Our teacher once said that learning English well depends on diligence and learning math well depends on thinking.
For some people who are not good at math.
I think there are only two kinds: one is poor foundation and the other is poor method.
For people with poor foundation, learning mathematics is the most difficult, because it will be more difficult for them to learn mathematics well than those with good foundation.
The foundation comes from primary school, and mathematics in primary school can be said to be the cornerstone of middle school. Many middle school students don't study hard because of their poor foundation, and finally they can't understand anything-but math tutoring must be faster than English. Poor English takes time, while poor math can solve all the problems as long as they master the skills-
However, some people have poor methods-they can't just think about math problems with their brains-unless they simply do oral calculations-some problems seem simple-but they often just think with their brains. After a long time, they get used to it and gradually forget that we still have hands. When I do a problem, no matter how difficult it is, as long as it is a math problem, I will put a long piece of paper on the table, grab a pen in my hand and write down my thoughts on the paper at any time, so that I can not only put my thoughts on the problem,
Talking about the representatives of junior middle school mathematics
Question 2: What kind of thinking mode is mathematics? Mathematics is more than just calculating and applying formulas.
The essence of mathematics is a way of thinking, a logical way of thinking of deductive reasoning and inductive reasoning.
Learning mathematics is not necessarily the goal, but to cultivate one's ability through learning mathematics.
At the same time, learn mathematics to understand the world and various phenomena related to it.
Question 3: What is the ability of mathematical logic? The ability of mathematical logic also refers to the ability of exponential logical thinking. Mathematical logical thinking ability is a strict rational thinking ability. Mathematical logical thinking ability refers to the ability to think correctly and reasonably, that is, to observe, analogize, induce, deduce, analyze, synthesize, abstract and systematize things, use correct reasoning methods and reasoning formats, express their rigorous rational activities accurately and orderly in the thinking process, and successfully complete certain activities. At the same time, it is the synthesis of various abilities necessary for people to engage in mathematical activities, and it is the core of mathematical ability.
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Conceptual decomposition of mathematical logical thinking
1. Mathematical thinking: It is an internal rational activity that the human brain interacts with mathematical objects (spatial form, quantitative relationship and structural relationship) and understands mathematical content according to the general thinking law. Mathematical thinking is mainly manifested in the operation of mathematical thinking, in the characteristics and operation methods of mathematics. Specifically, mathematical thinking has three characteristics: generality, problem and similarity. The generality and problems here (including "why, problem construction and solution") are not generality and problems in the usual sense, and only those who have enough knowledge of mathematics can understand them; Similarity refers to the similarity, consistency and non-contradiction of thinking results, which is different from other disciplines.
2. Mathematical logical thinking: correct and reasonable thinking, that is, observing, analogizing, inducing, deducing, analyzing, synthesizing, abstracting and systematizing things, and using correct reasoning methods and reasoning formats to accurately and orderly express their rigorous rational activities.
3. Mathematical thinking and attack ability: ability is a necessary personality and psychological feature for successfully completing an activity, which directly affects the efficiency of the activity. Mathematical ability is the synthesis of various abilities necessary for people to engage in mathematical activities, and mathematical thinking ability is the core of mathematical ability.
Question 4: Can learning mathematics really exercise logical thinking? Let me say something in general. First of all, there are two kinds of logic in connotation: formal logic in a narrow sense and dialectical logic, deductive logic and analytical logic in a broad sense. So when it comes to logic, it often refers to a certain kind of logic. For example, after completing the high school course of mathematics, you will learn and exercise logical thinking and expression skills such as formal logic, deductive logic, judgment logic, analytical logic, computational logic and graphic logic. Secondly, it is said that learning mathematics can exercise logical thinking, which depends on whether you study seriously or not, and what kind of logic you mean. It's impossible for you to learn logic well without learning it well. It is impossible to finish all the logic study after graduating from college.
You said you were good at math, but you didn't find your logical ability improved. On the one hand, it shows that you don't know the classification of logic, and you don't know what logical ability you can improve by learning mathematics; On the other hand, you may not have learned anything that can improve your ability, or you lack the vision of "discovering your progress".
Let me answer your little question again.
1, reading detective stories can exercise logical thinking ability, which is true. But is it necessary for everyone to study this course? Is it necessary to offer detective courses? What did you say?/Sorry? This course is complex in content and wide in knowledge, but it is not widely used in daily life ... Is it necessary to add this heavy burden to every student? You said that detective science is more interactive than mathematics because you didn't put yourself into it and didn't taste the sweetness of learning mathematics.
2. When it comes to whether the ancients had never studied mathematics, they had logical thinking ability, which depends on two aspects. First, we can't say that the ancients didn't learn mathematics. We can only say that mathematics was not popular in ancient times, and it was not a compulsory course for school students. That is to say, the preconditions you said don't really exist. Second, even if the ancients didn't learn mathematics, no one can say that they didn't have the ability of logical thinking. Because there is an ability, not just the way to school. It can only be said that if you don't learn mathematics, your logical thinking ability will be poor or even lacking; I have the ability originally, and it is difficult to get exercise to improve.
The learning methods in the west are different from those in our country. They use encouragement, guidance and heuristic teaching more. This learning method is conducive to stimulating students' interest in learning, consciously learning, and even conducive to innovation, invention and discovery. Therefore, it is hard to say that it is of much value for you to mention that western countries are lax in their studies and that students are not more stupid than us. Because you can't say that they are loose from the appearance of doing less homework. They just study in a different way from us.
You said, "Personally, I think ..." These are your own guesses. How do you prove that they are true? Even if it is true, it is true that the country wants to improve its national strength and grasp students' math scores. But you can't imagine * * * deceiving everyone under the pretext that "learning mathematics can improve logical thinking ability", because this kind of deception is very inferior. If mathematics can't improve logical thinking ability, how can he make up lies?
It is an indisputable fact that learning mathematics can improve logical thinking ability. It's just that not everyone can learn and not everyone can use advanced mathematics knowledge.
Question 5: What is mathematical thinking? 10 is not so mysterious. Your question is actually a common problem of many students. The problem lies in two possibilities. First, your thinking habits in learning are not thorough, that is to say, after you get the topic, you will often be proud of the first point you think of instead of continuing to think about the later things. This is called problem-solving thinking. The way to deal with this problem is actually to force yourself not to get excited before you get the answer. In addition, you should write down the topic. Students with this problem usually do well in unit tests, but they do poorly in the overall tests. The reason is that the knowledge of each chapter is not well connected, so we need to think about the relationship between them. In order to avoid platitudes, I'll give you three questions. You might as well think about it: What is the knowledge of 1 described in my own words? This knowledge: If I give a question, what will I take? How much knowledge can I find about this knowledge?
Question 6: What is logical thinking ability? Why do you say that learning mathematics well can enhance a person's logical thinking ability? In the process of cognition, people reflect the realistic way of thinking through concepts, judgments and reasoning. Different from thinking in images, it reveals the essence of things with scientific abstract concepts and expresses the results of understanding reality. Also called abstract thinking.
Mathematics is a subject under such a mode of thinking, which naturally complements each other.
Question 7: What does logical thinking mean? Logical thinking ability refers to the ability to think correctly and reasonably. That is, the ability to observe, compare, analyze, synthesize, abstract, summarize, judge and reason things, and the ability to express one's thinking process accurately and methodically by using scientific logical methods. It's completely different from thinking in images. Logical thinking ability is not only an essential ability to learn mathematics well, but also an essential ability to learn other disciplines and deal with daily life problems. Mathematics is a discipline that reflects the objective world with quantitative relations (including spatial forms), which is very logical and rigorous. Flexible use of logic and logical thinking ability does not mean that you can solve difficult problems. Logically speaking, it has the problem of using skills. How come practice makes perfect? Learning mathematics means that you solve more problems, and you know what must happen to solve these problems. This can be called mathematical philosophy. Generally speaking, this is the difference between liberal arts students and science students, not whether they have logical thinking. At the same time, in reality, people think that logical thinking ability is strong, but in fact, thinking ability is strong, and there is no distinction between arts and sciences. Moreover, this idea is not logically obtained, but logically explained. The idea of participating in the debate arises in the debate, including arguing with yourself.
Question 8: What is mathematical thinking? Some people have summarized a lot: for example, directional thinking, reverse thinking, diffusion thinking, innovative thinking and so on. But I always think that they are not as good as a kind of thinking-logical thinking. Logic has two meanings at different levels and angles: 1. Logic is a sequence and a law. 2. Logic needs to be classified and then summarized. Logic is the abstract thinking of human beings, and it is the thinking process that people know and distinguish the objective world through concepts, judgments, reasoning and argumentation. To put it bluntly, logic is to do things in an orderly way. Logical thinking is the basis of other thinking methods, and other thinking methods, such as extended thinking and reverse thinking, are basically derived from logical thinking methods. Therefore, to learn mathematics well, we can consider other ways of thinking, but we can't just remember the names of those ways of thinking. More importantly, we must first do things in an orderly way and cultivate and consolidate logical thinking!
Question 9: What is the ability of mathematical logic? The ability of mathematical logic also refers to the ability of exponential logical thinking. Mathematical logical thinking ability is a strict rational thinking ability. Mathematical logical thinking ability refers to the ability to think correctly and reasonably, that is, to observe, analogize, induce, deduce, analyze, synthesize, abstract and systematize things, use correct reasoning methods and reasoning formats, express their rigorous rational activities accurately and orderly in the thinking process, and successfully complete certain activities. At the same time, it is the synthesis of various abilities necessary for people to engage in mathematical activities, and it is the core of mathematical ability.
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Conceptual decomposition of mathematical logical thinking
1. Mathematical thinking: It is an internal rational activity that the human brain interacts with mathematical objects (spatial form, quantitative relationship and structural relationship) and understands mathematical content according to the general thinking law. Mathematical thinking is mainly manifested in the operation of mathematical thinking, in the characteristics and operation methods of mathematics. Specifically, mathematical thinking has three characteristics: generality, problem and similarity. The generality and problems here (including "why, problem construction and solution") are not generality and problems in the usual sense, and only those who have enough knowledge of mathematics can understand them; Similarity refers to the similarity, consistency and non-contradiction of thinking results, which is different from other disciplines.
2. Mathematical logical thinking: correct and reasonable thinking, that is, observing, analogizing, inducing, deducing, analyzing, synthesizing, abstracting and systematizing things, and using correct reasoning methods and reasoning formats to accurately and orderly express their rigorous rational activities.
3. Mathematical thinking and attack ability: ability is a necessary personality and psychological feature for successfully completing an activity, which directly affects the efficiency of the activity. Mathematical ability is the synthesis of various abilities necessary for people to engage in mathematical activities, and mathematical thinking ability is the core of mathematical ability.
Question 10: What is logical thinking ability? Why do you say that learning mathematics well can enhance a person's logical thinking ability? In the process of cognition, people reflect the realistic way of thinking through concepts, judgments and reasoning. Different from thinking in images, it reveals the essence of things with scientific abstract concepts and expresses the results of understanding reality. Also called abstract thinking.
Mathematics is a subject under such a mode of thinking, which naturally complements each other.