| Hyperbola is the core content of high school mathematics,is an important part of conic curve,is an important content to inspect the knowledge of students to master,but also the annual college entrance examination required content.However,since hyperbola is abstract in concept,equation or property,the connection between knowledge points is complicated,and the teaching method of teachers is relatively simple.In view of this,on the basis of investigation and research on the status quo of hyperbola in high school students’ learning,it is of theoretical significance and practical value to study the teaching design of hyperbola from the perspective of HPM.In order to make students better understand and master the knowledge of the hyperbola,and learn to apply it to solve the practical problems in life,in this paper,on the basis of combing existing literature,through the establishment of questionnaire and interview outline,for a certain middle school high school students learning situation of hyperbola,has carried on the interview,to teachers’ teaching situation under the perspective of HPM,Starting from the whole of hyperbola teaching design,the history of hyperbola is reconstructed,and the whole teaching design of hyperbola integrated into the history of mathematics is designed.The research conclusions are as follows:First,in the practical teaching of hyperbola,teachers are used to introducing the definition of hyperbola by analogy,drawing by mechanical drawing method or zipper principle,deducing equations according to the method of "twice square" in the textbook,and students are used to passively accepting.However,starting from the history of the concept of hyperbola to pursue the source of teaching,on the one hand changed the teacher’s teaching method,on the other hand,students after making clear the origin of the concept,take the initiative to accept the concept and nature of hyperbola.At the same time,it improves students’ motivation to explore knowledge and makes mathematics classroom more dynamic.Second,teaching design is the starting point of class,good teaching design has good teaching effect.The teaching design value of hyperbola from the perspective of HPM lies in:reproducing the historical situation,breaking conventions,conforming to the cognitive rules of students,stimulating students’ interest in learning,arousing students’ enthusiasm for learning,cultivating students’ core qualities and correct values,and showing the beauty of mathematics.Third,from the perspective of HPM,hyperbola teaching design is mainly designed with the reconstruction of history as the main line.In this paper,the concept of hyperbola is introduced through the model of dendlin’s double sphere from a historical point of view to break the isolation between the definition of hyperbola and the image and make it less strange and difficult for students to learn.It is more suitable for students’ cognitive level of hyperbola to deduce hyperbola equation by using "square deviation method" adopted by Young(1830)or L ’Hopital’s "sum difference technique".In the teaching of the simple geometric properties of hyperbola,the difficulties and obstacles encountered by mathematicians about the eccentricity are described,so as to eliminate students’ doubts about the provisions of eccentricity and learn happily.As we all know,the history of mathematics is not only for history and mathematics,but also for education.The teaching design cases from the perspective of HPM are becoming more and more abundant and popular with students.Further developing better HPM teaching cases is one direction of our efforts and also one of our responsibilities.It is no longer an empty talk to truly integrate the history of mathematics into the classroom. |
