Research On The Teaching Of High School Mathematics School-based Curriculum Based On Freidenthal's "re-creation" Theory

During the teaching practice,the author found that students often have the following wrong methods when seeking the inverse function of functiony=x~2?x~2=y?x=±?y?=±?x(x?0).hhe reason is that students have insufficient knowledge of inverse function"hhe relationship between two function images of reciprocal functions"is a content in the"exploration and discovery"column of compulsory edition a of senior high school mathematics teaching,which is a knowledge point that it is necessary to guide students to explore However,due to class hours,front-line teachers often do not pay enough attention to this knowledge point,rarely teach the content of inverse function,and often directly tell students the nature of inverse function In this way,the content of the"exploration and discovery"column in the textbook is not used well Moreover,the relevant knowledge of inverse function and the mathematical thought contained in inverse function are of great help to students'follow-up study of higher mathematics and science and engineering.hherefore,it is necessary to carry out the school-based mathematics course of"exploring inverse function".Due to the factors of class hours and progress,it is impossible to guide all students to explore the knowledge point of inverse function.hhe author puts the inverse function into the school-based curriculum of mathematics and compiles the teaching design of exploring inverse function hhe teaching experiment selects class 1 of senior high school as the control class,and the school-based class of senior high school(students taking school-based courses in Mathematics)as the experimental class hhe school-based class uses friedendal's"re creation"theory to explore the inverse function,and the control class does not carry out teaching experiments hhe same test papers(pre-test paper,post test paper and delayed test paper)are arranged for the two classes.hhe students of the two classes are selected for interview.hhrough the analysis of the test papers and interview results of the two classes,the following experimental conclusions are drawn:(1)the teaching experiment improves the accuracy of students'problem-solving and develops students'logical reasoning ability;(2)Under the guidance of"re creation"theory,students can promote the comprehensive use of the two methods;(3)Compared with the control class,the school-based class has significantly improved in problem representation and exploration,can connect exponential function and logarithmic function from the perspective of the combination of number and shape,has a deeper understanding of the concept and nature of function,and students'reverse thinking has also been improved.hhrough the analysis and summary of teaching experiment and experimental conclusion,this paper draws the following research conclusions School based students are strengthened in three aspects:(1)look at exponential function and logarithmic function from the perspective of connection;(2)hhe concept of function is recognized from another point of view,because inverse function is also a new kind of function based on the expansion of function concept,which is a recognition of the concept of previous learning function;(3)Improving reverse thinking is of great help to the follow-up study of higher mathematics and science and engineering.Finally,according to the research conclusions,teaching suggestions are given:(1)pay attention to the exploration and application of concepts;(2)Encourage students to"re create"knowledge;(3)Pay more attention to the content of inquiry.