Research On Teaching Of The Newly Added Topic "Matrix And Transformation" In Senior High School Mathematics

In the "Senior High School Mathematics Curriculum Standards (Experimental Manuscript)" enacted by national ministry of education in April 2003, a special topic "matrix and transformation" was added in section 4.2 as an elective part."Matrix and transformation" had been the major part in advanced algebra course (linear algebra part) in college, and it was the first time that this concept was introduced in senior high school curriculum standards as a special mathematical topic. Based on the purpose of the design of this "curriculum standards", the cognitive psychological characteristics and knowledge structure of current senior high school students in our country, plus special properties of the knowledge of matrix and transformation, we conducted an in-depth research on the presentation of its concept, the geometrical significance of basic elementary matrix, the expression of shift transformation in matrix form and its geometrical meaning, and also the strategy of how to conduct the course. In addition, a group of teaching suggestions are given based on our research and experimental result.Flex and shear transformations are the two fundamental deformations in the mechanical research, and they also have the corresponding mathematical models, namely the two kinds of basic elementary matrixes. However, the physical and geometrical significance of basic elementary matrixes are seldom mentioned in linear algebra. In Mathematics Encyclopedia, the concept "shift" is used to describe the mathematical model of an object's shear transformation, and its geometrical explanation is from a projective perspective, plus the use of some abstracted descriptions like "infinity" and "affine hyper plane". Then, it is important to observe the basic elementary matrix from a physical perspective in a visible space, and to provide its practical geometrical meaning, and this is also one of the major achievements of our research. This achievement would not only enhance the application of matrix theory and do some actual help for the unification and standardization of corresponding concepts in both physical and mathematical science, but also have some practical significance for the teaching of "matrix and transformation" in senior high school.