Teaching Research On The Solution Of One Variable Quadratic Equation From The Perspective Of HPM

In the preface of compulsory education mathematics curriculum standard(2011 Edition),it is pointed out that mathematics is an important part of human culture,and mathematics literacy is the basic literacy that every citizen in modern society should have.The history of mathematics and the human elements in the development of mathematics are the inexhaustible power to promote the development of human civilization,and also the important source to improve the mathematical literacy.One variable quadratic equation is an integral equation with only one unknown number and the highest unknown number is 2.The knowledge content of the quadratic equation of one variable includes the first-order equation of one variable,the square root of the open square,the square root of the arithmetic,the multiplication of polynomials and the factorization of factors,and is closely related to the knowledge of the quadratic inequality of one variable and the quadratic function.Therefore,the quadratic equation of one variable is an important equation model,which plays an important role in middle school algebra.The teaching of the solution of the quadratic equation of one variable plays a link role in the learning of the quadratic equation of one variable.It carries on the concept of the quadratic equation of one variable and plays an application of the quadratic equation of one variable.Therefore,to learn the content of this chapter well,the solution of quadratic equation of one variable is the key link,especially the matching method and formula method.Therefore,combined with the requirements of the curriculum standard and the solution content of the univariate quadratic equation,on the basis of the history of mathematics and the theory of MathematicsEducation(HPM),we should try to find the historical materials that have enlightening significance for classroom teaching from the historical river,and integrate the knowledge of Mathematics history into the core knowledge and key and difficult points of the teaching materials based on the cognitive reality and psychological basis of the students,so as to realize the history of mathematicsThe specific integration of knowledge and the teaching of the solution of one variable quadratic equation.On this basis,the relevant teaching inspiration is separated out,the teaching design based on HPM is carried out,so as to achieve the integration of theory and practice.After the teaching experiment,the pre-test and post test questionnaires are carried out.The students fill in the questionnaire and interview the teachers.Finally,the quantitative and qualitative analysis is carried out,and the following conclusions are obtained:(1)According to the theory of genetic epistemology,history of mathematics and mathematics education,the process of human understanding mathematics is consistent with the process of children's psychological development.To a certain extent,the history of mathematics and the theory of mathematics education integrate the two,making the content of mathematics teaching more in line with students' cognitive law and life reality,and then maximizing its value.(2)By abstracting the mathematical materials and methods about equation and univariate quadratic equation which are useful for teaching from the long history,we find that the history knowledge of equation and univariate quadratic equation is closely related to the natural environment,politics,economy and culture of our country and spans the ancient and modern world in a macro way,with strong accumulation;pay attention to the integration of algebra and geometry,pay attention to geometry intuition;be good at revealingThe connection and essence of the knowledge of each part of mathematics;a lot of mathematics knowledgecomes from practice.(3)Based on the history knowledge of equation and univariate quadratic equation,the researcher has designed the relevant teaching design.Its outstanding feature is that it absorbs and integrates the advantages of textbook arrangement and history knowledge of mathematics,and discards the disadvantages of avoiding them.Take the inquiry teaching based on students,inject the humanistic factors of mathematics,and realize its cultural value.(4)The quasi experimental research of "the solution of quadratic equation of one variable from the perspective of HPM" shows that this teaching experiment is helpful to arouse students' interest,stimulate learning motivation,promote mathematics understanding,and improve classroom efficiency(mathematics achievement and mathematics core literacy).