The Research Of Practice Counterexample Teaching Mode Of Middle School Mathematics

Counterexample plays a significant role in mathematics.In order to carry out effective and systematic counterexample teaching in middle school,make the counterexample teaching effectively,in this paper,we study the mode of middle school mathematics counterexample teaching.This thesis takes the strategy which combines the analysis of literature with practice.We come up with the mathematics concept of teaching of counterexample teaching mode.There are three parts,including the presentation of prototype(variation),explanation,practice of asking questions and feedback.At the same time,we give the three principles of the presentation of positive-negative examples,which include the matching principle,the difference principle and the progressive principle.Combining with the characteristics of mathematics,we come up with the counterexample teaching mode in the applications of mathematics.There are five parts in the mode,which include the design of problems,the analysis of problems,the construction of counterexample,the analysis of counterexample and generalization and summarization.The applications of mathematics,including the proposition analysis,error correction and the explore of discovery.Through the extreme or special circumstances,through the methods of classification,through the proof construction and through the methods of movement,we provide four cases of construction methods and strategies of the counterexample.We carry out the experiment of mathematics counterexample teaching for the 9th grade,the results show that the score of the counterexample teaching experimental class is 7 points higher than the untreated class.Though the independent sample test about their score,we can see that the value of sig is 0.032<0.05.There are significant differences in the score between the experimental class and untreated class.The results imply that it is helpful for the students to understand and grasp the mathematical concept by carrying out the counterexample teaching of middle school mathematics systematically.At the same time,it can improve the ability of students to find the problems,correct mistakes and explore.Also,it is benefit the ability of problem-solving and the efficiency of problem-solving of the students.