What kinds of mathematical thinking modes are there?

Mathematical thinking mode: transformation thinking, reverse thinking, innovative thinking, systematic thinking and analogy thinking.

Transforming thinking: When encountering a problem, transform the problem from one form to another, and seek the best method to make the problem simpler and clearer. Logical thinking: observing, comparing, analyzing, synthesizing, abstracting and summarizing things with the help of concepts, judgments and reasoning, and drawing conclusions.

Reverse thinking: reverse thinking about seemingly conclusive common things or viewpoints, making thinking develop in the opposite direction and exploring from the opposite side of the problem. Correspondence thinking: establishing direct connection between quantitative relations, which is common in general correspondence and quantity-rate correspondence.

Innovative thinking: the thinking process of solving problems with novel and unique methods. Through innovative thinking, we can break through the boundaries of conventional thinking and think about problems with unconventional or even unconventional methods and perspectives.

Systematic thinking: also known as holistic thinking, when solving problems, we have a systematic understanding of the knowledge points involved in specific topics, that is, we analyze which categories the topics belong to, and then recall which categories such topics are divided into and the corresponding solutions.

Analogical thinking: according to some similar properties between things, unfamiliar and unfamiliar problems are compared with familiar problems or other things to find the essence of knowledge and find its essence. Thinking in images: the thinking method of solving problems with intuitive images, the highest form of which is imagination.

Children usually go through the following stages when learning mathematics:

Shallow stage (before 3 years old): think that numbers are just a word.

Primary stage (3-6 years old): the amount of items, such as "I ate 4 blueberries".

Intermediate stage (6-9 years old): the relationship between things, such as 4 o'clock is always before 5 o'clock.

Advanced stage (9- 12 years old): These quantities can be compared and calculated.