Second, we must have the rigor of logical thinking. Mathematics is a rigorous subject. To solve any mathematical problem, whether algebra or geometry, proof or calculation, we need written evidence, so we should have evidence at every step when solving the problem. Even the most obvious facts should be justified. Sometimes writing can be simpler, but the process of thinking and reasoning should be rigorous.
Third, there must be flexibility in learning methods. The more content you learn, the wider the knowledge of each branch of mathematics involved, the more methods you have, and the greater the swing of solving problems. At this point, participants at home and abroad are handy; The poor are dazzled and at a loss. This requires children to be good at observing, thinking, imagining and summarizing when studying. We should be good at both creation and imitation. Only in this way can we raise our thinking from a lower level to a higher level.
First of all, build up confidence and develop good study habits.
I often hear some children say, "My brain is not good, and I'm not cut out for math." This is a sign of lack of self-confidence and weak learning will. In fact, if you want to learn mathematics well, you must first have the confidence and ambition to learn mathematics well, and there are rules to follow in learning mathematics. The key to learning well lies in whether you are interested in mathematics and have the courage to go forward.
If you want to study, you must form good study habits. It is necessary to change the simple and passive learning state of "attending class-doing problems" and develop the good habit of "previewing-attending class-reviewing-doing homework-summarizing".
Second, pay attention to learning methods and cultivate learning ability.
There are various learning methods, which should vary from person to person and should not be blindly applied. But learning math well must be gradual, which is the most basic learning method. We should pay attention to the understanding of basic concepts and the intensive training of basic skills, lay a solid foundation from easy to difficult, and avoid aiming too high. We should be diligent in independent thinking to prevent the phenomenon of being unintelligible, not seeking answers, and memorizing. So what are the specific ways to learn math well? How to improve the ability?
1. Learn to read math books and deeply understand every basic concept. There are many math books, but first of all, we should pay attention to textbooks, which are the basis of teaching and learning, the main source of basic knowledge, the guide to developing ability and the guide to acquiring learning methods.
2. Grasp the law, seek simplification and strengthen knowledge memory. Although rote learning is opposed in learning, the purpose is not to pay attention to understanding, not to forget. If some children face math problems, they can't find ideas and associate them, which is why they have too little knowledge in their minds. Only children with a solid memory of basic knowledge can be handy.
We should firmly grasp the important theorems, formulas and laws. Theorems, formulas and rules in mathematics are the basic tools to solve problems. Only by mastering them skillfully and flexibly can we have correct thinking methods and skills. For important formulas, we should be able to apply, reverse, change and use flexibly.
4. Study hard, conscientiously sum up mathematical thinking methods, and master common problem-solving methods and skills. As long as we know and summarize, master several commonly used mathematical thinking methods, and comprehensively use the knowledge of each branch, we can get twice the result with half the effort and achieve the effect of drawing inferences from one another.
Third, think hard and practice more to improve the ability to solve problems.
Because solving mathematical problems is a "practical" link in learning mathematics courses, solving mathematical problems is an important process to train children to use mathematical knowledge to solve problems. In the process of solving problems, children often encounter difficulties in understanding the meaning of problems and finding ways to solve them. To understand the meaning of the question, it is necessary to correctly examine the question, that is, to clarify the basic conditions, tap the hidden conditions, and clarify the requirements for answering questions. To find a solution to the problem, we should do three things, namely, recall, association and conjecture. As long as you think hard and practice more, you will certainly improve your problem-solving ability and make your thinking smarter, more rigorous and more flexible.
How to cultivate the logic and rigor of thinking 1 and train 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 process of reasoning is also included in calculation and drawing. Therefore, on the one hand, we should cultivate students' habit of rigorous reasoning, on the other hand, we should often help students correct logical errors in reasoning in time.
How to cultivate logical thinking ability is a purposeful, planned and systematic educational activity. Its role cannot be underestimated. Human nature has an influence on thinking ability, but the acquired education and training have a greater and deeper influence on thinking ability. Many research results show that the acquired environment can make a new person to a great extent. The main purpose of thinking ability training is to improve thinking quality and students' thinking ability. As long as we can grasp the quality of thinking in practical training and make targeted efforts, we can stick to it smoothly and effectively. Thinking is not a mysterious thing. Although invisible, intangible, and invisible, it is a real, characteristic and quality universal psychological phenomenon. (1) When you see, hear or come into contact with a thing, you should try your best to give it a new nature, get rid of the shackles of old methods, and use new ideas, new methods and new conclusions to reflect originality. Training students' thinking methods according to this idea can often get new results. (2) Aggregation abstract training method "aggregates" all perceived objects according to certain standards, showing their * * * nature and essence, which can enhance students' creative thinking activities. This training method should first understand the general outline of perceptual materials and find very prominent features from the senses; Secondly, the problem of feeling * * * should be dismembered and analyzed to form several analysis groups, and then the essential characteristics should be abstracted; Thirdly, it is necessary to describe the abstract essence of things in a general way, and finally form a rational result with guiding significance. (3) Step-by-step training method This training method is very beneficial to students' thinking, which can enhance leaders' analytical thinking ability and foresight ability, and can ensure that leaders carefully think about an idea in advance and push out the results in the form of logical reasoning in their thinking. (4) Doubt and query training method This training method is to be brave and good at or put forward new ideas and suggestions about things or things that have always been considered correct in the past or a certain fixed mode of thinking, and use various evidences to prove the correctness of new conclusions. This also marks the level of a student's innovative ability. The training methods are as follows: 1. Whenever you observe a thing or phenomenon, whether it is the first time or many times of contact, you should ask "why" and form a habit; Secondly, whenever you encounter problems in your work, you should try your best to seek the regularity of your own movement, or observe the same problem from different angles and directions to avoid being confused by perceptual illusions. (5) Brainstorming Training This training method is an organized group. With the help of thinking, we communicate with each other, concentrate the collective wisdom of many people, and extensively absorb useful opinions, thus improving our thinking ability. This method is conducive to the formation of research results, but also has the potential role of cultivating students' research ability. Because, when some students with personality get together, because of different starting points, different angles of observing problems, different research methods and different levels of analyzing problems, different viewpoints and methods of solving problems arise. Through comparison, contrast and discussion, we can consciously or unconsciously learn each other's thinking methods, so that our thinking ability can be improved imperceptibly.
Taking logical thinking as the basis of your writing and learning how to use inductive and deductive reasoning in your writing can help you avoid common fallacies. Inductive reasoning: When you start inductive reasoning, you start with some examples (facts or opinions) and use them to draw general conclusions. Whenever you explain your evidence, you are making inductive reasoning. Using possibility to form a general conclusion is called a leap in induction. Inducing arguments, rather than providing clear conclusions, will produce well-founded and credible conclusions. As you have more and more evidence, your readers will come to the conclusion you want to draw. You must make sure that there is enough evidence and it is not based on special or biased circumstances. Make sure that you have not overlooked information that will invalidate your conclusion (called "ignored aspects"), or that the evidence submitted only supports a predetermined conclusion (called "tilt"). Deductive reasoning: When you do deductive reasoning, start with universality (antecedent) and then specify an example, so as to draw a conclusion about this example. Deductive reasoning usually adopts syllogism, which consists of major premise, minor premise and conclusion. For example, all men are stupid (major premise); Smith is human (minor premise); Therefore, Smith is stupid. Of course, in order to accept your conclusion, your readers must accept your choice of ideas or values as a major premise. There is a major premise that is not explained. For syllogisms that do not explain major premises or minor premises, or even conclusions, we should carefully check them, because omitted explanations may contain inaccurate induction. Toulmin method: Another way to examine the process of logical thinking is to use Toulmin method. This model is less restrictive than syllogism, and leaves room for important elements such as possibility, support, premise proof and refuting readers' objections. This method regards argument as a process from accepting facts or evidence (data) to conclusion (statement) by establishing a statement (proof) of the reasonable relationship between argument and conclusion. This kind of proof is often implied in the argument, just like a syllogism without declared premise, which needs to be carefully tested before it can be accepted. The author can leave room for exceptions to the major premise. Qualifiers such as approximation, possibility, no doubt and certainty indicate the degree of determination of the conclusion; The wording of the disproof is as follows: unless the author can introduce objections in advance. Fallacy: Deductive argument must be both effective and true. A real argument is based on universally accepted and reliable premises. Learn to distinguish between facts (with verifiable data) and opinions (according to personal preferences). Effective argument is accompanied by reasonable thinking. Fallacy is often wrong in premise (truth) or reasoning (validity). They either abuse or distort the evidence, rely on the wrong premise, omit the necessary premise or distort the problem. The following are some major fallacies: Inference is invalid: a declaration is illogical from what has just been said, in other words, this conclusion does not follow this premise. Reckless induction: induction is based on too little evidence, or special circumstances or biased evidence. Personal attack: attacking the person who asked the question, rather than dealing with the question itself logically. Appeal to the public: In fact, the argument is, "Everyone is doing this, or saying this, or thinking this, so you should do the same." Change the subject: avoid the real question and ask an irrelevant question. Pseudodichotomy: It is claimed that there are only two options, but there are actually more than two. Improper analogy: because two things are the same in some aspects, they must be the same in other aspects. Word ambiguity: false assertions are based on terms with two different meanings. Landslide: If one thing is true, it will be the first step in a downward spiral. Simplification: a statement or argument that ignores the relevant considerations of the problem. Stealing the topic: an assertion reiterates the point just made. This assertion is circular because it takes the statement in the premise as the conclusion. False cause and effect: Because one thing happens at the same time as another, the first thing is the cause of the second thing.
How to cultivate strict logical thinking classroom teaching is the basic form of teaching and an important channel for students to obtain information, exercise various abilities and develop certain ideas. However, the time for classroom teaching is limited. In order to make students get the greatest progress and development in the least time, one of the problems that must be faced in the curriculum reform of basic education in the new curriculum is how to maximize the benefits of classroom teaching, and effective teaching is an important way.
Think a few more steps before you do something, and think about why you should do it. Reading some books on logical reasoning at ordinary times can also help you improve this level. Start (a disease)
How to cultivate logical thinking? Read more detective stories, observe others on the street, and know what they do through their clothes, conversation and actions. This is a very interesting thing.
By the way, am I a sister or a younger sister?
How to cultivate GMAT logical thinking What is GMAT logical thinking?
We must first find out what is at issue. Discussion consists of arguments, arguments and argumentation process (also called reasoning). The so-called argumentation process is the process of drawing arguments from arguments with strict logical rules.
Many students failed in GMAT because of wrong methods and detours. If you use the correct practice method, it only takes two months, four to five hours a day, from 60 to 750 GMAT.
The English involved in the GMAT exam is very standardized and standardized. You don't need a strong English ability to understand the article itself, but you should get used to GMAT's thinking habits.
The main reason why many students in China can't get high marks is that they pay attention to reading, rather than thinking about the way of thinking reflected by problems. In fact, this way of thinking is also very simple. We always use this kind of thinking in our daily life, but we just don't notice it.
Pay attention to the thinking process when you start practicing. In a month or so, you will naturally use GMAT thinking to do the problem, and after another month of practice, you will reach the realm of "experts have no tricks".
For a considerable number of candidates, it is possible to reach 750 points after correct practice. Of course, if you want to achieve better results, you need to have higher ability to analyze problems. It is also the purpose of GMAT to test the analytical reasoning ability of candidates through exams.
Most candidates in China have received strict university education, and their mathematical analysis and logical reasoning skills are very strong. Therefore, China students have the intellectual foundation to get high marks, and the rest is to practice in the right way.
Besides, regarding LSAT, I don't think we can overemphasize its influence on GMAT's high score. LSAT is beautiful in writing and rigorous in thinking, which can fundamentally improve the thinking ability of GMAT candidates.
Logical methodology
Logic is actually the easiest part to improve. The key to learning logic well lies in reading the argumentation structure of the article and mastering the laws of logical thinking. All logic questions are asked around a short passage (that is, discussion), and candidates are required to respond to the discussion.
Then, we must first understand what we are discussing.
Discussion consists of arguments, arguments and argumentation process (also called reasoning). The so-called argumentation process is the process of drawing arguments from arguments with strict logical rules.
So, what questions will GMAT raise to discuss?
Assumption (hypothesis)
Explain a problem or phenomenon, or explain an obvious contradiction.
Infer a reasonable conclusion from the given argument.
Identify the method and structure of argument.
Identify reasoning errors and their understanding and expression.
Rationality of analysis and argumentation, including evaluation of original argumentation. Evaluation) and the support of new information to the original argument (weakness).
In order to answer these questions correctly, we should master the corresponding logical rules.
The reasoning process of GMAT is a process from A to B, that is, the process of deducing unknown things from known things (A).
What is the relationship between A and B? That is to say, under what circumstances can we know for sure whether A can deduce B? First of all, we should clarify several relationships: sufficient conditions: A will definitely get B, marked as A → B; Necessary conditions: in order to get B, the conditions of A must be met, marked B → A; Necessary and sufficient conditions: A must get B, and in order to get B, the conditions of A must be met. Write it as a → B. These relations are the basis of all logical reasoning. Now let's see how to use it to do the problem. The first step in doing the problem is to read the argument structure of the essay clearly and distinguish the argument from the argument. Some GMAT questions simply ask what the argument of a paragraph is.
The above is the introduction of GMAT logical thinking, I hope everyone can understand it. Learn more about GMAT for reference and try to be foolproof.