Teachers ought to lead students in good time in order to gradually cultivate their logical thinking ability byway of using guidance instead of teaching step by step.(4)“The combination of graphics with form mustbe kept in mind." Teachers should often guide students to consciously use image to solve relevant functionquestions.(5) Keep in mind of thoughts and methods. Teachers should have the mind leading students torationally apply thoughts of combination of graphics and form, classification discussion and functionequation in function concept teaching.(6)Summarize the key points, lines, aspects as a whole. It is ofimportance for teachers to lead students to summarize the key contents after studying the whole functioncontents.(7)“Exercises training is necessary.” It is really necessary to pick carefully some typical problemsafter class finished. In addition, attention should be paid to function model and application in teachingprocess. The new curriculum standard has been implemented for many years and good effects are obtainedby teachers’ exploration. However, to get better teaching result, we should improve thinking models andmethods of teaching function in high school, strengthen the combination of teaching with informationtechnology, and enhance students’ abstract thinking and innovative abilities.