中国教育是怎样打击你的自信心的？一集看懂中西数学教材的根本差异！为什么你学不会微积分？｜数学｜学习｜心理学｜哲学｜教育｜历史｜大学｜自由学习｜

0:00 Hello everyone, I am Anthony Welcome to my channel On the topic of education and learning We have chatted for 4 videos. During this period Many netizens also started from their own experiences Write a lot of high-quality reviews Thank you very much for your participation In the previous video We said Due to the poor education system The learning trauma of Chinese people is very serious And because the whole system Tends to make students academically difficult I am not smart enough. This has further deepened the widespread learned helplessness We focused on mathematics education in China This is because in China's primary and secondary school stages Mathematics can be said to be the main factor affecting the overall score. The decisive discipline And because of good math grades More likely to be seen as intelligent

0:45 Demonstrates strong rational and logical thinking ability Therefore, mathematics scores It is also the easiest to hit the individual's self-esteem and self-confidence but Objectively speaking The main problem of mathematics education in China is The curriculum and teaching methods are not reasonable enough Not respectful enough But the content is basically correct. But liberal arts education is not just about learning methods. But a lot of the content has no logic at all This is complete nonsense. That's here I also want to talk to you about my own situation. I have been interested in mathematics since I was a child. and curious people and Mathematics has long been my favorite subject. Fortunately I grew up in a relatively An environment that is not inward-looking or utilitarian The reason why I say this This is mainly based on my subjective experience. I have a lot of free time.

1:32 Allows for undisturbed free association and exploration Although My math grades were very good from elementary school to college. But I didn't have the goal of furthering my studies. Sent to learn Mathematical Olympiad Run a competition This allows me to maintain pure interest I believe everyone still remembers In this video on December 1st, Points mentioned Free learning process is a continuous emotional and cognitive experience No need to follow any established subject classification standards In this seemingly chaotic and unsystematic exploration, people Accumulated a wealth of feelings And these feelings It can open up wider interests I am the same Later I found I am interested in a lot of knowledge Such as philosophy, psychology, sociology, etc. In fact, it can all be traced back to the A simple

2:18 In the hazy exploration This is what mathematics brings me Something much more important than education and grades But in this process I also gradually observed Many classmates around me Feeling great oppression and pain in learning Finally fell into a kind of learned helplessness I always feel that they are very smart people. But their potential and confidence But it was easily denied by the education system. That's my interest too. Gradually from mathematics One reason to turn to education and psychology So this video Let's compare Chinese and Western mathematics textbooks. Analyze from details Mathematics Education in China How does it undermine students' self-confidence? First, I chose The third edition of Calculus compiled by Tongji University and Calculus by James Stewart

3:05 These two textbooks In China and North America They all have a huge influence The reason why calculus is chosen as a comparison Not only because of his expertise in mathematics and many science and engineering subjects Has a fundamental and important position More because It especially demonstrates China and the West Huge Differences in Philosophies of Mathematics Teaching Just flipping through these two books We will first have an intuitive feeling that is Compilation of Chinese textbooks There is a very fixed routine It can also be said to be a mechanical template Let me give you a special case. Draw general conclusions by analogy Then give a strict theorem or definition Then give examples to reinforce the concepts Finally, the exercises These exercises are basically pure math problems. Lack of application in other disciplines Or cross-border connections

3:52 For example, in the chapter on multiplication The textbook first talks about multiple integrals The volume of the top cylinder can be calculated and the quality of the flat sheet Then in these two cases The double integral is given directly Definition of triple integral Then there are a lot of exercises In more times There is no introduction or foreshadowing. Just give theorems and definitions directly There's nothing wrong with the content But you do feel mechanical and stiff Lack of spirit and liveliness Of course, this style can also be called Focus on logical rigor and precision But it does violate the laws of human cognition. It is also easy to dampen students' interest in learning. The feeling is The author tells you that these theorems are correct You can use it to solve problems and calculate Western textbooks

4:38 When explaining a new concept or theorem It is paved in a variety of ways. With text description There is a mathematical formula There are graphics, illustrations, tables, etc. As intuitively as possible To help students understand for example When it comes to the definition of limit Western textbooks first lay the groundwork for a tangent problem The author first talks about Tangent means touch in Latin. That is, "touch" Then a very simple function is listed y is equal to x squared With lots of pictures and numerical tables Let students feel The process of gradually approaching two points on a function and a tangent line This is also what I admire very much From the origin of the word tangent To attract students' attention Make students feel that knowledge is interconnected

5:24 Another option is to choose a very simple function To explain the truth then The textbook lists two scenes from life One is the camera shutter This example makes students feel familiar The working principle of the camera is introduced at the same time The mathematical calculations it cites are very simple. This makes the students feel These mathematical knowledge are not that difficult It can also be connected with many scenes in life The second example is the problem of instantaneous speed The author says: "If you look at the speedometer while driving You will find The speed will not always remain stable at a certain value We assume that every moment Cars have a specific speed. But how should this instantaneous speed be defined? Let's study the case of a falling sphere."

6:09 I really appreciate this way of dialogue. The author is standing in your perspective Raise questions from life situations Then introduce a mathematical problem little by little Chinese textbooks This conversational style is rarely used. Most sentences simply omit the subject. Although some sentences use "we" But it's just a collective pronoun. There is no communication with students and emotionally resonant tone Similar to government documents "We want to do this and that" You can't feel Authors of Chinese textbooks I stand with you to explore these issues. The author seems unwilling to explain why Instead, it is directly defaulted Students can understand unconditionally The dense derivation process in the textbook and the pure language of mathematics No contextual explanation or introduction of life scenarios is required

6:57 For example, in the section on the limits of functions Western textbooks After laying the groundwork After the two scenarios we mentioned above This gives an intuitive definition of the limit That is, when x approaches a f(x) approaches L Then the limit of f(x) when x approaches a is called L This definition is of course not rigorous. But it is very understandable It is in line with human intuition The Chinese textbooks With basically no preparation The precise definition of the limit is directly derived That is, the epsilon delta language This definition is indeed precise and rigorous. It uses precise quantifiers such as "any" and "there is one" Avoid approaching approach, near This subjective and ambiguous statement

7:42 However This rigor For many freshmen is excessive Western textbooks It temporarily sacrifices mathematical rigor. Prioritize students’ comprehension abilities I will add a strict definition later. In my impression This definition confused many students. Some students don't even know how to read delta and epsilon. Some students Four years of college All of them have developed a fear of calculus Because they feel I don't even know such basic knowledge as the definition of limit. Can't understand The subsequent study will be more difficult. I immediately began to doubt my own intelligence. Even though they were in high school They are all students who are good at mathematics. However This definition that was thrown out at the beginning In fact, it is more than many contents after calculus.

8:28 More abstract and complex It is also much higher than the cognitive level of beginners. The Narrative Style of Chinese Textbooks Not only is it very authoritative And it does not conform to the history of the development of the discipline Many disciplines in history It is about constantly exploring and moving forward Rigorous and abstract definitions and expressions Often lags behind real-world applications For example, when Newton and Leibniz invented calculus The limit is not strictly defined More attention How to solve practical problems in physics and geometry Until nearly two hundred years after Newton's death Mathematicians such as Cauchy and Weierstrass Add this rigorous proof and definition If calculus starts from the beginning This requires starting with such an abstract definition Many historical applications may not be possible

9:15 Therefore, starting from the laws of human cognition Beginners are more likely to accept intuitive and visual concepts Rather than a formal logic language Calculus as a subject A discipline that “grows out of real-world problems” Should first demonstrate their ability to solve practical problems Let students see its instrumentality and intuitiveness As for the abstractness and rigor of the theory Should be used as a “higher-level goal” of teaching Rather than the first step to getting started But China's textbooks Tends to demonstrate the ultimate precision of mathematics quickly Try to get students to start Master the highest form of theory This is actually very easy to give beginners a Mathematics is very mysterious and cold and an awesome feeling It's as if these letters fell from the sky A group of geniuses Constructed using a very mysterious language

10:01 But in fact, the two Greek letters delta and epsilon There's no special meaning. It's the letter in front are used as other variables Their meaning is entirely artificial. So we can see It is because the whole society Lack of reflection on this abstract education method This has led many Chinese students to have a poor understanding of mathematics and science. Produced exaggerated and excessive worship Believe that the process of learning mathematics is mysterious Can only resort to unpredictable inspiration And the so-called talent, genius Therefore, this should be the most rational and logical field. But it has become the easiest place to create gods For example, the words "study god" and "great god" In schools in China Although it generally refers to students with good grades But in fact, it refers more to science such as mathematics Students with good grades

10:47 This is of course what motivated most students. Learned helplessness and inferiority complex This is largely It can be attributed to being out of touch with reality. and a difficult education model Narrative Style in Chinese Textbooks It is to directly present the conclusion It feels like showing a finished product. Rather than the process of mathematicians exploring and analyzing step by step This is also a dead end in Chinese textbooks. That is A student tries to learn mathematics by reading a textbook But you need to understand the textbooks First, build on what you have already learned This looks like a typical Chinese dilemma: A Chinese person needs a good tool to bypass the firewall To access the Internet But these wall-climbing tools First you need to connect to the Internet to get to some extent The idea of ​​compiling Chinese textbooks

11:32 It can be traced back to the Soviet model Before 1952 Chinese universities basically use European and American textbooks But since 1952 Calculus Textbooks and Mathematics Education Model in the Soviet Union Completely occupied mainland China Western textbooks have basically disappeared but China learns from the Soviet Union But they mainly learned the shortcomings of the Soviet model That is too fine-grained. The Soviet higher education system emphasized Students should directly serve the national planned economy The curriculum system focuses on imparting skills Not paying attention to interdisciplinary literacy and humanities education In 1952, China converted many comprehensive universities into Split into professional colleges For example, various engineering colleges, normal colleges, agricultural colleges, etc. This leads to too narrow professional settings in colleges and universities.

12:18 Students’ knowledge structure is single Lack of penetration and connection between disciplines In 1954, scholar Zhu Binglin stated in his article We study every subject on weekdays It's like learning elementary school math. The teacher says one is one Two means two All I learned were isolated, abstract doctrines. If someone were to ask us The relationship between mathematics and other subjects We couldn't say a word. In the subsequent Anti-Rightist Movement The Great Leap Forward and the Cultural Revolution Various disciplines Basically in a state of stagnation After the Reform and Opening Up Although Chinese universities try to break the Soviet model Moving towards the European and American model But what can be done It is nothing more than combining several professional colleges Merged into one giant university Symbolically offer some general education Humanities education course

13:04 It can be called a comprehensive university In fact, it is just a facade Because this merger It is only an external, mechanical, superficial juxtaposition. He only needs an executive order to do it. However, the internally solidified departmental structure and professional barriers Still hard to break The reason is The logic of administrative dominance in Chinese universities Nothing has changed Comprehensive universities need Interdisciplinary integration, crossover and free exploration It is built on the university Have greater autonomy to adjust departments and courses But this free academic atmosphere It will inevitably weaken the executive power in this case The fragmented state under the Soviet model is most conducive to bureaucratic control and manipulation In contrast Mathematics education in the United States

13:49 Although it has undergone many adjustments But overall it's moving in the right direction. for example In 1985, American universities launched a series of On the Reform of Calculus Teaching Be aware of current teaching methods Many students failed the exams We should focus on cultivating students' conceptual understanding ability and train students to use computers and information technology To reduce tedious calculations Compared with China's mathematics education Still obsessed with computing power And they are very opposed to technical means The United States is far ahead in this line of thinking. That's it for today's video Then let me say it last. If you have any confusion or questions Want to communicate with me Just contact my email directly for example You want to discuss an article or a paragraph with me

14:36 A video, a social phenomenon Or your diary Please send me the relevant text in advance. I will read it before the formal communication Or you want to discuss your life experience with me Confusion and emotion All are possible If you are concerned about privacy, security Any questions about payment and communication methods Please also tell me in time If you are unable to pay or join the membership Please contact me too I will provide other ways Please refer to this picture for details I will post this video Put it in the list of "Psychology and Education" Also recommend to everyone Check out my other videos in this list Thank you for watching, goodbye!