Vector Methodology And Its Applications

The modernization of math teaching in middle school is more of a change of teaching styles than contents,highlighting styles that stress on the study of mathematical methodology. In this context,a teaching style featuring vector methods will proved to be of great practical importance in various dimensions such as improving the ability of problem solving, promoting the creative thinking and improving mathematical quality in general.The first part of this paper contains a tour into vectors in middle school in which you will familiarise yourself with the contents as well as the requirments of this part of math in middle school.Four frequently made mistakes are also visited in this part.Then base on a better understanding of vectors in middle school,as a branch of math built on a rich ground of physics knowledge,as a component in geometry,as a component in algebra,as a bridge to connect geometry and algebra,as an important mathematical model and as an eccence in math curriculum in middle school,we propose a new definition------vector methodology and give its connotation as a subset of the vector knowledge,an insight into vector knowledge and a set of reccesive knowledge.In the second part,basing on its connotation and its potential in teaching,five applications of vector methodology on math teaching in middle school are given.They are enforcement of the "mathematics curriculum standard",showcase of the beauty in simplicity of math,renewing the space methodology,bridging math in middle school and math in college and constructing a vector oriented method of integrating the subject to prepare the students for the college entrance examination.And finally,to illustrate our method and provide a quick glance at this new method,a quantity of well chosen examples from various branches of math such as functions,inequality, plane geometry,plane analytic geometry and solid geometry are presented.Through these examples we mean to improve the students'understanding of vector methodology and demonstrate its dramatic effects in simplifying the solutions.