1. ?

Correspondence is a way to think about the connection between two groups of elements. In primary school mathematics, the idea of correspondence is generally embodied in the form of charts, such as the one-to-one correspondence between the number axis and the specific number.

2. suppose.

Hypothesis is to make some assumptions about the known conditions or problems in the topic first, and then calculate according to the known conditions in the topic; Make appropriate adjustments according to contradictions and finally find the correct answer. Hypothetical thinking is a meaningful imaginative thinking, which can make the problem to be solved more vivid and concrete after mastering it, thus enriching the thinking of solving problems. ?

3. Contrast?

Comparative thinking is one of the common thinking methods in mathematics, and it is also a means to promote the development of students' thinking. In the application of teaching scores, if teachers are good at guiding students to compare the known and unknown quantities before and after the change of the problem, they can help students find the solution quickly.

4. Symbolization. ?

Symbolic thinking is to use symbolic language (including letters, numbers, graphics and various specific symbols) to describe mathematical content. For example, in mathematics, all kinds of quantitative relations, quantitative changes, and deduction and calculation between quantities all use letters to represent numbers, and use condensed forms of symbols to express a large amount of information.

Step 5 be similar

Analogy refers to the idea of transferring the attributes of one type of mathematical object to another based on the similarity between the two types of mathematical objects. Such as additive commutative law's sum-multiplication commutative law, rectangular area formula, parallelogram area formula, triangle area formula, etc. The idea of analogy not only makes mathematical knowledge easy to understand, but also makes the memory of formulas natural and concise.

6. transformation. ?

Transformation is a way of thinking from one form to another, and its own size remains unchanged. For example, the equal product transformation in geometry, the same solution transformation in solving equations, and the deformation in formulas are also commonly used in calculation.

7. classification.

Classification is not a unique method of mathematics, and the idea of mathematical classification is manifested in the classification of mathematical objects and its classification standards. For example, the classification of natural numbers can be divided into odd and even numbers according to whether they can be divisible by 2; According to the number of divisors, it can be divided into prime numbers and composite numbers. For another example, triangles can be divided by edges or angles. Different classification standards will have different classification results and produce new concepts. The correct and reasonable classification of mathematical objects depends on the correctness and rationality of classification standards, and the classification of mathematical knowledge is helpful for students to sort out and construct their knowledge.

8. assemble. ?

Set thinking is a way of thinking that uses set concept, logical language, operation and graphics to solve mathematical problems or non-pure mathematical problems. Primary schools use intuitive means, graphics and objects to infiltrate and gather ideas. When talking about common divisor and common multiple, we adopt the thinking method of intersection.

9. Combination of numbers and shapes. ?

Number and shape are two main objects of mathematical research. Number cannot be separated from form, and form cannot be separated from number. On the one hand, abstract mathematical concepts and complex quantitative relations can be visualized, visualized and simplified with the help of graphics; On the other hand, complex shapes can be expressed by simple quantitative relations. When solving application problems, we often use the intuitive help of line segment diagram to analyze the quantitative relationship. ?

10. Statistics?

Statistical charts in primary school mathematics are some basic statistical methods, and the application problem of average value embodies the thinking method of data processing.

1 1. limit. ?

From quantitative change to qualitative change, the essence of limit method is to achieve qualitative change through the infinite process of quantitative change. When talking about the area and perimeter of a circle, the idea of limit division is to turn a circle into a square and a curve into a straight line. On the basis of observing finite splits, imagine their limit states. In this way, students can not only master the formula, but also sprout the limit idea of infinite approximation from the contradiction transformation between curve and straight line.

12. Replace. ?

It is an important principle to solve equations, and one condition can be replaced by other conditions when solving problems. For example, the school bought four tables and nine chairs and spent 504 yuan. 1 table 3 chairs are exactly the same price. What is the unit price of each desk and chair?

13.？

It is the basic idea in logical thinking. When positive thinking is difficult to solve, we can start from the problem to find a solution, and sometimes we can reverse it by drawing lines. For example, a car from A to B traveled 65,438+0/7 in the first hour, and traveled 65,438+06 kilometers in the second hour, with 94 kilometers to go. Find the distance between a and b.

14. Back. ?

Through the transformation process, the problems that may exist or have not been solved are classified into one category, so as to solve the problems more easily. This is called "transformation". Mathematical knowledge is closely related, and new knowledge is often the extension and expansion of old knowledge. In the face of new knowledge, it is undoubtedly of great help to students to think with transformed thinking methods, which will help them acquire new knowledge independently and improve their ability. The direction of transformation should be to turn the hidden into the obvious, the complex into the simple, the difficult into the easy and the unknown into the known.

15. Hold the same in change. ?

Grasping the quantitative relationship and the constant quantity in complex changes, and taking this as a breakthrough, often problems will be solved. For example, there are 630 kinds of science and technology books and literature and art books, of which science and technology books account for 20%; Later, I bought some science and technology books. At this time, science and technology books account for 30%. How many science and technology books did I buy?

16.？

The so-called mathematical model idea refers to the simplification and hypothesis of a specific object in the real world by using the processes of observation, experiment, operation, comparison, analysis and generalization, starting from its specific life prototype. It is a way of thinking to turn practical problems in life into mathematical problem models. Cultivating students to understand and deal with the surrounding things or mathematical problems from the perspective of mathematics is the highest realm pursued by teaching and the goal pursued by improving students' mathematical literacy.

17. The whole. ?

It is often a more convenient and time-saving method to observe and analyze mathematical problems and grasp them as a whole.