Research On The Teaching Of High School Mathematics Concept Courses From The Perspective Of PCK

In terms of mathematics,PCK theory mainly consists of five subsystems: specific mathematics knowledge,general pedagogical knowledge,knowledge about students and situation and technical knowledge.This is the theoretical basis of this study.PCK theory,which is related to the teaching design of mathematics concept courses,emphasizes that teachers should present their existing mathematics knowledge to specific students in their own unique ways,select the most suitable teaching methods and strategies according to the actual situation of students.In order to understand the teaching situation of trigonometric function concept course guided by PCK,the author first interviewed the mathematics teachers in the internship school.In order to make the interview process real and effective,the author adopts a semi-open interview method,and lists the interview topic table according to the above five subsystems.The interview content focuses on teachers' understanding and application of PCK theory.Based on the interview results and analysis,the author finds that the teaching age of teachers is not directly proportional to the mastery of the PCK theory,but there is a positive correlation with the teachers' ability to use the PCK theory.The higher the teaching age,the better the application of PCK theory,the more thorough understanding of subject knowledge,the more comprehensive understanding of students,and the more appropriate use of teaching strategies.Then,the author makes further research on using PCK theory to guide the teaching of the concept of trigonometric functions.On the one hand,because textbooks are the most important and powerful information medium for knowledge-giving activities in school education,it is necessary to study the textbooks on the concept of trigonometric functions.After analyzing the contents of the "triangular function concept" section of the human education edition,Soviet education edition,and North Teacher's edition from textbooks and cases,the author found that the three editions each have their own advantages in different constituent elements of the PCK theory.On the other hand,because the design of teaching presupposes the bilateral activities of teachers and students,which directly reflects teachers' educational ideas,in order to really use PCK theory to guide the teaching of mathematics concept course,teachers need to write a teaching design from the perspective of PCK theory.Combined with the analysis of three versions of teaching materials and cases and other materials,the author wrote a teaching design of "trigonometric function concept of any angle",hoping to arouse the high school mathematics teachers' attention to the theory from a new perspective,and constantly improve the level of teachers' professional development.Finally,the author puts forward some thoughts on how to improve the PCK theory of mathematics teachers,hoping to effectively promote the professional development of teachers.Compared with previous studies,the innovation of this study lies in that it not only combines PCK theory with the specific topic of trigonometric function concept,but also to analyze the advantages and disadvantages of this topic from the perspective of PCK theory in the textbooks of human education edition,Jiangsu Education Edition and Beishi edition.In addition,the author has made a complete teaching design of "trigonometric function concept course at any angle" under the guidance of PCK theory by referring to excellent teaching plans,listening to the opinions of key teachers and combining with his own experience,hoping to promote the teachers' attention to the theory and improve the teaching of concept course to a certain extent.The study of PCK theory is of great significance not only to students and teachers,but also to the development of mathematics.On the one hand,PCK theory can guide teachers' teaching correctly and efficiently,thus promoting students' learning;On the other hand,PCK theory provides a growth platform for the development of mathematics,making mathematics educators look at mathematics,analyze mathematics and apply mathematics from a brand-new perspective,and providing useful help for our mathematics classroom teaching.