** I.** Introduction ** Engels said: "Mathematics is the relationship between the amount of real world science and space in the form.** Contradictory unity of the two studies in mathematical object "number" and "shape" the internal factors of the development of mathematics. The Combination is a thread throughout the development of mathematics, mathematics in practice more extensive and far-reaching. On the one hand, by virtue of the nature of the graphics to visualize abstract mathematical concepts and quantitative relationships, simplistic, giving the intuitive sense, on the other hand, the graphics problems into algebraic problems can get accurate conclusions. "Number" and "shape" of information conversion, mutual penetration, not only to make problem solving a simple and neat, but also to develop problem-solving ideas, has opened up an important way to study and explore mathematical problems. Shuxingjiege is connected to the "number" and "shape" of the "bridge", it is not only an important method of problem-solving, is an important mathematical ideas. High school mathematics learning the thought Shuxingjiege throughout.

Based on the intrinsic link between the conditions and conclusions of the mathematical problem, it is necessary to analyze the algebraic sense, they reveal the geometric intuition, to accurately characterize the spatial form of the number of relevant visually clever, harmoniously together, and take full advantage of this Shuxingjiege looking for problem-solving ideas, anything easy, simplify, and thus be successfully resolved the problem of

Review: the use of the number-shaped knot thinking not only intuitive and easy to find problem solving ways, but also to avoid the complex calculations and reasoning, and greatly simplifies the problem-solving process. In the solution of multiple-choice, fill-in more superior, the need to cultivate this ideology, in order to develop their own

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Reviews: Shuxingjiege thought can make some abstract mathematical problem intuitive, vivid abstract thinking can change the image of thinking helps to grasp math the nature of the problem, to simplify the calculation.

Comment: Many of the functions of most value, there is a geometric background, with the form of intuitive problem solving is an important method of seeking problem-solving ideas, to the problem through a graphical geometric intuitive description, identify problems in Shuxingjiege logical relations, inspired thinking, problem Solving.

Review: vector has a good set of arithmetic nature, through the establishment of a Cartesian coordinate system, the geometry of nature can be transformed into vector operations, becomes abstract logical reasoning for vector operations, with the accurate specification to clarify the three-dimensional geometric rigor the properties, both to simplify the difficult problem of spatial imagination, especially simple.

Using Shuxingjiege ideological analysis and problem-solving, to pay attention to three things: first thoroughly understand the geometric meaning of some of the concepts and operation as well as the curve of the algebraic features analysis of its geometric meaning both on the the math topics conditions and conclusions and analysis Algebra is appropriate to set parameters, with reasonable parameters, build relationships, and by the number of Si-shaped to form want the number, good number of shape transformation, the third is the right to determine the parameter ranges.

Already full implementation of the new curriculum of teaching content hierarchy teach the new curriculum syllabus requirements and knowledge point of view, Shuxingjiege method of teaching through three main stages:

The first stage is the number of conformal maps, it is Shuxingjiege foundation, through the usual concept of teaching gradually penetrate students through learning, training, experience, and gradually comprehend and master. On one hand, the point on the real number corresponding with the number of axis points, flat with corresponding ordered pairs of real numbers, corresponding to the function and image corresponding to the curve with equation, etc., as well as the background of geometric elements and geometric conditions established concepts such as vectors, trigonometric functions, etc., to create conditions for Shuxingjiege provide theoretical support. On the other hand, the high school math concepts with strong abstraction, generality, students have a greater difficulty in understanding. Can make use of the geometric shape to achieve the purpose of helping students understand intuitive. For example, the function and image combine functional relationship expressed by geometric methods to help students understand the function of abstraction.

The second stage is the number of shape transformation, it reflects the number and shape relations in the problem-solving process, how as a method to be used. The mathematical problem is a prerequisite for carrying out mathematical thinking, problem-solving process, in essence, is a process of mental training. We can Shuxingjiege penetration in the problem solving process, mainly in the following three aspects:

Throughout the years of the College Entrance Examination, the clever use Shuxingjiege the thinking methods to solve abstract mathematical problems, tend to do more with less. Therefore, the need to strengthen the teaching of high school mathematics Shuxingjiege to improve the quality of students' mathematical and problem-solving ability. Links to free papers Download Center http://eng.hi138.com

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