Research On The Teaching Of Acute-angle-trigonometric Function From The Perspective Of HPM

Acute trigonometric function is one of the most important contents and difficulties in middle school mathematics teaching.It is the basis of learning arbitrary trigonometric function in high school mathematics and the content of entrance examination in junior high school every year.In the preface of Mathematics Curriculum Standard for Compulsory Education（2011 Edition）,it is mentioned: "Mathematics is an important part of human culture,and mathematical literacy is the basic literacy that every citizen in modern society should possess." The humanities component in the history and development of mathematics is an inexhaustible motive force to promote the development of human civilization,and it is also an important source to improve mathematics literacy.From the perspective of HPM,this paper adopts the method of experimental research.First of all,through the investigation of the ninth grade mathematics teachers in a middle school,we know the teaching of acute trigonometric function and the present situation of the integration of mathematics history into teaching.According to the above survey results,three concept courses in acute trigonometric function are selected,and the teaching design is made according to the theory of historical similarity,generative teaching method and the corresponding mathematical history.Then,students from two parallel classes in Grade 9 of a middle school are selected as the research objects,and different teaching modes（traditional teaching and teaching from the perspective of HPM）are used to set up the control class and the experimental class for teaching.Finally,collect the research data such as interviews,questionnaires and test papers,and analyze the influence of acute trigonometric function teaching on students from the perspective of HPM qualitatively and quantitatively.This paper mainly studies the following three issues:（1）Are there historical similarities in the cognitive logic order of ninth grade students when they learn acute trigonometric functions?（2）In the teaching of acute trigonometric function,how do students view the integration of the history of mathematics into classroom teaching?（3）Through experimental research,can the teaching of acute trigonometric function from the perspective of HPM help students overcome the knowledge barrier? What is the impact on students’ emotional attitudes and values?Through the analysis of experimental research,this paper draws the following conclusions for the above three research problems:（1）There is historical similarity between students’ cognitive order and the development of acute trigonometric function.（2）Students are curious about the integration of the history of mathematics into the classroom.With the deepening of knowledge,this brand-new perspective stimulates their interest and thirst for understanding the emergence and development of mathematical concepts.（3）In the process of integrating the history of mathematics into mathematics classroom,by understanding the development of trigonometric function history and carrying out corresponding inquiry activities,this accords with students’ cognitive logic,helps them overcome knowledge barriers,has a positive impact on their emotional attitudes and values,improves students’ mathematical literacy ability more efficiently,and the moral education connotation brought by the history of mathematics can also cultivate students’ rational spirit.To sum up,the teaching design of integrating the history of mathematics into the acute trigonometric function classroom is of educational value and worth trying by middle school teachers.