The part about space vector in the new mathematics textbook for senior high school accounts for about 14 class hour (of course, its application is not limited to this 14 class hour), which is included in Chapter 9 "Lines, Surfaces and Simple Geometry" (referred to as "9 (b)"), and the mathematics textbook for the second semester of senior high school with space vector is referred to as "Volume 2 (part b)"; In parallel, the textbook Volume II (Part A) still uses the traditional method to explain the content of solid geometry in senior high school. The title of the ninth chapter of the two textbooks is the same, and both of them use 36 class hours for teaching.
To sum up, according to the footnote on page 10 of the syllabus, the content of "space vector" can only choose one of two schemes (9 (a) and 9 (b)), which has the duality of "must learn" and "choose to learn", and 9 (b) is optional. However, the outline takes "straight line, plane and simple geometry" as the required content. If students don't study according to the textbook Volume II (Part A), then space vector is their compulsory content.
The content of "space vector" can be roughly divided into two modules: "space vector and its operation" and "application of space vector"
(1) space vector and its operation. Including:
(1) Experience vector and the process of its operation expanding from plane to space.
② Understand the concept of space vector, master the addition, subtraction, multiplication, division and coordinate representation of space vector, and understand the basic theorem and significance of space vector; Master the space coordinate system, can express the space vector linearly with the unit vector on the coordinate axis, and master the coordinate representation of the space vector.
(3) Master the quantity product of space vector and its coordinate representation, and judge the * * * line or vertical line of the vector by using the quantity product of the vector.
(2) Application of space vector. Including:
① Understand the concepts such as the direction vector of a straight line, the normal vector of a plane and the projection of the vector on the plane.
② The vertical and parallel relationships among lines, lines and planes can be expressed by vector language.
③ Some theorems about the positional relationship between line and surface can be proved by vector method.
④ Using space coordinate system and vector method to solve the calculation problem of included angle and distance, and realize the role of vector method in studying geometric problems.
In teaching, students should be guided to use analogy to experience the process of vector and its operation spreading from plane to space, and pay attention to the influence brought by the increase of dimension.