Research On Several Types Of Maximum Or Minimum Problems In High School Mathematics Teaching

The maximum or minimum problem is an important part of high school mathematics,and it is also a hot topic in the college entrance examination.The maximum or minimum problem is often combined with the knowledge of other chapters,such as inequalities,functions,sequences,geometric figures,conic curves,etc.,to test students’ mastery of related concepts,theorems and properties.The knowledge of the maximum or minimum problem is widely distributed,with many types,strong comprehensiveness and large difficulty span,which brings great challenges in teaching and learning.In this paper,the maximum or minimum problem systematically classifies and connects the maximum or minimum problem according to the development of students,and gradually explores from the explanation of exercises to the expansion of the maximum or minimum problem.There are six main aspects: First,through the research background and related literature review,the new curriculum reform in China and foreign education reform,contact China’s middle school students in the maximum or minimum problem of learning to explain the theoretical and practical significance of the study.Second,based on learning theory and educational thought,such as Comenius’ educational thought and the theoretical basis of meaningful learning,life learning and constructivism,it emphasizes that learning should be based on students’ original knowledge and experience to guide in-depth learning.Thirdly,it introduces the distribution and application of the maximum or minimum problem in learning through common questions,that is,to provide students with some problem-solving skills,and also to provide focus for the research direction of the maximum or minimum problem.Fourthly,the relevant basic concepts are introduced,including approximation,limit,functional derivative and so on.Fifth,determine the main types of research on the maximum or minimum problem.(1)Cauchy inequality,from the basic inequality,the relationship between quadratic function and Cauchy inequality to introduce the maximum or minimum problem in the comparative relationship;(2)Derivative and Taylor expansion,through the definition of derivative and Taylor expansion to determine the important position of function in the study of the maximum or minimum problem;(3)trigonometric function,through the problem solving skills and Euler formula to explain the conversion relationship between trigonometric function and other functions,which also makes the complex trigonometric function to solve the maximum or minimum problem to provide new ideas;(4)the objective function,through the introduction of linear programming and Lagrange multiplication,and the application of unconditional extreme value and conditional extreme value in learning and life,provides the corresponding solution to the actual maximum value problem.(5)Euler tour and Hamilton circle,they are the maximum or minimum problem in the trade-off of interests in life,such as the least cost,the shortest distance,the least time-consuming and so on,but also the embodiment of mathematical life.Sixth,by introducing the mistakes that are easy to occur in the knowledge learning and problem solving skills of the maximum or minimum problem,it helps students to think,migrate and consolidate the knowledge related to the maximum or minimum problem.This paper hopes that the research on the maximum or minimum problem can help teachers to teach from multiple perspectives,help students to study and explore in depth under the existing learning background,stimulate students’ interest and motivation in learning,and thus promote the healthy development of mathematics education.