Teaching Design And Practice Of The Cultivation Of High School Students' Intuitive Imagination Literacy From The Perspective Of HPM

History and Pedagogy of mathematics(HPM)is one of the hot topics in recent years.The educational value of the history of mathematics is clearly reflected in the curriculum standards and the compilation of textbooks.Intuitive imagination is one of the six core qualities proposed in the Mathematics Curriculum Standards for General Senior High School(2017 Edition).It is the cornerstone for students to observe the world with mathematical eyes,and has a huge influence and role in the development of students' lifelong education.As a front-line teacher,we are faced with the problem of how to implement it in place.It is a good choice to design and practice it from the perspective of HPM.By drawing on the thoughts and wisdom of previous mathematicians,we can gradually improve students' intuitive imagination with relevant geometric models and classical counter examples.Integrating the previous mathematical thought and scientific spirit into the classroom is helpful for students to establish a correct outlook on life and values,which can promote students to form a logical and rigorous philosophical thinking ability and help students to think about the world with the dialectical materialist world outlook and methodology.Based on these backgrounds,this article uses literature analysis,testing,statistical analysis and other research methods to specifically study the following two issues:Question 1: Is it feasible to cultivate the intuitive imagination literacy of high school students from the perspective of HPM?Question 2: How to cultivate the intuitive imagination literacy of high school students from the perspective of HPM?Based on the orientation of developing student,cultivating the spirit of science and innovation and improving the core accomplishment of mathematics discipline,we take the teaching of senior high school as example to collect the historical materials related to the basic inequality,the sine formula of the sum of two angles and the definition of prism for teaching case design.And then,we carry out teaching experiments and studies the feasibility of cultivating the intuitive imagination accomplishment of senior high school students from the perspective of HPM.The experimental process is as follows: First,by studying relevant literature and based on relevant historical materials of mathematics,the teaching cases reflecting intuitive imagination in concept class,formula class and theorem class from the perspective of HPM were designed,as well as the pre-test and post-test papers of intuitive imagination ability.Secondly,the experimental study is carried out for one year in high senior school of Wanzhou District,in which the class 1(8)is the experimental group and the class 1(7)is the control group.According to the designed teaching cases,the present situation of the students' intuitive imagination in the two classes was tested before the experiment to control the related variables.The intuitive imagination ability of the students in the two classes was tested after a one-year experiment.SPSSAU statistical software is used to compare and analyze the data of the pre-test and post-test of the two classes,and on this basis the analysis and summary are made.Finally,based on the changes of the experimental pre-test and post-test data,a comparative analysis was conducted from the horizontal and vertical levels,and reasonable suggestions for the cultivation of intuitive imagination literacy were given from the perspective of HPM..The main conclusions of the experimental study are as follows:1.The pre-test data of the experimental group and the control group show that the intuitive imagination ability of the two classes is basically the same.With the advance of teaching practice,the improvement of the intuitive imagination of the experimental group is significantly higher than that of the control group.2.By analyzing the intuitive imagination ability of the two classes before and after the experiment,it is found that the intuitive imagination of the experimental group has been significantly improved,while the intuitive imagination literacy of the control group has not changed significantly.3.When teachers implement the teaching of cultivating intuitive imagination from the perspective of HPM,they should select appropriate materials and adopt the teaching methods of integrating mathematical history,multiple strengthening of conceptual theories and reasonable application of information technology.This study shows that teaching from the perspective of HPM is helpful to improve students' intuitive imagination.The cultivation of core qualities from the perspective of HPM can carry forward the wisdom of predecessors in today's students to the greatest extent.