Practical Research On High School Mathematics Unit Teaching From The Perspective Of HPM

Nowadays,more and more attention is paid to the penetration of mathematics culture in mathematics classrooms.There are more and more cases where mathematics history is integrated into teaching design,and the value of mathematics history is more and more reflected.Therefore,in classroom teaching,the selection,integration method and The case analysis from the perspective of HPM is worthy of more in-depth study.With the deepening of the curriculum reform,the overall teaching design of the unit has also become a big trend.Its purpose is clear,and its significance lies in the ingenious methods used in the teaching process as much as possible.It takes relatively less time,but the effect is better.In this paper,the complex number unit is selected,not only because it is an important operation object,but more importantly,it can organically link trigonometric functions,algebra,vectors and plane geometry together,fully reflecting its wide applicability.However,the knowledge of complex numbers is relatively abstract,and students have certain cognitive barriers to the generation of imaginary numbers,the meaning of symbols and the expansion of complex numbers.In view of this,on the basis of studying and analyzing the existing literature,this paper compiled the "Questionnaire on the Learning of Mathematics History" and "Questionnaire on the Knowledge of Complex Number Units before and after the Test".A survey was conducted on second-year senior high school students in a city and interviews were conducted with relevant teachers.By comparing the results of the pre-and post-test surveys of students and the analysis of the interview results between teachers and students,combined with the overall teaching design of HPM’s plural units,the following conclusions are drawn:1.Through the questionnaire survey,it was found that students have certain cognitive barriers to the concept of imaginary numbers and the generation of the symbol "i",they cannot understand the necessity of introducing imaginary numbers,and they cannot flexibly use the algorithm of "i".Some related concepts and theorems are not fully understood,understood,and applied in place.2.By studying and screening historical materials,reproduce the historical occurrence and development of the concept of pluralism.First,through the introduction of the impossible problem of the "flat-topped pyramid",students have a conflict in cognition and a strong interest in the learning of complex units;The stories of imaginary numbers,Bombelli and imaginary numbers allow students to understand the development process of complex numbers,as well as the application of complex numbers such as Wessel’s geometric representation of complex numbers,Gauss’ s complex plane,and Hamilton’s algorithm,so that students can naturally understand the concept of complex numbers,algorithm and complex number representation;finally,let students experience the puzzles and problems encountered in the development of complex number knowledge,and learn the strong quality and perseverance of mathematicians.3.Through the analysis of students’ questionnaires and interview results and classroom case teaching,students generally reflect that the organic integration of plural unit teaching into the history of mathematics has not only aroused students’ enthusiasm for learning,but also stimulated students’ desire for knowledge.More importantly,in the new knowledge In the process of exploration,the understanding of the mathematical ideas behind the knowledge points has been deepened.At the same time,mathematical literacy has been further improved,and core literacy such as intuitive imagination,logical reasoning,and mathematical operations have been cultivated.4.Through the analysis of the interview results of teachers,the organic integration of the history of mathematics into the plural units for teaching,the requirements for teachers are higher,and teachers need to pay attention to the popularization of mathematics history in classroom teaching,because only by letting students know why,Only by understanding the origin and value of knowledge can better stimulate their interest in learning and improve their innovative ability;at the same time,teachers should devote more attention to teaching,and explore more and better HPM teaching cases related to the teaching content.It enriches students’ learning content and stimulates their enthusiasm for inquiry.