Solid Geometry Counterexample Usage Investigation

The counterexample has its special function in the solid geometry teaching,the ordinary high school mathematics curriculum standard has put forward the corresponding request to the counterexample,also often inspects the student's ability to use solid geometry counterexamples.Through the investigation on the use of part of the city of Xining middle school geometry examples,the conclusion is: first,most of the teachers and students are limited to the understanding of the counterexample definition,but know little about the types of counter-example;second,most teachers are not familiar with the effect of counter-example,understanding of the constructor is not comprehensive;third,only a handful of teachers and students has not used,and this part of the teachers and students all feel not necessary,the use of positive examples is enough;fourth,main reason for the teachers use counterexample is to deepen students' understanding of solid geometry knowledge,followed by correcting students' mistakes,and main reason for the students to use the counterexample is in order to improve the speed of solving problems;fifth most of the teachers in teaching can timely use counterexamples and counterexamples is mainly from textbooks,reference books,publications and cyber source;the students obtain the counterexamples is mainly from textbooks,books and network resources,teachers' classroom speaking;teachers and students rarely choose to construct counterexamples for themselves;the effects of teachers and students use counterexample are students' reverse thinking ability improved,thinking extending,the speed of solving problems increased,deepening the understanding of knowledge;the difficulties of teachers and students use counterexamples are constructed with difficulty and counterexample understanding of students;sixth,the influence factors of teachers and students use counterexamples is mainly the understanding ability of students,the abstract degree of the content of solid geometry,and the thinking ability of students.In the case of the function of the counter-example,the author conducts the pre-and-post test experimental research in the First Affiliated Middle School of Qinghai NormalUniversity,and draws the conclusion that the use of counter-examples can improve the students' achievement.At the same time,the author gives a constructive method of stereo geometry anti-examples,and lists some teaching suggestions.