Research On High School Mathematics Functions Generalization

Nowadays, the teaching of mathematics thoughts and methods hasbecome one of the important goals of mathematics teaching. Themathematical generalization is one of the mathematical thoughts, whichpermeates in almost all the knowledge points in mathematics. Function is amajor section in mathematics, which runs through the whole mathematicalteaching in high school. In high school mathematic teaching, we couldimplement mathematical generalization research in order to train, improvestudents’ mathematical thinking abilities and help students to strengthen whatthey have been learning in mathematics.This research uses high school function as an example to illustrate how toimplement mathematical generalization teaching in high school. Theresearch focuses on function’s nine latitudes and their applications in everyfunctions appeared in high school’s mathematics, which grasps the nature ofthe high school’s function. This research provides the theoretical andpractical basis for the future research of functions. The research is dividedinto five sections. The specific content is as follows:Section one IntroductionThis section mainly introduces the purpose, significance, status, methodand innovation of this mathematical generalization research.Section two The generalization of high school functions’ definitions andelementsThis section systematically generalizes high school functions’ analysisformulas, domains of definition and ranges.Section three Generalization of properties of functions in five aspectsThis section focuses on the research of generalization of properties offunctions in aspects of functional images and the image transformation,symmetrical characteristics, monotonicity of a function, periodicity offunctions and function model.Section four Conclusion Based on this research, we could conclude the following:1. In the process of mathematics teaching, teachers should show thestudents as much mathematical thought and mathematical methods tolet the student as possible, which lets students feel that learningmathematics is a process of cultivating students’ logical thinking.2. The teaching has two meanings–teachers’ teaching and students’learning. Teachers need to research how to implement generalizationmethods in their teaching practice. Moreover, students’ learningpsychological characteristics also need to be put into considerationsince any teaching method that is suitable for students’ thinkingpatterns could be regarded as effective teaching methods.3. Generalization is a philosophy, and it is a principle that should befollowed in the teaching practice, which cultivates students’ habits ofgeneralizing whatever they are learning in their school days.4. The implementation of research on generalization in mathematicalteaching mainly serves for how to solve problems in daily lives.Teachers need to be able to generalize problems and simplify thecomplicated ones, which helps students to get out of the boring andheavy workbooks and endless exercises. Moreover, teachers need touse the generalization method to help students to make knowledgetransformation as a means of consolidating the knowledge they havebeen learning.