How to improve the rigor of thinking? How to improve the rigor of thinking? Thinking is a positive and purposeful cognitive activity, and it is a general, essential and indirect reflection of the human brain on objective things. Thinking is the core of intellectual structure, and Engels praised human thinking as the most beautiful flower on the earth. Einstein, a master of science, believes that "the development of general ability of independent thinking and independent judgment should always be in the first place, not the acquisition of professional knowledge." He also stressed: "Learning knowledge should be good at thinking. After thinking and thinking, I became a scientist by this learning method. " Academician Wu Jieping, Vice Chairman of the National People's Congress Standing Committee (NPCSC) and a world-famous urologist, pointed out in the article "Wisdom lies in thinking": "I think the difference of human wisdom lies in the ability to apply thinking. Brain power also needs exercise. If you persist in thinking hard all your life, your thinking ability will continue to improve. " The rigor of thinking (scientific, dialectical, profound and logical) is mainly manifested in understanding the essence of things from intricate connections and relationships through careful analysis. In order to fully reflect the whole thing, the essence and inherent regularity of things, and more importantly, for the smooth implementation of thinking results in the process of putting them into practice, we must think and demonstrate from multiple perspectives, aspects, factors and dimensions. We must investigate and predict the possible situations, possible factors and possible consequences one by one, and then make a scientific choice or decision based on the basic judgment of the main contradiction and the main contradiction through analysis and synthesis. The grasp of choice and decision depends on the rigor of multi-dimensional thinking. Without the premise of rigorous thinking like "mercury pouring down the ground", there can be no "lightning" decisive choice and decision.
Think with a frown, and then touch your chin.
Need to exercise
Think more at ordinary times
How to improve the rigor of high school mathematics thinking is a question of practice, but don't think that doing more exercises must be extrapolated, divergent thinking will make you get twice the result with half the effort.
How to improve the flexibility of thinking? Practice mental arithmetic. Brainstorming or something.
Learning piano and other music is also a good way.
First, how to improve the rigor of thinking? What exercises can improve the rigor of thinking? You can grasp the overall situation without ignoring the details. Like thinking like a German. Thinking is a positive and purposeful cognitive activity, and it is a general, essential and indirect reflection of the human brain on objective things. Thinking is the core of intellectual structure, and Engels praised human thinking as the most beautiful flower on the earth. Einstein, a master of science, believes that "the development of general ability of independent thinking and independent judgment should always be in the first place, not the acquisition of professional knowledge." He also stressed: "Learning knowledge should be good at thinking. After thinking and thinking, I became a scientist by this learning method. " Academician Wu Jieping, Vice Chairman of the National People's Congress Standing Committee (NPCSC) and a world-famous urologist, pointed out in the article "Wisdom lies in thinking": "I think the difference of human wisdom lies in the ability to apply thinking. Brain power also needs exercise. If you persist in thinking hard all your life, your thinking ability will continue to improve. " The rigor of thinking (scientific, dialectical, profound and logical) is mainly manifested in understanding the essence of things from intricate connections and relationships through careful analysis. In order to fully reflect the whole thing, the essence and inherent regularity of things, and more importantly, for the smooth implementation of thinking results in the process of putting them into practice, we must think and demonstrate from multiple perspectives, aspects, factors and dimensions. We must investigate and predict the possible situations, possible factors and possible consequences one by one, and then make a scientific choice or decision based on the basic judgment of the main contradiction and the main contradiction through analysis and synthesis. The grasp of choice and decision depends on the rigor of multi-dimensional thinking. Without the premise of rigorous thinking like "mercury pouring down the ground", there can be no "lightning" decisive choice and decision. Second, the importance of improving thinking ability: thinking is the core of intelligence 1. Thinking is the core of intelligence, and it is the main sign to examine a person's intelligence. Engels praised thinking as "the most beautiful flower on the earth", and all human creative activities are related to thinking ability. Fundamentally speaking, human progress is the progress of human thinking. Whether a person can become a success depends on whether he can develop effective thinking ability from an early age. Looking at those people who have made outstanding contributions in the world, they all have one thing in common, that is, their thinking ability is extremely agile. Edison, the great inventor, was a child who loved to use his brain and was good at thinking since he was a child. It can be said that thinking is as important as the soul, whether for society or for individuals. All human activities are based on thinking activities, and people without thinking activities are like walking dead, not to mention intellectual activities. And the simplicity and complexity of brain thinking directly determine a person's intelligence level. A person without good thinking quality will not have a high level of intellectual development. 2. The basic theory of improving thinking ability (thinking training) (1) The broad and narrow sense of thinking training exists in all aspects of people's lives. Everyone has been receiving all kinds of thinking training since birth, whether it is a mother teaching children to eat and walk or a teacher teaching students to write and draw; Whether accepting an idea or forming a habit is essentially a mental thinking training. Narrow thinking training refers to specialized thinking training, specifically, it is an advanced thinking training. To use a popular metaphor, thinking training in a broad sense means that children learn to doodle with the help of their mothers, while thinking training in a narrow sense means that students learn to draw under the guidance of masters. Although the essence of the two is the same, the levels are quite different. (2) the emptiness and reality of thinking training Many people feel that training thinking is "empty" when they first encounter thinking training. It is neither so practical as drawing and typing, nor so visible as learning math and Chinese. If we regard thinking as virtual and think that thinking training is useless because it is invisible and intangible, it is wrong. Thinking training seems empty, but it is real. In terms of use, any practical skill training is ultimately thinking training, and painting itself is real, but if you don't master imaginary things such as painting techniques and artistic creation rules, it is impossible to draw good works. Learning to digest these techniques and laws is actually a kind of painting thinking training. From a hierarchical point of view, the more intelligent training, the more virtual, and the more developed society, the more people need to develop their own abstract thinking. (3) The source and process of thinking training is the most popular and effective intellectual development method in the world at present, but it is not a unique patent in modern times. Nowadays, thinking training is based on the latest scientific achievements of thinking and ancient brain training techniques. As early as ancient Greece, the famous philosopher Socrates created the famous "brain midwifery". In modern society, thinking training is widely welcomed by people, and the promotion of commercial factors is indispensable. In western developed countries, large companies generally pay more attention to the training of employees, especially the training of creative thinking is almost a compulsory course for general managers and executives, because they really feel that there is a great difference between receiving thinking training and not receiving thinking training in practical work. 3. Principles to follow in improving thinking ability (1) Simplicity and complexity The thinking of analyzing problems (even simple small problems) from multiple angles, levels and ways is called complex thinking mode. The kind of thinking that can only look at problems from one angle, one level and one way is called simple mode. The purpose of thinking training is not to find answers, but to transform the way of thinking from simple to complex, that is, to cultivate the thinking habit of looking at problems from multiple angles, levels and ways, finding problems, analyzing problems and solving problems. Complex thinking mode enables us to deal with complex problems simply, quickly and effectively. Can see the big from the small, the complex from the simple, the law from the ordinary, and the true meaning. It is a first-class keen mind that reaches this level of thinking ability. The simplicity and complexity of thinking training questions are not the key to training, but the key lies in whether the thinking mode of the brain is complex or simple. Therefore, in thinking training, we should carefully distinguish between simplicity and complexity of thinking mode and simplicity and complexity of thinking training questions. Without such effective training, even knowledgeable and experienced people will use simple thinking mode to analyze and solve complex problems. (2) Low-level thinking is different from high-level thinking and low-level thinking, and has the characteristics of relativity. The level of thinking is mainly reflected in the way of thinking. Comparatively speaking, abstract thinking mode is higher than image thinking mode, creative thinking mode is higher than imitation thinking mode, three-dimensional thinking mode is higher than plane thinking mode, horizontal thinking mode is higher than vertical thinking mode and so on. In the process of thinking training, we should treat the relationship between low-level thinking mode and high-level thinking mode dialectically. We should not abandon the low-level way of thinking because we pursue the high-level way of thinking. Because low-level thinking mode is the basis of high-level thinking mode, and high-level thinking mode is the development of low-level thinking mode. The two are interdependent and interrelated. It is neither desirable nor possible to cross the low-level way of thinking in order to reach the high-level way of thinking. In the process of thinking training, thinking should be gradually developed from low level to high level. The training of low-level thinking mode is helpful to broaden and consolidate the foundation and create conditions for the development of thinking to advanced level. Advanced thinking mode is conducive to rapidly improving thinking level and broadening horizons. Only through sequential training and cross-training between them can we grasp the correct scale in thinking training and achieve the best training effect. (3) Process and Result People tend to pay attention to the result and despise the process. But the focus of thinking training is the process of thinking. In general school education, there are usually two teaching methods, one is to tell students the result of the problem directly, and the other is to teach students the process of obtaining the result. The former way is very convenient, but it is not good for students. The latter way is troublesome, but students can benefit for life. Of course, this does not mean that thinking training should not be centered on results. The emphasis on process here is to make trainees learn to observe problems more accurately, analyze problems more efficiently and solve problems more scientifically. The purpose of training is not just to get an answer. The answer is not the key to the problem, but how to find the answer is the most important. (4) Methods and training thinking methods are the crystallization of wisdom summarized from the experience and lessons of countless thinking activities, which can be divided into two categories: one is how to improve thinking intelligence, such as image memory method can improve memory, associative creation method can improve creativity, etc. The other is how to observe, analyze and solve problems scientifically, such as dialectical thinking, logical thinking, reverse thinking and systematic thinking. Although mastering the correct thinking method can greatly improve the thinking ability, there is still a long training process from mastering the thinking method to transforming it into thinking skills. Only after a long period of thinking training can we skillfully use thinking methods to guide the solution of various problems in thinking practice. In the process of thinking training, a lot of training is very important and scientific methods are also very important. If we don't pay attention to the study of methods, a lot of training will only be low-level repetition and futile. Without strengthening training, the learned methods will not be transformed into skills and have no practical value. The learning of thinking methods and the training of thinking skills are two processes, which cannot replace each other. Bias or lack of any of them can not be regarded as scientific thinking training. (5) Stereotyping activates thinking stereotyping or forms a mindset, which is an inevitable trend of thinking development and cannot be avoided. The crux of the problem is that if our brains can't consciously shape efficient and correct thinking patterns and let them develop freely, they may form inferior and wrong thinking patterns. Stereotyping or forming a mindset is not terrible. The terrible thing is to form a wrong mentality or a bad mentality. Thinking set in thinking training is not only inevitable, but also necessary. The key to the problem lies in how to shape thinking and what kind of thinking mode to make the brain give full play to its intellectual potential. Knowledge education pays most attention to the process of knowledge accumulation, and regards systematic learning of knowledge as the core task of education. This easily leads to abnormal development and stereotype of thinking. Thinking education is to put the development of students' thinking ability and the cultivation of correct thinking mode at the center of education. Thinking training is not only a simple thinking pattern generation training, but also includes thinking activation and thinking innovation training. To some extent, all thinking modes have a certain binding effect on the mind, and it is even more difficult to change the rigid thinking mode. The purpose of thinking activation training is to get rid of the shackles of fixed patterns and transcend the limitations of fixed patterns. This kind of training can awaken thinking from the unconscious "sleep state", transcend the old thinking level, and look down on your thinking activities from a higher position. At this time, all thinking modes and patterns have become thinking tools. (6) The purpose of potential and skill thinking training is to develop individual intellectual potential in the final analysis. Talent is only a kind of potential, and only through long-term skill training can it be transformed into practical ability. The core of thinking training is to train brain thinking into a skill, just like training painting skills and sports skills. The instinct of thinking is not equal to the ability of thinking. The formation of any kind of ability is the result of repeated skill training, and thinking must be regarded as a skill training. Training thinking into a skill is a professional requirement for intelligence. The core training of thinking skills is mainly divided into two parts. One is to train the ability to turn thinking methods into reality according to the types, difficulties and simplification of problems. The second is to train the ability to solve problems by using various thinking methods comprehensively.
How can we train the rigor of thinking?
The rigor of thinking means that we should strictly abide by logical rules when studying problems, so as to achieve clear concepts, correct judgments and well-founded reasoning, which embodies the rigor and meticulousness in thinking activities.
Due to the limitation of junior high school students' cognitive level and psychological characteristics, there is often a phenomenon of imprecise thinking. To cultivate the rigor of students' thinking, we should pay attention to the following aspects:
1, training accurate expression
Whether we can accurately understand the meaning of mathematical concepts, formulas, rules and theorems is an important sign of rigorous thinking, and the degree of students' understanding is often reflected in their language expression. In addition to the teacher's language demonstration, students should be guided to pay attention to some key words in definitions, formulas, rules and theorems to make them accurate and learn to express them correctly in symbolic language.
2. Train strict reasoning.
Reasoned reasoning is the core requirement of rigorous thinking. It means that every step of reasoning should be reasonable and logical. The completion of proof depends on strict reasoning, and the reasoning process is also included in calculation and drawing. Therefore, on the one hand, we should cultivate students' habit of strict reasoning, on the other hand, we should often help students correct logical errors in reasoning in time.
3. Comprehensive consideration of training
It is common for students to solve problems incompletely or even make mistakes because of their incomplete consideration of problems. In order to help students learn to think comprehensively and carefully and overcome carelessness, we should pay attention to selecting some suitable contents and exercises for training in the teaching process.