A Study On Cultivating Students' Ability To Solve Functional Problems

"Standards for Senior High School Mathematics Curriculum"(2017 Edition)takes the development of students' application awareness as one of the new curriculum concepts,emphasizes the practical background of basic content into the high school mathematics curriculum,emphasizes the application value of mathematics,and explicitly requires mathematical modeling.Learning activities,special courses are required for some important applications to promote students'formation and development of mathematics application awareness.After three years of teaching in the first line,the author found that the ability of high school students to solve mathematics application problems is quite different from the requirements of new curriculum standards.Function is the most important content of high school mathematics.The application of function involves many aspects.The ability to improve students'application of solving function helps to embody the concept of new curriculum standard.This research is mainly devoted to exploring the factors that influence the ability of high school students to solve functional application problems.The article uses literature analysis method,questionnaire method,comparative analysis method,teacher-student interview method and so on.The types of functions learned by high school students are divided into five types,quadratic functions,power functions,exponential functions,logarithmic functions,and trigonometric functions.The survey was conducted from both teachers and students,and different questionnaires were set up for teachers and students.The teachers conduct research on the four factors of teaching age,education,degree of emphasis and teaching methods.The students conduct research on the four factors of psychological factors,importance,calculation habits and knowledge reserve.The standard of measurement is a set of test questions designed by the backbone teachers.Finally,combined with the teacher-student questionnaire and the scores of different types of students,the mathematical statistics method is used to find out the factors that affect students' ability to solve different types of functions.The study found that the degree of attention and knowledge of the students in the quadratic function,the degree of teacher's attention will have an impact on the students'ability to solve problems.In the power function,exponential function,and logarithmic function,the degree of attention,psychology,and knowledge reserve of the students,the way the teacher teaches,and the degree of emphasis have an impact on the students'ability to solve problems.In the trigonometric function,the students'calculation habits,degree of emphasis,and knowledge reserve,the teacher's teaching age and the degree of emphasis have an impact on the students' ability to solve problems.Based on the results of the study,some suggestions were given for each type of function application and some successful teaching cases were presented.