Interpretation And Reconstruction Of Typical Trigonometric Textbooks

With the development of astronomy,navigation,physics and other sciences,trigonometry came into being to solve practical problems.In the middle school mathematics study,trigonometry occupies a large proportion,is the teaching focus and difficult point.The construction of trigonometry content of the program and the redaction of textbooks,both in theory and teaching level has important significance.This study is qualitative research,mainly using literature research method.Through the existing research on the status quo of trigonometry learning research to understand the students learning trigonometry content of the difficulties and researchers on these issues proposed solutions.Taking the representative mathematics textbooks used in teaching before and after the founding of our country as well as the mathematics textbooks of several countries that have had an important influence on the teaching of mathematics education in our country as the research objects.Focus on the construction of trigonometry of mathematics textbook.Comb and comment on the trigonometric construction scheme not included in the teaching materials.Based on the construction plan of xiong huimin,a textbook of middle school trigonometry was prepared.The preliminary results of the study mainly include the following:(1)Through the arrangement of the construction of trigonometry content in multiple versions of textbooks,summarized three kinds of typical trigonometry content construction program:(i)From trigonometric functions of acute angle to trigonometric functions of arbitrary angle.First,define trigonometric functions of acute angles irn a right-angled triangle;then expand the corners to any angle and define the trigonometric functions with the end-defining method or the unit circle definition method;learn the function images,properties,and trigonometric formulas,law of sines and law of cosine.(ii)In the logical order,it's still the trigonometric function of the triangle to any Angle,but the technical means are different.In the triangle,the trigonometric functions of acute angle defined by the ratio of edges to edges are given in the triangle.And create a unit circle in rectangular coordinate system,given definition of a certain range of trigonometric function with unit circle,or the two steps exchange order,the first use of unit circle given the definitions of trigonometric functions within a certain range,then return to the triangle to find the geometric meanings and give the definition of the edge ratio.In this process,we introduce some induction formulas established in a certain range,law of sines and law of cosine.Then expand the angle to any angle and define the trigonometric functions of arbitrary angle with the end-defining method or the unit circle definition method,and then the induction formulas,function images and properties and trigonometric formulas are presented.(iii)From trigonometric functions of arbitrary angle to trigonometric functions of acute angle.Firstly,define the trigonometric functions of arbitrary angle with the end-defining method or the unit circle definition method,and the image and properties of the function are studied.The construction of the trigonometric function as a function is completed.Then the trigonometric function is connected with the triangle,the trigonometric functions defined by the ratio of edges to edges are given in the triangle,and gives law of sines,law of cosine;Finally learn the triangle formula.(2)This paper analyzes and contrasts the construction scheme of trigonometry in textbooks and constructs the trigonometry which is not included in teaching materials.Based on this,it uses one of the constructing theories as theoretical basis to reconstruct the teaching materials of trigonometry in middle school.