The thought of conversion is the most basic thinking method in middle school mathematics. It transforms the original problem into a new one through observation, classification, analogy, association and other thinking processes, and achieves the purpose of solving the original problem by solving the new problem. Moreover, if the idea of reduction is properly applied in analytic geometry, we can achieve the effect of simplifying the complex and getting twice the result with half the effort.

1, mutual transformation between fixed point and fixed point

The fixed point and the fixed point are relative, and the same object can flexibly choose and change its role as needed, especially to solve the problem of multiple fixed points. According to the meaning of the question, one (or several) points are regarded as fixed points first, and some conclusions are drawn, and then they are considered as fixed point problems.

2. Number-shape conversion

The core method of analytic geometry is "algebraic method to study geometric problems" and the core idea is "combination of numbers and shapes". By using shapes to help numbers or substitute shapes, geometric conditions are algebraic and algebraic operations are geometric, so that complex problems are simplified and abstract problems are concretized, and the purpose of optimizing problem-solving methods is achieved.

Extended data:

The difference between remoulding thought and remoulding thought.

First of all, it refers to differences. Transformation thinking can also be called transformation thinking in a narrow sense. Applications in trigonometric function, geometric transformation, factorization, analytic geometry, calculus, etc. The process of changing a problem from difficult to easy, from complex to simple and from complex to simple is called transformation, which is the abbreviation of transformation and attribution.

Second, the transformation methods are different. Transformation ideas: number-shape transformation, structure transformation, association transformation and analogy transformation. Transformation ideas: special transformation, equivalent transformation, complex transformation and simple transformation.

Mathematical thought

Mathematical thought is the essential understanding after summarizing mathematical facts and theories; The thought of basic mathematics is the basic, summative and extensive mathematical thought embodied or should be embodied in basic mathematics, which contains the essence of traditional mathematical thought and the basic characteristics of modern mathematical thought and is historically developed.

Through the cultivation of mathematical thinking, the ability of mathematics will be greatly improved. Mastering mathematical thought means mastering the essence of mathematics.

Function thought refers to analyzing, reforming and solving problems with the concept and nature of function. The idea of equation is to start with the quantitative relationship of the problem, transform the conditions in the problem into a mathematical model with mathematical language, and then solve the problem by solving the equation (group) or inequality (group). Sometimes it is necessary to transform functions and equations into each other in order to achieve the purpose of solving problems.

When a problem may lead to different results because of different situations of a certain quantity or number, it is necessary to discuss the various situations of this quantity or number in categories. Such as solving inequality | a-1| >; 4. It is necessary to discuss the value of A in different categories.