Research On Teaching Design Of Trigonometric Function Concept From HPM Perspective

The relationship between the history of mathematics and mathematics education has emerged from becoming an independent discipline.The educational value of the history of mathematics has attracted more and more researchers' attention.It not only has important theoretical value,but also has great importance for first-line mathematics teachers.The use of mathematics history in mathematics teaching plays an important role in maximizing classroom benefits,completing teaching goals,and improving the quality of personal mathematics.Education-oriented research on the history of mathematics,teaching practice research into the history of mathematics,HPM and teacher professional development are the main research areas of HPM,which are consistent with the concept of emphasizing the cultural value of mathematics in the new curriculum reform,which requires mathematics teachers to teach Knowledge of the history of mathematics should be used reasonably in the process.Trigonometric functions,as one of the important basic elementary functions,belong to the difficult and difficult part of mathematics knowledge in high school,and the concept of trigonometric functions with arbitrary angles as the basic concept of trigonometric functions is a knowledge point that students must understand,master and use flexibly.As the content of trigonometric functions rich in historical materials of mathematics history,the concept of using trigonometric function mathematics in classroom teaching in actual teaching has not become a consensus,and even some teachers or students are repulsive.Based on this,240 students in the first grade of Longxing Senior High School were taken as the survey object.The experimental group and the control group were set up.The teaching design research under the HPM perspective was conducted for the problems in the classroom of the trigonometric function concept at any angle,in order to explore mathematics.Suggestions for the integration of history into the mathematics classroom and cognitive barriers for students to learn the concept of trigonometric functions at arbitrary angles.This article mainly carried out the following two aspects of research:1.The problems of the first grade students in learning the concept of trigonometric functions of arbitrary angles.Through the classroom observation method and questionnaire survey method to learn the students 'learning methods and concepts,andanalyze the question type,difficulty and other factors on the students' flexible use of the concept of arbitrary angle trigonometric functions,and in the form of interviews with teachers Questions and answers to understand the feelings and suggestions of different teachers on the teaching process under different teaching modes.2.Teaching design of the concept of arbitrary angle trigonometric function from the perspective of HPM.Aiming at the teaching status of the concept of arbitrary angle trigonometric functions in practical classrooms,through concrete analysis through examples,problems are found,focusing on how to integrate the history of mathematics into teaching materials,and the research design of the concept of arbitrary angle trigonometric functions based on the history of mathematics is carried out.Under the two teaching modes,comparatively analyze the differences of students,especially whether the classroom using the history of trigonometric mathematics produces different learning effects,and then analyze the impact of the use of mathematics history from the perspective of teachers.