Research On Problem Solving Of Mathematical Functions And Derivatives In Senior High School

Function is the most basic concept of modern mathematics.It is the most basic mathematical language and tool to describe the relationship and laws of variables in the objective world.It plays an important role in solving practical problems.Functions occupy a very important position and role in high school mathematics,and derivatives are an important tool for us to study the properties of functions.Using derivatives to study the properties of functions is a skill that all high school students must master.Functions and derivatives are closely related and closely linked.They occupy a considerable amount of points in the mathematics of the college entrance examination,and are difficult for most high school students.It is very necessary to summarize the related problem-solving skills of functions and derivatives.The main contents of this research are:(1)through a questionnaire survey of students,to know the students' mastery of functions and derivatives;(2)through interviews with front-line teachers,to know that front-line teachers have a lot of knowledge about functions and derivatives.Views related to learning;(3)By analyzing the real questions of the college entrance examination in recent years,we can know the score of functions and derivatives in the mathematics of the college entrance examination,the distribution of the questions,the types of questions that are often taken,and the mathematical ideas of the regular exams;(4))summarizes the important problem types of functions and derivatives in the mathematics of the college entrance examination and gives corresponding problem-solving strategies.The main conclusions of this research are:(1)mathematical ideas such as number-form combination,classification discussion,function and equation,transformation and reduction are permeated in the problem-solving process of functions and derivatives;The related problem types such as nature,periodicity,symmetry,parity,extreme value,zero point,and tangent are summarized;(3)The constant establishment parameter problem is classified and the corresponding problem-solving strategies are summarized;(4)The application of functions in inequalities,number sequences,and analytic geometry is studied.