The Research On The Teaching Of Solving Function Problems In High School

Function is a masterstroke of the high school mathematics and a hot spot of the college entrance examination. Grasping the function is nearly equivalent to mastering the high school mathematics.However, due to the complexity and abstract of function itself, the immature development of students’thinking abilities, as well as the teachers’poor understanding of problem-solving instruction, make the situation of the students’function solving unsatisfactory. Therefore, in-depth study of the teaching of solving function problems in high school has very important significance.This article discussed the theory of function problem-solving and the teaching principles of function problem-solving.Through careful reading of the function in the high school math courses, researching and analyzing of the functions in the college entrance examination of the past years, combining with my own experience of the function solving and the front-line teachers’function solving teaching experience, I put forward that function problem-solving teaching should be "highlight the key point, break through the difficulty". Domain, range, and corresponding relationship are the three major elements of function, while concept, property and image are three parts of function knowledge. To the problem-solving teaching of function, I attempt to analysis the concept, property and image of function, summarize errors and difficulties that may occur in the students’ problem solving process and explore its solution methods, also select the periodic function and convex function,which students generally believe it is difficult, to discuss how to judge and apply. In this article, two typical cases of the function problem-solving instruction are discussed,which the first one is how to apply the knowledge and methods to inequality solving teaching and the second is diagnostic error correction function.The end of the article, combined with the basic problem-solving teaching theory of function, I puts forward some function problem-solving teaching suggestions, which are to highlight the key points and break through the difficulty, to pay attention to the concept and property of the function during the teaching process, also to pay more attention to mathematical thought penetration and special function thought and numeral-form combination method of thinking, as well as to pay attention to the teaching skills on the base of outstanding the general methods...