1, Function and Equation Thought:

Function is the backbone of algebra content in senior high school, and mastering the idea of function is helpful for positive thinking. The idea of equation emphasizes the study of the equivalence relationship between known quantity and unknown quantity, and achieves the purpose of evaluation by setting unknown quantity, setting equations or equations and solving equations or equations.

2. Combination of numbers and shapes:

The idea of combining numbers and shapes is to combine the quantitative relationship in mathematics with geometric figures, and solve problems intuitively through geometric figures. In high school mathematics, such as the maximum value of quadratic function in closed interval, the deformation and flexible application of trigonometric formula, etc. You can use the idea of combining numbers with shapes.

3, the idea of classification and integration:

The idea of classification is to divide the problem according to some characteristics and discuss each sub-problem separately. The idea of integration is to integrate the solutions of sub-problems on the basis of classified discussion and get the overall solution of the problem.

4. Inductive and deductive thinking:

Inductive thinking is to sum up general laws according to specific cases, while deductive thinking is to deduce specific cases from general laws. In high school mathematics, such as permutation and combination application problems, probability problems, etc. Both inductive and deductive ideas can be used.

5. Variables and parameters:

The idea of variable is to regard the quantity in the problem as a variable quantity and solve the problem by observing the changing law of the quantity. The idea of parameters is to introduce one or more parameters into the problem and transform the problem into a function or equation about parameters, thus solving the problem.

6, reverse thinking and structural thinking:

Reverse thinking is to start from the opposite direction of the problem and seek a solution. The idea of construction is to solve the problem by constructing a new mathematical model and transforming it into a known mathematical model.

7. Transformation and transformation of ideas:

The idea of transformation is to transform a problem into a known problem type, so as to solve the problem by using the existing methods. The idea of transformation is to solve the problem by changing the form of the problem and transforming the problem into a known problem type.

When students master these mathematical thinking methods in senior high school, they can better cope with various mathematical problems and improve their problem-solving ability and thinking flexibility. In the process of learning, we should pay attention to active thinking, sum up laws, strengthen practice and improve our mathematics literacy.