This is the most effective way to learn

Chapter 11 Doing homework not for homework's sake - the way top students do their homework (2)
Association refers to the phenomenon that one kind of mental process leads to another connected mental process. It is not blind, it is a logical association based on existing knowledge and experience.How can we find the correct problem-solving thinking?Exercises are generally designed to test a certain knowledge point. To find the correct way to solve the problem, you must first distinguish what the problem is testing.Then, according to the requirements of solving the problem, it is easy to get the correct conclusion.For example, given the area of ​​a triangle and the length of a side, find the height of the triangle on that side.This question examines the area formula of a triangle. As long as you list the area formula of a triangle: area = (base × height) / 2, you can solve this question by substituting the known ones. The third link is the generalization of the subject .Refers to the integration of current topics into similar knowledge systems.In general, formulas are our most common generalizations.For example, the formula (a+b)2 is a class in the process of solving the problem [(8a+6)+(7c-5)]2.Although the topic looks complicated, it is actually just a deformation of the formula.In the question, (8a+6) is equivalent to a in the formula, and (7c-5) is equivalent to b in the formula.After classification, the problem is easily solved.At the same time, it can be said that any exercises that cannot be classified are of no practice value.

The most critical step in doing homework is to review the questions. Even if the questions are judged wrong, the content of the homework will be all wrong.The same is true for solving any problem. The first step is to examine the question carefully. To examine the question carefully, you need to ponder, think carefully, and think deeply.When reviewing questions, the first thing is to figure out the content of the topic, the conditions given, and what restrictions are there?any request?What knowledge is needed?etc.; the second is to consider the problem-solving ideas, methods, and steps. You must be good at dividing a problem into several parts, turning the big into the small, turning the difficulty into the easy, distinguishing the known from the unknown, clarifying the connection between each part, and designing Take care of the entire problem-solving steps, and you must let yourself not do the questions if you don’t understand the meaning of the questions, and don’t write if you don’t know the methods and steps.

The third step: do the questions carefully.

Doing questions is the whole process of expressing ideas, which requires both brains and hands.The key to doing the questions is to ensure "standard" and "accurate".To achieve these two points, students are required to carefully copy the questions, the writing format must be correct and standardized, strictly follow the problem-solving requirements of various types of questions, carefully calculate each step of the problem-solving, and get the correct result.Only when you do the questions carefully, with complete steps, correct thinking, rigorous expression, and accuracy, can you follow this good habit during the exam.

After reviewing the questions, the process of expressing the thinking of solving the questions is a process of brainstorming and hands-on.When doing the questions, pay attention to the quality, that is, to achieve the six words of "accurate, standardized, and fast".

① Accuracy.It is to ask us to strive for "right once" when doing the questions.Qian Xuesen once said: "Science is serious, strict, and rigorous, and no slack is allowed. Therefore, scientific and technical workers must first have good scientific work habits." This scientific work habit does not come out of thin air.He asked us to start with small things, every exercise, homework, and every punctuation mark must strive to be accurate and standardized.From an early age, we must cultivate the study habits of the "Three Stricts" and establish a style of study of the "Three Stricts".

② normative.It is to ask us to strictly follow the prescribed format when solving problems, and the writing should be neat, clear, concise and easy to read.Lines should be straight and sides should be aligned.It is necessary to leave the necessary blank space so that it is convenient for reviewing, convenient for the teacher to review, easy to check for mistakes, and easy to correct wrong questions.Another measure to achieve standardization is not to write lightly, first figure out the problem-solving ideas, get the method steps right, and then write.

③ Rapidity.It requires us to be more efficient in solving problems.You must ask yourself to complete a certain amount of homework within the specified time, actively participate in competitions in various subjects, and train your speed through various channels to make your homework and exercises faster and better.

The effect of practice depends not only on the number of exercises, but also on the quality of the exercises.The key to determining the quality is whether the exercises done have good practice value.Generally speaking, the example exercises in the textbooks are of higher value, and the exercises in the textbooks are also of higher practice value.Proficiency in the textbook exercises can enable you to master the most basic question types, and you will naturally win the exam when you take the exam.

In addition, top students have some skills in doing exercises.

①Start from the most confident place.In order to better stimulate interest in learning, it is best to avoid setbacks at the beginning.Therefore, it is best to start practicing from the parts that you are sure of. If you can get most of the questions right, you will be in high spirits.

②The exercises in the teaching materials must be familiar with everything, as the first reference book.On this basis, if you have energy and time, you might as well read a few more reference books and absorb the essence of them.

③The answer must not be written next to the exercises.Some students think that after marking the answers next to the exercises, they will not make mistakes again.On the contrary, because of the answer, the next time you do this question, you will easily become dependent and unable to practice independently, and the practice effect will naturally not be good.In order to know right or wrong in time, you can note the answer in the back of the book or other notebooks.

④ When choosing a reference book, choose the one with the answer, the more detailed the answer, the better.If there is an error analysis, it is the upper choice.The questions that have been practiced should be marked, and the correct ones should be ticked, and the wrong ones should be crossed out.But the answer must not be filled in.After finishing it once, after a period of time, redo it again. Similarly, tick the right ones and cross them out if they are wrong.After a period of time, you can put aside what you did right and only do what you did wrong until you do it right.

If you can practice according to the steps of the top students, I believe that your grades will be significantly improved.

Top students will check their homework.

Doing homework is a process of using knowledge to solve problems, but our goal is to be able to use knowledge correctly and solve problems correctly.Solving the problem wrong is the same as not being able to solve the problem. It is not advisable, and it is not our goal.Therefore, it is imperative to get the homework done right.The purpose of reviewing questions and conceiving is to achieve this goal, but the final conclusion and whether the answer is correct must also be checked and verified.This point is often overlooked when we do our homework.

Careful inspection after finishing homework is one of the important means to ensure the quality of homework.In the process of homework, due to various reasons, it is inevitable that there will be various loopholes and problems. Therefore, after the homework is finished, it must be checked carefully before handing it in, so as to avoid mistakes and omissions in the homework. .

Homework inspection is generally divided into four steps:
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Is it to check whether the title is copied correctly?
The second is whether the examination questions are correct?

Third, is the calculation correct?

The fourth is whether the methods, ideas and steps are correct.

Usually, the top students will check carefully after finishing the questions, and form a habit, and they will naturally follow the habit during the exam.

After checking out the error, the next step is of course to correct the error.

First of all, the top students will carefully analyze the reasons for the mistakes in the homework.If it is a mistake in understanding, they will go back and study the teaching materials (including old knowledge related to new knowledge) carefully until they understand it.If it is due to deficiencies in mastering knowledge and skills, quickly strengthen extracurricular self-study to make up for it.

Secondly, the top students will redo the homework that they have done wrong.If time permits, they will choose more similar topics to do to deepen and consolidate their understanding of new knowledge and mastery of new skills.For some questions, try to answer and test in different ways as much as possible.

Again, if the top students can't figure out the reason for doing the wrong homework after repeated independent thinking, and the mistakes can't be corrected, they should write down the questions and ask the teacher or discuss with their classmates.

Finally, the top students found that some difficult problems were caused by improper learning methods.Throughout the learning process, we must give full play to our learning initiative and form the best learning method that suits our own characteristics.

In the process of self-examination, top students also have a good habit. They have prepared a special notebook. Whether it is homework or exam papers, the teacher will send them back after reading them. They will single out the wrong questions and write them in this notebook. "Registration".The first step is to copy down the wrong question in its original form, draw the wrong place with a red pen, and then, under the wrong question, do it again according to the correct method; finally analyze the cause of the error, and use the red pen to highlight the type of error Mark it out (whether it belongs to the wrong understanding of the concept, or the meaning of the question is not clear; it is not good at analysis, reasoning, or a calculation error...).Each wrong question registration must go through such three procedures.

What are the benefits of "registering" wrong questions?

If a student wants to grasp the knowledge correctly and firmly, on the one hand, he must rely on listening to the teacher's narration, delving into the text by himself, and mastering the inner connection of knowledge.On the other hand, it is necessary to expose the problems in one's own understanding and application from homework and exams, and seize these problems for "remedial lessons" and re-study in the "question-and-answer" style.In particular, the key points, key points, and difficulties that need to be understood and mastered, although the teacher repeatedly emphasizes them in lectures, students often cannot go deep into them until they are "trapped" by them.Until the time of use, such as homework or exams, the problem will often go out in these places.If students are good at catching these mistakes in the re-examination, "magnify" these mistakes, go around a few times before and after the mistakes, and fill up the loopholes, they can transform it into a more practical and solid "re-examination" Learn".

In short, there are three advantages of compiling "Wrong Questions Collection": first, you can start from the negative side, and deepen your understanding of the correct things;

The top students compiled the "Wrong Questions Collection" according to the categories of Chinese, mathematics, foreign languages, physics, chemistry and other subjects.In the "Wrong Question Collection" of each subject, they record all the wrong questions in the exams, homework or exercises, and carefully correct them next to or below the mistakes to figure out where the mistakes are.In order to deepen the impression of "wrong questions", they also summarized the wrong questions.

Compiling "Wrong Questions Collection" is a good way to learn, you might as well try it.

Top students use the best method to solve the problem.

Today, my mother took the "Mathematics Olympiad" to read. I was always very interested in mathematics, so I watched and did it together with my mother, but I don't know why my mother always does it faster than me.I asked my mother: "Mom, how do you do it so fast?" It turns out that my method is different from that of my mother, and my mother's method is much simpler than mine.

其中有一题是找规律题，按1、4、9、16顺序填下面的两个数。妈妈一看就知道这是自然数的平方数，接下来的两个数是25和36。而我是用这样的方法做的，按照1＋3＝4；4＋5＝9；9＋7＝16，规律是相邻两个数的差是3、5、7、9、11……，于是我用16加9等于25；25加11等于36。这样才算出了结果，可用这样的方法比妈妈慢多了。

Through this incident, I know that the calculation problem is not only to be correct, but also to master the correct method and the tricks in order to do it correctly and quickly.

The philosopher said: "When you are doing something, if you only have one idea, that idea is the most dangerous."

Don't be bound by authority and theories mentioned in books. Top students are not satisfied with solving this problem, but what method they used to solve it, and is there a better method.They try to use their unique thinking to find unusual perspectives. Only by finding unique thinking angles can they open up new ideas.

But some people don't know how to be flexible, and go all the way to the dark.The top students, however, in their unique thinking, penetrated the phenomenon of things, penetrated into the inner structure and essence of things, and grasped the deeper and more essential things hidden behind the appearance.

Many people saw the oil lamp hanging in the church of Pisa swinging back and forth, but Galileo made a valuable discovery from it and invented the pendulum.

There are not one but many solutions to difficult problems in learning. If you want to take the lead, you must use a different method from others.You have to be good at comparison and open your mind from comparison.Don't seek the only correct answer, but force yourself to achieve the same goal through different ideas.From the comparison, discover new problems, new situations, discover new solutions to old problems, and discover new changes in known situations, so that your creativity will be stimulated in the persistent pursuit, and you will develop your habit of creative problem-solving. A habit of solving problems in one way.

Top students take every assignment seriously.

The usual homework is laying the foundation and training for basic knowledge. Only with a solid foundation can you master more knowledge and achieve excellent results in the final exam.

It can be seen that it is very important and necessary to complete every homework seriously!

If you want to get good grades, you have to start with taking every homework seriously!
We must not only complete the homework carefully, but also pay attention to the method of doing the homework.If you have a method, you can beat others' three questions by doing one question; if you don't have a method, you may beat others' one question after doing three questions, and the effect is very different.

Focus on the questions you don't know.

Many students make such a mistake: repeat what they can do, like to engage in "repetitive construction", and ignore what they can't do, and resolutely don't take the initiative to find it. This is a misunderstanding of the problem.This is not the case for students who are good at learning. They do less of the questions they have mastered, and practice repeatedly on the questions they do not know. Only in this way can they learn new things and improve their learning ability.

Organize homework frequently.

Some students often throw away their homework after finishing it, and at the same time breathe a sigh of relief: "Oh, I finally finished it." They will ignore the homework they have done in the future.Some students cherish the fruits of their labor, organize their homework by category, and constantly summarize and discover new problems.Only by organizing homework frequently can the knowledge learned form a knowledge chain and become the knowledge that truly belongs to you, and you can use it with ease.

From time to time, look through the organized homework.

After finishing the homework, it should be placed in front of the desk or in the most conspicuous position like the textbook, and remind yourself to read it from time to time, which plays the role of review.Otherwise, what's the point of organizing it well?

Grasp the information revealed by the topic.

One of the biggest differences between students who are good at learning and students who are not good at learning is who can grasp important information, know what the question is mainly about, and what information is revealed.Instead of grabbing eyebrows and beards and treating them equally, although a lot of questions have been done, the effect is not necessarily good.

(End of this chapter)