The vector, one important conception in contemporary mathematics, has become the common tool to study the problems of geometry and algebra. The content of vector has been added into the new mathematical curricular criterion in senior high school, which means that the students in the period of high school should learn to solve the ordinary mathematical problems using vector.Against this backdrop, the topic, solving problems by the vector, receives rebound attention. In this paper, an elementary and detailed research is made on this topic through combining the author's practice on teaching, which also aims at the current mistaking about its conception.First, based on the introduction of vector's origin and development, the signification of this topic is expatiated. It may lead students to understand the basic knowledge about mathematics, and master the basic method to solve the mathematical problems. It also may help students to construct and improve the configuration of knowledge.Second, the thought and its principle in solving problems by the vector are studied. Our opinions come from the mathematical psychics, which may induce the students to understand the process to solve problems by the vector. Moreover, during this process, the related principle should be complied with, such as the combination the number with figure, analogical principle.Third, we discuss the necessary and the function of introducing the vector. The necessary may be seen from the need of development of advanced sciences and technology, the trend to net knowledge, as well as the need to improve the reform of teaching material, optimize the ability to cognize and derive the inquisitive study. Besides, its function can be found from updating the way to think, cultivating the students' qualities of thought and abilities to construct the model, intensifying the moral teach, as well as bringing up the mathematical culture. |