The Teaching Of Algebraic Inequalities From The Perspective Of HPM

Inequality is one of the most important chapters in high school mathematics,and also one of the important contents of college entrance examination.The "element","degree","number of items" and "structure" in inequality are applicable to all the contents of high school mathematics.To learn inequality well is to learn high school mathematics well.In recent years,as the educational value of the history of mathematics has been paid more and more attention,mathematics teaching integrated into the history of mathematics is very important in the new curriculum reform and quality education.However,there is a lack of teaching cases in the history of mathematics in our country,and the integration method is single and the integration depth is not enough.Adding the teaching of mathematics history can integrate mathematics history and mathematics education,and effectively improve the teaching effect of mathematics teachers and the core quality of students.Based on this,this paper develops HPM teaching cases for two parts: compulsory Volume 1 2.2 basic inequality and elective 4-5 lesson 3 Cauchy inequality.Firstly,we collect and process the history of Mathematics according to the above two teaching contents;secondly,we design teaching cases of inequality based on HPM perspective,reveal the historical background and historical development process by reconstructing history,predict the cognitive obstacles and errors that students may have in the learning process,and design mathematics classroom activities based on the history of mathematics,through the cooperation of teachers and students to solve difficult points.Finally,through the investigation and feedback of teachers and students after class,the teaching effect of integrating mathematics history into the classroom is discussed.Through the teaching practice and investigation and analysis,the following conclusions are drawn: the inequality teaching cases integrated into the history of mathematics can effectively stimulate students’ interest in learning,establish students’ self-confidence,inspire students’ personality growth,broaden students’ horizons,and make them understand multi-cultural mathematics.This paper discusses the design and teaching effect of HPM cases for specific problems,and promotes and sublimates each case.The purpose of this paper is to provide reference for teaching cases of integrating mathematical history into inequality.