1, transformation method: transformation thinking is both a method and a kind of thinking. Transformational thinking 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.
2. Logical method: Logic is the basis of all thinking. Logical thinking is a thinking process in which people observe, compare, analyze, synthesize, abstract, generalize, 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.
3. Reverse thinking method: Reverse thinking, also known as divergent thinking, is a seemingly conclusive way of thinking about common things or opinions. 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.
4. Correspondence method: Correspondence 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.
5. Analogical thinking method: 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, finding the essence of knowledge and finding its essence, so as to solve problems.
Ways to Cultivate Mathematical Thinking Logic
1, cultivate the flexibility of thinking: be good at getting rid of old patterns and general constraints and finding the right direction; Since knowledge can be used freely, dialectical thinking can be well used to balance the relationship between things, analyze specific problems and adjust ideas flexibly. These are the direct manifestations of the cultivation of thinking flexibility.
2. Cultivate the rigor of mathematical thinking: under the premise of clear thinking, slowly and steadily, gradually deepen, and master enough reasons as the basis for reasoning; When practicing test questions, we should be good at paying attention to the hidden conditions in the stem, answering questions in detail, and writing out the ideas for solving problems without stint.
3. Cultivate the profundity of mathematical thinking: Students should look at the essence of mathematics through phenomena, master the most basic mathematical concepts and gain insight into the relationship between mathematical objects in their usual study, which is the main manifestation of profound thinking.