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, also known as divergent thinking, is a way of thinking about common things or opinions that seem to have become conclusive. Dare to "do the opposite", let thinking develop in the opposite direction, conduct in-depth exploration from the opposite side of the problem, establish new concepts 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 novel and unique methods. Through this kind of thinking, we can break through the boundaries of conventional thinking, think about problems with unconventional or even unconventional methods and perspectives, and come up with unique solutions. It can be divided into four types: difference type, exploration type, optimization type and negative type.

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 between things, discovering the essence of knowledge and finding its essence, so as to solve problems.

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

Eight, systematic thinking is also called holistic thinking. Systematic thinking method refers to having a systematic understanding of the knowledge points involved in specific problems when solving problems, that is, analyzing and judging what the knowledge points belong to when getting the problems, and then recalling what types of such problems are divided into and the corresponding solutions.