? There are hundreds of ways of thinking, including abstract thinking, logical thinking, dialectical thinking, image thinking, structured thinking, critical thinking, systematic (holistic) thinking, creative thinking, combinatorial thinking, divergent thinking, inspirational thinking, intuitive thinking, reverse thinking, scientific thinking and philosophical thinking.
? Here, we emphasize dialectical thinking. To have flexible thinking, we must be familiar with and deeply understand dialectical thinking. The Secret of Mathematical Thinking Method-1mentioned the vocabulary of dialectics, dialectical thinking and dialectical thinking, which listed many pairs of words. At first glance, most of them are pairs of words with unity of opposites, such as abstract and concrete, special and general. Their relationship can not only be understood as affirmation and negation, but should be understood from the perspective of dialectical universal connection, and anyone who has connections can join this vocabulary. There may be the following forms of relationship between interrelated objects: mutual generation, mutual resistance, mutual change, similarity and mutual infiltration. Common growth: for example, out of nothing, with or without common growth. In mathematics, an object or structure is constructed by construction method; Mutual restriction, mutual restriction or one side restricting the other is opposite or negative, such as water and fire. In mathematics, such as reciprocal, square root, function and inverse function, the former method hit a wall in the process of solving problems. When this road is impassable, we will deny this method. Failure is the mother of success, and the method of failure is also valuable, because we can get the correct problem-solving method or operation according to the method of failure, and the method of failure and the method of success are different from each other. Phase transformation, mutual transformation or mutual change, abstract transformation into concrete, concrete transformation into abstraction, such as equations and inequalities, are related, so some equations can be solved by inequalities; Similarity is similar to imagination. Being close to Zhu Zhechi and Mexico is black. Infiltration means that you have me, and I have you, infiltrating each other. Similar to mixing sand in cement. In mathematics, the combination of numbers and shapes is tangible, and there are numbers in the shape. In the process of solving problems, the combination of numbers and shapes is used. For example, algebra problems are generally the negation of logarithm-shape-(and then to number), rather than just one link: number-shape.
The most vivid understanding of dialectical thinking dialectics is the dynamic three-dimensional Taiji fish of yin and yang, which vividly reveals the two sides of dialectics, such as mutual development, mutual resistance, mutual change, similarity and mutual infiltration. Similarly, the two yin-yang fish models are the same; Mutual infiltration: knowing black and keeping white, snakehead has white fish eyes, knowing white and keeping black, and white fish has black fish eyes.
? Dialectical thinking is thinking under the guidance of dialectics, which mainly uses interrelated viewpoints to guide thinking. Dialectical thinking can learn the entry of Baidu Encyclopedia: dialectical thinking.