Teaching Research On The Concept Of "trigonometric Functions Of Arbitrary Angles"

The concept of trigonometric function is a special type of function,and as the core of the knowledge system of trigonometric function,the concept of "trigonometric function of arbitrary Angle" is an important basis for further study of induction formula,trigonometric identity and image properties of specific function type.However,it has been a long-standing problem for high school students to understand the concept of trigonometric functions.Students do not understand why trigonometric functions are defined in this way,do not understand the connection and difference between this definition and the acute Angle trigonometric functions they have learned in junior high school,and do not understand the use of this definition after learning it.In order to solve the difficulty of learning arbitrary Angle trigonometry,we must thoroughly analyze the teaching textbooks and teaching methods,and re-examine the previous classroom teaching of trigonometry.This paper mainly studies from the following two aspects:1.Understanding and analysis of the concept of trigonometric functions.Through literature analysis,combing the domestic to the " The Mathematics Curriculum Standard of General Senior School(2017 edition)" with the guidance of a new batch of high school mathematics teaching textbook and some of the people of arbitrary Angle trigonometric function concept version of the old teaching textbook,the content of the sort of arbitrary Angle trigonometric function is introduced in the textbooks and describe details discussed and reviewed,and analysis the contents of the reference of the handful of trigonometry foreign textbooks,summarizes some of arbitrary Angle trigonometric function concept teaching overall train of thought,the concept of teaching process,in order to offer the reference other direct use in teaching or research.2.Teaching design and experimental research.Based on the analysis of a large number of teaching textbooks,combined with the literature analysis and questionnaire survey found in the trigonometric function teaching problems,based on “Conceptual Fields” theory,a new teaching design of arbitrary Angle trigonometric function is formed and implemented in the actual classroom.Through the method of questionnaire survey and interview,the students are studied to analyze the students' grasp of the concept of arbitrary Angle trigonometric function through this design,so as to illustrate the effectiveness and feasibility of this new design.In addition,through interviews with teachers,we understand some views of teachers as classroom implementers on the new teaching of trigonometric functions.Through the above research,the following suggestions are concluded for teaching arbitrary Angle trigonometry:(1)Classroom teaching is not necessarily in accordance with the arrangement and content of the textbook;(2)Introducing teaching from the actual situation can help students quickly enter the learning state;(3)It is recommended not to introduce it from acute Angle trigonometry.The relationship between it and acute Angle trigonometry in junior high school is proposed after learning the concept of arbitrary Angle trigonometry.(4)As far as possible,introduce the number lines of triangular correspondence in the teaching links,and deepen students' understanding of concepts through geometric intuition;(5)The use of Sketchpad teaching tools is added to facilitate dynamic demonstration and help improve classroom efficiency.