Research On Teaching Design Of Arbitrary Angle Trigonometric Function Definition

Arbitrary angle trigonometric definition is one of the core concepts of high school mathematics and has a high value of teaching research.The collection,study and review of the literature were carried out from the perspectives of“the teaching of the definition of arbitrary angle trigonometric functions”,“the unit circle definition method and the ratio definition method”,and“the unit circle and the triangle function line”.These literatures are instructive,instructive,and instructive for the study of the teaching design of the definition of an arbitrary angle trigonometric function.An in-depth study of the teaching materials of the People's Education A edition was conducted.It was found that the definition of the trigonometric trigonometric function has two defects,and it was modified and improved.A questionnaire survey was conducted on the four classes of students in the first grade of high school.The results showed that there was no significant difference in the scores of boys and girls;there were significant differences in the scores of liberal arts and science students;most students failed to accurately understand the nature of the definition of any angle trigonometric function.The interviews with five first-line mathematics teachers showed that the transformation,understanding,and fusion between the unit circle definition method and the ratio definition method are difficult to define the definition of an arbitrary-angle trigonometric function.Considering the thoughts caused by literature research,investigating the problems in the research,and based on the theories of problem-driven theory,APOS theory,mathematics core literacy and so on,three teaching design cases of arbitrary-angle trigonometric functions are defined,that is,problem-driven mathematics.Instructional design,eight-step instructional design based on APOS theory,mathematics instructional design from the perspective of core literacy;an analysis of the classroom records of three famous teachers;and suggestions for the integration of the unit circle definition method and the ratio definition method.