Senior Students' Understanding Levels On The Eigenvalue And The Eigenvector Of 2 By 2 Matrix

The eigenvalue and the eigenvector of 2 by 2 matrix are one of the optional series4-2 of the new curriculum in senior high school. The knowledge about the matrix and the counterchange have never appeared in former teaching materials. Therefore, the author is determined to research and conduct a survey about the understanding of the students of senior2 on the eigenvalue and the eigenvectorThe thesis mainly introduces how to make the survey test, the whole course of conducting the survey, and the result of the survey research. Through the related teaching survey research, the author finds out that most of the teachers and students think that it's difficult to understand and adopt the knowledge on the eigenvalue and the eigenvector of 2 by 2 matrix. There are many reasons. First of all, the concept on the eigenvalue and the eigenvector is very abstract. Secondly, there are too many contents about the concept. In addition, the math symbols used are complicated. Finally, the fully understanding about it is based on the related knowledge. The two math theories about the understanding guide our math teaching practice. The teaching design plays an important role in the level of students' understanding. Students' understanding on the eigenvalue and the eigenvector of 2 by 2 matrix is dynamic. That students can apply the concept to problem-solving skillfully and accurately doesn't necessarily mean they can master the concept well.Finally, according to the result of the survey, the author provides some suggestions: maths teachers should spare no efforts to track and study the theories about maths understanding; maths teachers should try to set appropriate preliminary knowledge and problem situations in maths teaching; maths teachers should make great efforts to systematize students' cognition system in maths teaching; maths teachers should try their best to reinforce sensible and visual teaching in relation to abstract concept as well as strengthen figures in relation to graphs in maths teaching; maths teacher should attempt to spare more time to communicate with students; exercise used for training should be carefully selected and scientifically rated.