Shulou(Shulou.com)11/24 Report--

This article comes from the official account of Wechat: back to Park (ID:fanpu2019), by Wu Jinyuan

There is nothing wrong with criticizing or even complaining about the designated teaching materials of the university, but there is also a problem that deserves more attention, that is, the learning methods of college students.

Write an article | Wu Jinyuan

There is a periodic post on the Internet complaining about college textbooks. Some words are quite fierce, for example, when it comes to the linear algebra textbook of a university, some complainers say it is "garbage in the garbage". What exactly happened? One classmate said that he had no pressure to read Landau's books, but he was "confused" when he read the linear algebra textbook of this university. Later, it was only after watching Father Gilbert's open class that it was considered thorough. More interestingly, some people claimed that they had failed in linear algebra and later passed the open class. These words still sound worrying, but the worry is not how well the textbook is written. Of course, any textbook in the world cannot be perfect and must be constantly improved, so there is nothing wrong with criticizing or even complaining about textbooks, but this is a relatively minor issue by comparison. What is really worrying is how some college students, like primary or junior high school students, rely so much on textbooks and teachers to give lectures. If the teaching materials are not good or the teachers are not good at teaching, they will not be able to learn good courses, or even fail the subject. If these situations are really reflected by students, then the most urgent problem to be solved is the learning methods of college students. This article mainly discusses how college students should study, hoping to help readers.

1. Mastering learning methods, the quality of university teaching materials is really not that important. We will learn a lot of knowledge in university, but what is more worth learning is learning methods and scientific research methods, which is very different from primary school or junior high school. From the beginning of senior high school, a student should gradually and consciously study and explore suitable learning methods for himself. If a person learns effective learning methods, he can greatly improve his learning efficiency and master more knowledge in less time. More importantly, after a person has mastered effective learning methods, even if he leaves the university, he can continue to study and acquire new knowledge.

A basic skill in learning any knowledge is to observe and understand a thing from many different perspectives. We sometimes say that the two concepts are easy to be confused. In fact, it is often not that the two concepts themselves are really unclear, but that in many cases, this is the problem caused by a single perspective of observation. If you look at it from a different perspective, people often find that the two concepts are clearly distinguished. When it comes to learning a subject, the simplest point is that you can't just hold a book there, but should read more books or related content on the Internet. Different people write different books from different perspectives. Some contents can be verified by each other, while some different contents mostly explain the different aspects of things. After we have read these books, we can make up the complete image by thinking for ourselves.

As a result, the impact of whether a book is well written or not has been greatly reduced. Even if one book has any defects, it can be diluted and averaged by other books. But more often, these "defects" are just different features in different books, and they can complement each other to help us fully understand the relevant knowledge.

Use linear algebra as an example. The basic concepts in linear algebra can be expressed in many ways. Some people like to express them in pure algebraic symbols. I personally like to express them in the plane where space intersects. Father G likes to express them in the way of column space and row space. These expressions are all useful, and only when you understand them all step by step can you learn through linear algebra. However, there is no rigid order between which to learn first and which to learn later. in fact, there is a relationship between four steamed buns and a bowl of porridge. On the other hand, if the MIT students do not read other reference books and simply listen to Father G's lessons alone, they may not have one or two "confused faces". Some of these students read Feynman without any pressure. Can we conclude that Grandpa G's class is "garbage in garbage"?

If a person has mastered this learning method of observing and understanding things from multiple angles, will he still be unable to learn thoroughly because of the "rubbish" of the textbook or the teacher's poor lecture, or even fail the subject? Some readers may say that they fail because they play games, but in fact, they may not fail even if they play games. If you master a good learning method, the learning efficiency will be improved and a lot of time will be saved. Save time, you can study, play games (but don't be addicted to it) and date (find someone who is equally passionate and good at learning) without delay.

Of course, in college, it is valuable to read more hard-core books when you are young and have a strong learning ability. When I was in college, I went to the library to borrow books such as general chemistry, general biology, general geology, and general geography, and taught many courses with the word "ordinary" by myself. What you have learned in this way may not necessarily be used at work, but this knowledge will benefit people for a lifetime.

In such complaints, it is often seen that words like "Chinese is incompatible with science" and "Chinese hinders science" sound "profound". It seems that it has become a fashion to say this now, which is too outrageous. The method of observing and understanding things from multiple perspectives that I mentioned earlier is also the most basic method in our scientific research work. This scientific research method is succinctly summed up by two Chinese idioms: listening together makes sense, and learning from strong points to make up for weaknesses. The former idiom comes from "Guanzi", about 2400 years ago. The latter one is from Mencius, about 2300 years ago.

2. Search up and down, don't be too afraid to build buildings on the beach. To a large extent, people's knowledge is learned from nature. Phenomena seen from nature are often at the top, and their foundations are usually not seen first. The previous generation of scientists and mathematicians traced down the vine and gradually established the logical relationship between these phenomena and the basic laws of nature from the phenomena formed by a variety of complex factors at the top, so as to find out the structure of the building of the laws of nature. to form the discipline structure we see now.

For example, we can easily see that arbitrary quadrilateral plates can cover the entire plane with tight seams. The reason is that the sum of the four interior angles of any quadrilateral is equal to 360 degrees, and the reason for this is that the sum of the three interior angles of the triangle is equal to 180 degrees. Further exploration will lead to a deeper understanding of the logical relationship between several axioms of Euclidean geometry and these natural facts.

When people figure out the internal logical relationship of a discipline, the textbooks written and the teaching courses in the school are often chosen to build gradually from the foundation to the top. This kind of education and learning path is also very successful in many cases. People sometimes compare the basic knowledge to building buildings on the beach.

However, such a bottom-up learning path should not be absolute. Sometimes, it may be more effective to explore from the top down, as our predecessors did.

For example, Xiaoming's height has increased by 1%. With the same fat, thin and body tissue density, we can quickly estimate that Xiaoming's skin surface area has increased by 2% and weight by 3%. This kind of quick estimation is used in our scientific research every day, even when we go to a pizzeria for dinner. This method can be seen by simply expanding (1) n in high school algebra, but it takes a small differential book to fully prove the reasonableness of doing so.

Therefore, although it seems that this quick estimation is a castle in the air, it actually has a fulcrum. From these fulcrums, you can see the fulcrums of more fulcrums. Following this train of thought, we can gradually understand why Cauchy and others have come up with so many theorem criteria, and why we should consider the sudden emergence of a pit in the middle of the function curve, or even the cliff jump, or the dead corner of the function curve.

For each of us, it is not certain which path is easier to learn when taking a course. I raise this question here mainly in the hope that members will not reject any kind of path and not be too afraid of building buildings on the so-called beach. The knowledge we learn is not what we build, but what exists in nature. We are just exploring the logical connections within these layers of buildings. Even if we do not explore the support of the ground floor for a short time, the building is not so easy to collapse.

We mentioned earlier that we should observe and understand things from multiple perspectives. In fact, what we are talking about here from the bottom up and from the top down are two different perspectives. "it's a long journey, and I won't stop pursuing it." this is a sentence from qu Yuan's Lisao, about 2300 years ago.

3. Don't expect to never forget that most of us don't have the ability to learn at once, so we shouldn't expect to read a course and understand it. Even if you have such a good memory that you can memorize it once, you don't necessarily understand it. There are many disciplines in science that need to be understood and exemplified ("inference" comes from the Analects of Confucius, about 2500 years ago). Therefore, the more reliable learning method is to "learn and learn from time to time" as stated in the first sentence of the Analects of Confucius.

This multi-wave learning method can be used in different time and space scales. For example, velocity and acceleration are physical concepts that are often used to understand the concept of derivatives. When arranging courses in universities, calculus and general physics are often placed before and after the semester or even in the same semester. When taking a course, as we said earlier, we should find a variety of related books. In this way, we can learn it over and over again when we get different perspectives.

When learning a book, sometimes we tend to keep reading and are reluctant to stop to do exercises, which interrupts the train of thought. This requires us to consciously overcome this tendency, consciously interrupt our own thinking at an appropriate time, go out of the comfort zone, and change from reading to doing topics.

Doing exercises often gives us a different perspective from reading, not to mention that doing exercises moderately is very helpful to improve test scores.

4. Read the books of great masters as ordinary books. Among the posts that complain about college textbooks, they often praise another batch of books. In addition to the Gilbert Strang mentioned earlier, there will be Feynman, Jackson and so on. In the early years, there were Landau, Frith, Smirnov, Jimmy Dovic and so on. However, in the past decade, lighthouses and hairy bears are not very good to deal with, so there are fewer posts about the latter few people in China.

One corollary of the spirit of science is that whether a statement is correct or not has nothing to do with who said it. Anyone who does not owe a fee for scientific literacy will not be superstitious about the individual. A few days ago, the kind of "research and judgment" of so-and-so was enough to give people goose bumps. Later, it turned out to be "only believe in so-and-so in the future", and even said that believing in so-and-so means believing in "science". It was too funny. In fact, this kind of personal superstition is precisely contrary to science. By the way, science itself does not require people to "believe" science at all.

When we go back to reading, who explains a question does not affect the right or wrong of its content. Therefore, the books of great scientists should not be read as bibles, but as ordinary books. In fact, all the authors of books, including myself and, I believe, these great scientists, want people to read their books as ordinary books with a scientific attitude. What is a scientific attitude? That is, when you read, you should have doubts, think, and not believe blindly. Only in this way can we really understand the thinking methods of these authors and turn their thoughts into the spiritual nourishment of the readers.

I study physics, but I haven't read Feynman's physics handouts so far. Maybe this will make me fall to the bottom of the chain of disdain in the eyes of some readers, but the chain of disdain itself is empty. Being able to learn physics well is not exactly the same as having read or not reading a particular book. To take an extreme example, Feynman himself certainly did not become a great physicist by reading Feynman's handouts. I have no objection to reading Feynman's physics handouts. I think anyone, including myself, can read it under appropriate circumstances. It's just that you don't need to raise the role of any book too high, just read it with a normal state of mind.

In fact, treating people as gods will only prevent us from learning from others. Let's take an example of Feynman, who had an interview complaining about physics teaching in Brazil. He talked about teachers saying every word in class, students copying every sentence, and going back after class to memorize for exams. This criticism is quite correct. However, in this text, there is no distinction between acceleration and angular acceleration, and the text is not very rigorous. If we think that we can only believe in God, we can only completely negate Feynman, because God cannot make mistakes. On the other hand, if we treat Feynman as an ordinary person, we can distinguish his insights into physics teaching from the lax words used when it comes to angular acceleration, and only absorb its essence.

This kind of scientific thinking can be summed up by a mantra of a relative who graduated from junior high school: "one yard is one yard."

5. teach each other and improve yourself while tutoring your classmates. from the encyclopedia, we found that the idiom of teaching and learning originated in the Western Han Dynasty. In Dai Sheng's Book of Rites, he wrote: "learn and then know the deficiency, teach and then know the difficulty." know the deficiency and then be able to rebel, know the difficulty and then be able to strengthen yourself. therefore, it is said that 'teaching and learning learn from each other'. "

Coincidentally, it is said on the Internet that Feynman also has a Feynman learning method that uses output to force input. The basic meaning is to find a way to teach a content to children. By preparing for such a teaching, you can figure out the concepts that you don't understand. Although some people have questioned putting this method on Feynman's head, if we ignore the textual research of the origin, it is indeed a good way to use teaching to drive learning.

Of course, in real life, there are not so many regular audiences for you to output, because everyone is very busy and has no time. But as long as you set your mind to it, there will still be opportunities to teach. In the school environment, sometimes some students encounter difficulties in learning. In this case, being able to coach students will be of great help to themselves in understanding the corresponding courses. We often see that the grades of the study committee members in the class are very good. In fact, many study committee members do not have much talent, but because they often tutor students and improve themselves through teaching and learning. Myself, I have been a study committee member who is not a genius. Of course, sometimes everyone is high achiever, it's hard to say who can teach whom all the time. In this case, if students can often discuss each other, it will also help everyone sort out their ideas and deepen their understanding.

Your parents, or male (female) friends, are not familiar with your major in many cases. It would be a great experience to go home during the holiday or on a date and try to tell them what you learned at school. You don't have to expect them to understand everything. As long as they don't yawn, they will be very successful.

In addition, many people now have their own official accounts. You can write down what you have learned and put it in your official account. In writing, when you try to make the layman understand, such a process of thinking arrangement and language choice will benefit you a lot.

A friend of mine will even write a book of his own, which may not be printed by a publisher, but it will make you find many ambiguities in the past and force yourself to figure them all out.

6. I wish you all every success in your studies.

Welcome to subscribe "Shulou Technology Information " to get latest news, interesting things and hot topics in the IT industry, and controls the hottest and latest Internet news, technology news and IT industry trends.