A Practical Study Of Junior High School Mathematics Counterexample Teaching Based On Mathematical Understanding

Mathematical understanding and mathematical example teaching have always been the hot topics in educational research.The mathematical counter example has its unique function and position,which is based on mathematical understanding and ACTS on mathematical understanding at the same time.This paper studies the connotation of mathematical counter-example and mathematical understanding,explores the teaching mode of mathematical counter-example in junior high school,and tests it with the help of micro-experiments,aiming at developing effective and systematic mathematical counter-example teaching in junior high school to help students to have a profound mathematical understanding.In this paper,using literature method,observation method,interview method and experimental method were studied.The literature analysis method is used to summarize the existing relevant research,and it is found that there is a lack of research on the combination of mathematical counterexample and mathematical understanding,as well as systematic research on the teaching of mathematical counterexample.This paper defines the concept of mathematical understanding and mathematical counterexample in the light of cognitive psychology.By means of observation and interview to understand the teaching status of counterexample in junior middle school,the author finds out that it is difficult to construct counterexample in mathematics,and proposes four methods to construct counterexample in mathematics.A mathematical counter example is constructed according to the essential attribute of the object.Using geometric intuition to construct mathematical counter examples;The mathematical counter example is constructed by the method of classification.Combining with practice and theory,this paper puts forward the teaching principle,model and case design of mathematics counterexample for junior middle school mathematics concepts,formulas and theorems.In the counter-example teaching of junior middle school mathematics concept,the organization of positive and negativeexamples should follow the principles of matching,difference and progressivity.The teaching process of counter example of mathematics formula in junior high school includes prototype(variant)presentation and error presentation.The teaching mode of counter-example of mathematics theorem in junior high school includes five links:proving theorem,setting false proposition,constructing counter-example,analyzing counter-example and reflecting theorem.Finally using the experimental method to understand the junior middle school mathematics counter-example teaching two weeks of miniature experiment was carried out,based on the experimental measurement data before and after the analysis of the test data,experimental classes than that in comparative classes about 4.7 points above the average,two classes of the testing results of independent sample inspection,sig(double side)value of 0.028 < 0.05,suggesting that the two results show significant difference.To some extent,the experiment verifies that the systematic counter-example teaching of junior middle school mathematics can effectively help students to understand mathematics.