What are the mathematical thinking methods 1 and transformation methods?
Transforming 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 foundation 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 method
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.
4. The corresponding method
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.
5. Innovative methods
Innovative thinking refers to the thinking process of solving problems with novel and original 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.
6. Systematic approach
Systematic thinking is also called holistic thinking. Systematic thinking refers to having a systematic understanding of the knowledge points involved in a specific topic when solving a problem, that is, analyzing and judging what the knowledge points belong to when getting the topic, and then recalling what types of such questions are divided into and the corresponding solutions.
7. Simulation 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, discovering the essence of knowledge, finding its essence, and thus solving problems.
8. Systematic approach
Systematic thinking is also called holistic thinking. Systematic thinking refers to having a systematic understanding of the knowledge points involved in a specific topic when solving a problem, that is, analyzing and judging what the knowledge points belong to when getting the topic, and then recalling what types of such questions are divided into and the corresponding solutions.
9. Image method
Thinking in images mainly refers to people's choice of images in the process of understanding the world, and refers to the thinking method of solving problems with intuitive images. Imagination is the advanced form and basic method of thinking in images.
The Importance of Mathematical Thinking People with good mathematical thinking ability not only learn to do things more efficiently, but also communicate with others more easily. In other words, mathematical thinking ability almost determines the difficulty of a child's life.
Mastering mathematical thinking is equivalent to mastering the learning keys of all subjects. The charm of mathematics is infinite. The beauty of mathematics is that it is the foundation of all sciences, the lifeblood and the birthplace of self-energy explosion.
In the future world, if you master mathematical thinking and make good use of it, it will surpass millions of soldiers and let you have an open life.
How to Cultivate Mathematical Thinking 1 and Thinking Flexibility
The flexibility of thinking refers to the timeliness of being able to adapt to the changes of things without being too affected by the mindset. If we lack the flexibility of thinking, our thinking will be more inclined to a specific way and method, and it is easy to go into a dead end and unilaterally pursue the mode and procedure of solving problems, which will lead to the inertia of thinking in the long run.
Good at getting rid of the old model 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.
The rigor of thinking refers to the rigor and justification of considering problems. To improve the rigor of students' thinking, we must be strict and strengthen training.
Implementing it in children's study life means starting with the basic ideas when learning new knowledge, steadily and steadily under the premise of clear ideas, developing the habit of serious thinking in this relatively slow process, and mastering enough reasons as the basis when 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.
Thinking depth refers to the abstraction and logical level of thinking activities, as well as the depth and difficulty of thinking activities. I believe that most students have experienced such a situation. Sometimes, when the teacher is marking papers, it is easy to understand the problem-solving process of wrong questions and suddenly realize that he has made such a low-level mistake.
But once you leave books and teachers, you can't understand the method and essence of solving problems and realize independent problem solving. This requires students to see 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.
4. Cultivate the openness of thinking
The broadness of thinking means that a problem can be considered from many aspects. Specifically, it can explain a fact in many ways, express an object in many ways, and put forward many solutions to a topic. In mathematics learning, paying attention to multi-directional and multi-angle thinking and broadening the thinking of solving problems can promote students' thinking broadening.
5. Cultivate critical thinking.
Critical thinking refers to being good at strictly estimating thinking materials and carefully examining the thinking process in thinking activities. In the process of mathematics learning, students should be good at extracting what they want from the existing answers and problem-solving ideas, and express their views.
We should not blindly follow, but learn to reflect and test in various ways with critical thinking. Even if you completely accept something ideologically, try to improve it and put forward new ideas and viewpoints.
In the process of social development, mathematics, as a cultural phenomenon, has attracted people's attention. In recent years, mathematical culture