The Vector Application And Teaching Study Of Mathematics

Vector is one of the important and basic concepts in modern mathematics. It is also a tool that links up algebra, geometry, and trigonometric. It has widely applied in solving problems for its general operations, geometrical visualization, and conciseness in expressing ideas. Therefore, the teaching and learning of vectors does not help students build an integrated body of mathematical knowledge, but also enhance their abilities to solve the proof problems in geometry.Relative literature shows that it is still a very difficult topic in school mathematics due to the negative influence of traditional mathematic knowledge. Specifically, both teachers and students experience a lot of difficulties in grasping the basic knowledge of vector, in promoting the application of vector, and in the teaching and learning of vectors.In this thesis, we shall first focus on the basic knowledge about vectors including those that are already presented in the current mathematics textbooks used in schools and those that are not yet presented in school textbooks, but basic in certain sense. This effort is made to form a complete structure of basics in vector.We then make a systematic analysis of those topics in vector in school mathematics. Particularly, we discuss the various applications of vector in school mathematics with examples. We also compare its applications with those traditional methods. This kind of comparison helps us see the advantages of vector method over traditional methods.Finally we did a survey to investigate the current status of vector's teaching and learning in schools. We found that both teachers and students are aware of the potential usage of vectors. However, they only use it when the traditional methods do not help them solve their problems. In this case, the vector method is used as a backup. We also found that the vector method obviously superior to the traditional methods in the accuracy of mathematic problem solving and the vector method is a little more efficient than the traditional methods even though the difference has not reached a significance level in solving solid geometrical problems.Some suggestions are also made at the end of the thesis for improving the teaching and learning of vectors in schools.