A Case Study On The Cognition Of Trigonometric Function Auxiliary Angle Formula By Practical Mathematics Teachers

Teachers' cognitive understanding of mathematics knowledge directly affects whether teachers are competent for teaching tasks,and it is also one of the important contents of teachers' professional development.For a long time,mathematical cognitive understanding has been a hot topic in the field of pedagogy.Nowadays,many researches on mathematical cognitive understanding focus on the meaning,characteristics and level of mathematical cognitive understanding.However,there is little research on the process of cognitive understanding of a specific mathematical knowledge.In particular,there is little research on the cognitive understanding of trigonometric function auxiliary angle formula by practical mathematics teachers.On the basis of previous research theory,this paper combines the assistant angle of trigonometric function by practical mathematics teachers.The present situation of formula teaching,the following three questions are studied:(1)Through a case study,this paper explores the cognitive understanding process of the auxiliary angle formula of trigonometric function by practical mathematics teachers.(2)the analysis of the factors that affect the cognition and understanding of the angle formula of trigonometric function by the teachers of practical mathematics.(3)some reasonable suggestions on the study of the auxiliary angle formula of trigonometric function for practical mathematics teachers are put forward.In this paper,a practical mathematics teacher is used to study the process of cognitive understanding of the "auxiliary angle formula of trigonometric function" by the method of case study.It is concluded that the practical mathematics teachers have some characteristics in the process of cognitive understanding of the "trigonometric function auxiliary angle formula" : 1)the practical mathematics teacher is lazy in the process of cognitive understanding of the "trigonometric function auxiliary angle formula".2 practical mathematics teaching Teachers' cognitive understanding of "trigonometric function auxiliary angle formula" is a passive process.3.Lack of reflection on the cognitive understanding process of "trigonometric function auxiliary angle formula" by practical mathematics teachers.4 practical mathematics teachers' understanding of "trigonometric function auxiliary angle formula" is assisted by trigonometric function.The cognitive comprehension process of the auxiliary angle formula "seeks to enrich" Related knowledge.Through a seven-week follow-up survey,it is found that the factors that influence the teachers' cognitive understanding of the "trigonometric function.Auxiliary angle formula" are: first,the lack of the relationship between the new and the old mathematics knowledge.Second,the practical mathematics teachers are not familiar with the whole module of mathematics knowledge.Third,practice mathematics teachers lack of after-school reflection.Fourthly,the influence of examination-oriented education on mathematics teaching in senior high school.Fifth,do not pay attention to reading literature materials.This paper puts forward some rich suggestions on how to improve the professional level of practical mathematics teachers.