1. Transformational thinking in solving mathematical problems refers to changing the direction of the problem from one form to another from different angles when encountering obstacles in the process of solving problems, and seeking the best way to make the problem simpler and clearer.

Second, reverse thinking is also called divergent thinking. It is a way of thinking, which in turn seems to be the final conclusion of the same thing or viewpoint. Dare to "do the opposite", let thinking develop in the opposite direction, explore deeply from the opposite side of the problem, establish new ideas and shape new images.

Thirdly, logical thinking is a thinking process in which people observe, compare, analyze, synthesize, abstract, summarize, judge and reason things with the help of concepts, judgments and reasoning in the process of cognition. Logical thinking is widely used to solve logical reasoning problems.

Fourth, innovative thinking refers to the thinking process of solving problems with innovative and novel methods. Through this kind of thinking, we can break through the boundaries of traditional thinking, think about problems with unconventional or even unconventional methods and perspectives, and put forward different solutions. It can be divided into four types: difference, exploration, optimization and negation.

5. Analogical thinking refers to the thinking method of comparing unfamiliar and unfamiliar problems with familiar problems or other things according to some similar properties of things, so as to find out the essence of knowledge and find out its essence.

6. Corresponding thinking is a way of thinking that establishes a direct connection between quantitative relations (including quantity difference, quantity times and quantity rate). General correspondence (such as the sum and difference times of two or more quantities) and ratio correspondence are more common.

Seven, thinking in images, mainly refers to people in the process of understanding the world, choose the form of things. It refers to the way of thinking to solve problems with intuitive images. Imagination is the advanced form and basic method of thinking in images.

Eight, systematic thinking is also called holistic thinking. Systematic thinking refers to the systematic understanding of the knowledge points involved in specific problems when solving problems, that is, first analyze and judge which knowledge points belong to which knowledge points, and then recall the types of such problems and the corresponding solutions.