Research On The Teaching Design Of High School Mathematics Concept Course Based On PCK Theor

Mathematical concept is an essential reflection of human beings on the spatial form and quantity relationship of the real world,and is a special way of mathematical thinking,including mathematical theorems,definitions,formulas and inferences,etc.,which is the core content of students’ mathematical learning.The concept of function is one of the most important basic concepts in high school mathematics,which is not only an important basic knowledge in high school mathematics,but also an important tool and way of thinking for problem solving.In secondary school textbooks,content related to function ideas and functional models runs through the entire mathematics teaching.In addition,due to the particularity of the order of content arrangement of function textbooks,students’ learning of function concepts will have a great impact on the learning of related content later.For the teaching and research of mathematical concepts,although there are many research results at this stage,due to the complexity and high abstraction of mathematical concepts,there are still many research perspectives to be in-depth.The full name of PCK theory is Pedagogical Content Knowledge,which is defined as a special integration of teachers’ personal teaching experience,subject content knowledge and pedagogical knowledge,which refers to teachers’ transformation of subject knowledge into the most acceptable teaching knowledge by students or the "transformation wisdom" contained therein,and is also one of the important indicators to judge teachers’ professionalism.For mathematics teachers,PCK theory is mainly composed of the following types of knowledge: knowledge about mathematics,general pedagogy,curriculum knowledge,knowledge about students,knowledge about creating teaching situations,etc.This paper aims to integrate PCK theory into the teaching design of mathematics concept courses,advocate teachers to interpret teaching materials and design teaching plans from the perspective of PCK theory,and provide a certain practical reference for teachers to transform subject knowledge.The research methods of this paper include literature research,interview method and comparative research method.The main research content in the early stage includes the detailed analysis of PCK theory,concept course teaching and teaching design practical research studied by domestic and foreign scholars,and determines the research breakthrough by exploring the correlation between the two.In terms of practice,this paper carefully interprets and analyzes the content of the "concept of function" topic textbooks and high-quality teaching cases in the People’s Education Edition(2019A Edition).He also discussed with 20 subject experts,teachers and front-line teachers how to teach and prepare lessons on the topic of "The Concept of Functions" in the new textbook.The SPSS reliability analysis of the discussed data and collected data is carried out,and the teaching design of "function concept" is drafted with PCK theory as the center of the textbook,and the proposed teaching design is later analyzed by actual teaching and interview teachers,so as to test the feasibility of the study and summarize the "general" conclusions.It is found that interpreting teaching materials and understanding students from different knowledge perspectives of PCK theory is of great help to improve the integrity of teaching design,and can help teachers to deal flexibly with teaching problems in actual teaching as much as possible.Because the PCK theoretical level of teachers has a great impact on students,teachers of different ages have different PCKs,only in subject knowledge(PK)and teaching knowledge(CK)there are significant differences,young teachers have more advantages in teaching knowledge(CK),mature teachers have a better understanding of subject knowledge(PK),and this directly affects the focus of teachers’ teaching and the problem points of student learning.Teachers with a high overall level of PCK theory will have a more thorough understanding of teaching materials and instructional design,and will be more comfortable in controlling and adjusting the classroom atmosphere,so it is necessary to strengthen teachers’ learning of advanced learning cognitive theory.In addition,it is crucial to find that students’ learning status affects learning outcomes in actual teaching,and teachers should reasonably use PCK theory to formulate reasonable pre-class,in-class and after-class learning plans for students to enhance students’ enthusiasm for learning.