Guildford, a famous psychologist, pointed out: "People's creativity mainly depends on divergent thinking, which is the main part of creative thinking." Divergent thinking here refers to a way of thinking as opposed to centralized thinking. Divergent thinking explores problems from different angles, analyzes problems from different levels, and compares them from positive and negative poles, so it has a broad vision and active thinking, and can produce a large number of unique new ideas. Centralized thinking means that people's ideas for solving problems converge in one direction, thus forming the only definite answer. Divergent thinking is characterized by enthusiasm, diversity, extensiveness and association. Consciously grasping these characteristics in mathematics teaching can not only improve students' divergent thinking ability, but also improve the quality of mathematics teaching. Stimulate curiosity and train the enthusiasm of thinking. Thinking inertia is an obstacle to divergent thinking, while thinking enthusiasm is the bane of thinking inertia. Therefore, cultivating the enthusiasm of thinking is an extremely important basis for cultivating divergent thinking.
Under the premise of thoroughly understanding the problem and grasping the essence of the problem, the key is to be able to break the mindset, change the single way of thinking, and use association, imagination, conjecture and inference. We should expand our thinking as much as possible, and make flexible and agile thinking from all angles, aspects and levels of the problem, forward, backward, vertically or horizontally, so as to obtain many schemes or assumptions.