In this paper, we discuss an improvement of teaching the vector in the high school mathematics. First, we compare the current objectives of studying the vector with those of 1960's when the vector was introduced in the high school as a teaching material for the first time. Then, we point out that current students do not have so much experience to see the efficient use of vectors other than mathematics and that the role of the vector to cooperate with the space analytic geometry is currently insufficient. However, our assertion is that an improvement of teaching the vector along with a mathematical activity is important, and that students should learn to expand the mathematical methods through the utilities of the vector, the utilities to represent movements and sites of figures and to apply the vector operation in various ways. We show three teaching materials of the vector to illustrate the above points. The first material describes the efficient use of vectors in explaining the function of a contraction tool, the second suggests the valid use of the orthogonal projection when we introduce the inner product of vectors, and the third is a vector expression of the inner center of a triangle, which shows a typical use of the vector operation in analyzing figure properties.
