Investigation And Research On Junior High School Students Learning Situation Of Irrational Number

Irrational number is an important part of the rational number domain expansion to the real number field, and an important basic content of the middle school mathematics learning. In order to understand the junior middle school students mastery of irrational numbers learning situation, the author through the analysis of the literature research to develop a corresponding questionnaire test, and some different schools of Shijiazhuang to visit the pretest. But finally I selected the ninth grade 132 students of Shijiazhuang 22 th middle school for a sample, and in the way of scoring the formal test. The questionnaire mainly from the concept of irrational numbers、the irrational numbers on the number axis、the method to solve the problem of the irrational number、four fundamental operations of the problem of irrational number、the mixed operation of rational numbers and irrational numbers、and the application of irrational operation properties in six aspects to test. And after the questionnaire survey, I talked with the individual students and teachers. In order to make up for the shortage of the questionnaire.Eventually concluded that junior middle school students by sorting out and analyzing the concept of irrational numbers, the irrational numbers on the number axis,the method to solve the problem of the irrational number、four fundamental operations of the problem of irrational number、the mixed operation of rational numbers and irrational numbers、and the application of irrational operation properties all have some difference. Specific conclusions are as follows:(1) most students’ understanding of the concepts of irrational Numbers in multivariate structure level, only 7.1% of the students can master basic concept of irrational Numbers;(2) only 22.8% of the students can understand and master the irrational Numbers correspond to the points on the number axis and accurately on the number axis;(3) most of the students can accurately compare two simple irrational number and molecular size, but not a very good use of irrational numbers(denominator) rationalization;(4) the vast majority of students of the four fundamental operations of the irrational problems to grasp the situation in multiple structure level, only 23.6% of the students reach the level of correlation structure;(5) most of the junior high school students can’t have a good command of rational numbers and irrational numbers mixed operation, only 7.1% of the students can completely solve the two questions of questionnaire about investigating this knowledge;(6) Only 17.3% of the students can answer the questionnaire in the examination subjects irrational operation properties of solution, the students’ level of the irrational operation properties application is generally low.In view of the junior high school students about mastering the situation of irrational knowledge,I put forward some teaching Suggestions:(1) To strengthen the understanding of irrational Numbers essential characteristics;(2) Combined with rational knowledge to irrational teaching;(3) Draw lessons from the development history of the concept of irrational Numbers for irrational teaching;(4) Combined with definition and operation knowledge teaching in the form of irrational Numbers.