Investigation And Research On Junior High School Students Learning Factorization

In the compulsory education stage, "Number and Algebra" is an important part of mathematics education. It can help us understand, describe, and grasp the real world and solve the real world problems more accurately and clearly from the perspective of quantitative relation. It is the basic mathematical literacy students should have. Factoring is an important part of "Number and Algebra" for learning mathematics, which has a profound influence on it.In order to know how junior high school students master factoring, the author finally selected a sample of 127 students in grade eight in Shijiazhuang No. 23 Middle School through the analysis and study of the document and making the corresponding questionnaire, and then visiting many schools of different levels in Shijiazhuang to have pre-test, then is formal test ungraded. The questionnaire is mainly based on seven aspects, that is the concept of factoring,extracting the common factor method, the formula method, cross multiplication, the integrated use of formula method, Metacognitive factorization method, and the application of factoring. Then the analysis and statistic are made according to students’ answers. After questionnaire the author interviewed individual students and teachers to make up for the shortage of the questionnaire.Finally it is concluded that junior middle school students exist certain differences in the mastering of the concept of factoring, extracting the common factor method, the formula method, cross multiplication, the integrated use of formula method, Metacognitive factorization method, and the application of factoring by analyzing and sorting.The specific conclusions are as follows;(1) most students’ understanding of the concepts of factoring is in the former structure level, and only 1.61% of the students can basically grasped the concept of factoring;(2) most of the students can master the use of extracting common factor for factoring;(3) most of the students can accurately use factoring formula method;(4) only about 30% of the students can use simple cross for factoring multiplication problem correctly, and half of the students’ method is not cross, but the distribution method;(5) the majority of people cannot completely use a variety of methods for complex polynomial factorization, and they just use one way, failing to factoring into the minimalist form;(6) students met- cognitive ability is not strong, and the student shall be able to correctpolynomial factorization, but the reasons sometimes go awry;(7) in terms of the application of factoring, the difference of the difficult places is very big, and key classes obviously better than the ordinary classes he difficult.There are some specific teaching suggestions aimed at junior high school students’ mastering of factorization.(1) to strengthen the understanding of the essence of the concept of factoring;(2) to strengthen the understanding of the factorization method.(3) strengthen the thinking ability of using knowledge comprehensively.