The number of thought should be linked between two groups of elements, the figure should be intuitive, and the straight line point (number axis) of function thought should correspond to specific numbers.

2. Hypothetical thinking

Assume that the topic has known conditions or problems, make some assumptions, calculate according to the known conditions of the topic, adjust according to the contradiction of quantity, find the correct answer, imagine the meaning, grasp the thinking, make the problem to be solved more vivid and concrete, and enrich the thinking of solving the problem.

3. Comparative thinking

Comparing ideas, seeing numbers, thinking, means to promote thinking development, and teaching mathematical application problems, teachers are good at guiding situations before the known and unknown numbers of comparative problems change and helping to find solutions quickly.

4. Symbolic thinking

Symbolic language (including letters, numbers and figures) is used to describe the contents of numbers, symbols and ideas, the changes of various quantitative relations and the deduction between quantities. Letters are used to express the laws and formulas of quantitative information in the condensed form of numbers and symbols.

5. Analogical thinking

The idea of analogy refers to the idea of transforming the other digital image according to the similar performance of the two digital images, and adding the exchange law, shape area formula and parallelogram area formula. Analogical thinking only makes mathematical knowledge easy to understand and formulas simple to remember.

Step 6 change your mind

The idea of transformation is to transform from one form to another, its own geometric equivalent product transformation, solution homosolution transformation, formula deformation and so on. Are calculated by a-b = a×1/b.

7. Class ideology

Class thought Sudoku thought embodies whether the number image class and its standard self-number class can be divisible by 2; According to divisor, prime number, composite triangle, edge and angle, similarity standard, similarity production, new concept and precision of number, reasonable class depends on the precision of class standard, and rational number knowledge class helps to sort out and construct knowledge.

8. Collect ideas

Set thought uses set concept, logical language, operation, graphics and other ideas to solve the problem of number or impure number, uses intuitive means, uses graphics to infiltrate set thought, tells the common multiple of common divisor, and adopts intersection thought.

9. the idea of combining numbers with shapes

The study of number and shape The concept of complex number relationship is abstracted from the number surface, and it is visualized, intuitive and simplified with the help of graphics. The complex shape on the other side is expressed by simple number relation, and the application problem is solved by line segment diagram.

10, statistical thought:

Some basic statistical application problems of digital statistical charts reflect the idea of data processing.

1 1, extreme thoughts:

The limit of quantitative change and qualitative change of things is the essence of quantitative change and qualitative change. Talking about the idea of circle area, circle, circle, curve and straightness, observing the basic idea of limit section and imagining the limit state can only change the idea that the germination limit approaches the limit by mastering the contradiction between formula and straightness.

12, substitution idea:

Solve an important principle by solving a problem. Replace a certain condition with other conditions. It costs 504 yuan to buy 4 tables and 9 chairs. The price of 3 chairs per table is equal, and the unit price of each table chair is less.

13, inverse thinking:

The basic idea of logical thinking is that positive thinking is difficult to answer conditions or questions and solve problems. Draw a line for the whole journey from A to B 1/7, and find the distance between A and B for the second line 16 km 94 km.

14, turn to thinking:

Solvable or unsolvable problems can be solved through the transformation process, and it is easier to solve problems, and the restored knowledge is closely related to new knowledge. It is often to extend and expand old knowledge, so that new knowledge can be applied to thinking and thinking, and the ability to acquire new knowledge independently can be improved.

15, change your mind:

Numerous and complicated changes, how to grasp the quantitative relationship and how to grasp the breakthrough of variables are often solved: 630 science and technology books, of which 20% are science and technology books and 30% are science and technology books.

16, the idea of number model:

The so-called mathematical thinking refers to the application of observation, experiment, operation, comparison, analysis and comprehensive generalization to a concrete image in the real world, and so on. It is the goal of high mathematics literacy to cultivate the idea of transforming practical problems into model problems of numbers from the perspective of numbers.

17, general idea:

The observation and analysis of mathematical problems is often more convenient and economical to lose species at the macro level.