Research On The Instructional Design Of "Trigonometric Functions Of Arbitrary Angles" Concept Based On Mathematical History

The new curriculum reform emphasizes the cultural value of mathematics and advocates the integration of the history of mathematics into the teaching of mathematics,while the concept of "trigonometric function of arbitrary angles" has undergone a long process of development,which inevitably contains a large number of contents of mathematical history.However,based on the history of mathematics,the concept of "trigonometric function of arbitrary angle" has not been widely concerned by the senior high school mathematics teachers,and the teaching status is not completely satisfactory.Therefore,it is of great significance to carry out the teaching design research of the concept of "trigonometric function of arbitrary angle" based on the history of mathematics.This paper mainly studies the following aspects:1.The history of the development of trigonometric functions.Through consulting relevant data and sorting out the historical evolution process of trigonometric function,this paper lays the foundation for the analysis of the teaching status of "triangle function of arbitrary angle" and the research of "triangle function of arbitrary angle" based on the history of mathematics.2.The teaching status of the concept of trigonometric function at arbitrary angles.First,we use the method of classroom observation to compile "the triangle function of arbitrary angle" concept teaching mode observation record table.Secondly,with the help of this table,the teaching of 3 teachers in any selection is observed in class,and the main teaching activities of teachers in every link are recorded in time;finally,according to the recorded classroom observation table The present situation of "trigonometric function of arbitrary angle" is summarized and the main problems are pointed out on the basis of the history of Mathematics:(1)introduction of concept: the necessity of understanding is not in place;(2)concept formation: extension is too hard;(3)conceptpresentation: "unit circle fixed sense method" has not been paid attention to.3.Instructional design of the concept of trigonometric function of arbitrary angle based on the history of mathematics.In view of the existing problems in the teaching situation of "trigonometric function of arbitrary angle",under the guidance of relevant theories,the study of "triangle function of arbitrary angle" based on the history of mathematics is carried out and applied to practical teaching.