Don't cry if you smash the math test, he will come to your rescue
Author | Xiao Yao, senior reporter of Nanfeng Window
At 5 p.m. sharp, the college entrance examination mathematics finally ended.
As one of the most hardcore subjects in the college entrance examination, at this moment of year, the students who pour out of the examination room are all mixed. Some people are relieved, some people are heavier, some people cry, maybe because they feel defeated, maybe they have to get rid of the secret joy.
But a cruel reality is that for most candidates, the college entrance examination is over, but the entanglement with mathematics is not over.
There is a rumor in the rivers and lakes: "There is a tree in the university with many people hanging on it, and this tree is called High Numbers." "Except for some liberal arts majors, compulsory higher mathematics courses have always put countless college students in dire straits.
Now, a man known as the "savior of high numbers" has surfaced.
In the statistics of "10 videos with the highest cumulative playback time" released by Station B in early May this year, Song Hao, associate professor of the School of Statistics and Mathematics of Shandong University of Finance and Economics, single-handedly occupied the first, third and fifth places on the list.
The top "Tongji Edition Full Teaching Video of "Advanced Mathematics" has more than 100 million views, and the fault surpasses the second place. Followed by "Linear Algebra" and "Probability Theory and Mathematical Statistics", they were also played more than 48.39 million times and 32.83 million times respectively, with an average daily playback of 400,000 times per day.
Station B announced the highest 10 videos with the longest cumulative playback time, and Song Hao's higher mathematics class ranked first and dominated the three yuan
In recent years, university professors and scholars from different disciplines have settled on video platforms, breaking the temporal and spatial limitations of knowledge dissemination. But Song Hao teaches high numbers, which makes this seem a little wonderful.
From childhood to adulthood, our fear of mathematics, a highly abstract, logically dense subject, seems to be innate. At university, among the students who have been struggling for high mathematics, the significance of mathematics for professional study and long-term life has been raised again.
In Song Hao's video, barrages such as "lifesaver", "savior" and "mentor I have never met" rushed to the face. Someone watched Song Hao for a semester, never failed the high mathematics exam to the eighties, and even offline students, full of emotion wrote a "confession book", telling how Song Hao made him fall in love with mathematics and life.
At the beginning, Song Hao did not expect that he would become a super "Internet celebrity" college teacher. Back in around 2012, he started recording classes and uploading "Youku" or "Tudou" just for students to review and review. At that time, the term "online lessons" was still in its early stages of development.
In 2014, Song Hao officially began to record classes. Until five or six years later, he began to be frequently recognized by strange students in the school, and there were always students from outside the class in offline classes. There are even students listening to Song Hao in the classroom while watching Song Hao in the video with their mobile phones, echoing back and forth, and assaulting before the exam.
Song Hao on the podium
But Song Hao clearly feels that he has only begun to become a kind of "Internet celebrity" in the education industry, which has only begun in the past two or three years. One day in 2020, he met a student from another school in the Jinan mall who recognized him excitedly and asked for an autograph and a group photo. In the same year, people from Station B also approached him. At that time, he already had more than four million followers, and now has nearly 5.47 million.
In fact, Song Hao is not like some eloquent scholars who can turn the classroom into an encyclopedia and talk show, and he himself understands that "no one will watch a few episodes of line generation when they go to the toilet and wait for the bus." He would occasionally tell a few jokes and jokes, but most of them were a little cold. Sometimes he would use his hands and feet to explain a formula, and would use probability theory to talk about his emotional history and love views.
As an "Internet celebrity" professor, he seems too "ordinary", but as a university professor, he seems too "lively".
What is the difference between the high numbers taught by this "100 million-level UP master" and other college teachers? From primary and secondary schools to universities, why is mathematics always scary? Why do some people who can get high scores in middle school can't learn math when they get to university?
Beyond teaching and testing, how can we understand the status and significance of mathematics in the current era? What other guidance and echo does its beauty bring to life?
Song Hao
After becoming a "red man", Song Hao's life was stuffed into something unprecedented. On the last weekend of May, he attended an exchange meeting on Friday afternoon, attended a graduate report organized by Station B in the evening, and went to Liaoning on Saturday to meet with freshmen and sophomores.
Between this busy weekend, I spoke with Song Haotong. Early Sunday morning, just after eight o'clock, he was ready for the interview. I was sleepy, and he was as breathy as he was in class. We talked about the "beast" of high numbers, and also talked about mathematics and mathematics education in this era.
01
Math lessons from scratch
As a liberal arts student who did not attend high school, thirty minutes after opening Song Hao's video, I had the illusion of returning to the high school classroom in a trance——
In middle school, you may have met a teacher who uses the simplest colloquial language and the most primitive board book to guide you with the ultimate goal of "making you understand". I'm afraid that you won't understand, and I'm afraid that you won't be able to take the exam, like a worried old parent.
In Song Hao's eyes, the key to learning "advanced mathematics" is not "advanced", but the word "basic".
"Compared with middle school mathematics, high numbers are very abstract, and there are many formulas and symbols at first, and many students are scared away at first sight. It is very important to get everyone started and make the basic topics first. ”
Students sent barrage at the beginning of the teaching video of Song Hao's B station: Where the dream began
Among Song Hao's online students, comments such as "finally understood", "it is better to listen to Teacher Song Hao for two minutes after listening to a morning class", "one sentence explained what I did not understand in several classes" and so on, most of the evaluations came from first-year and second-year junior high school students, including many "college upgrade book" check-ins.
Song Hao almost wanted to start from scratch about what mathematics was all about. Simplify and complex, take the formula apart, and restore the derivation process of a theory with your own method.
Speaking of limit definition, he interprets the symbol "∀" as "arbitrary Any", but writes A backwards;
Write the English word "exist" upside down, and there is a "∃" existence;
Speaking of second-order determinants, he takes the expression "|a,b; c,d|=ad-bc" translates to "love you for a (-) lifetime";
Talk about the volume of the cylinder "V=S*h", "S" is the base area, "h" is the height, and then laugh: "Sh, Song Hao".
"Sh, Song Hao"
Some witticisms are actually not very novel and flattering, and even some of the earthy sense of age, like teachers in middle school classrooms, with the only purpose of making students remember, but it is the simplicity of this purpose that makes Song Hao's witticism particularly cute.
For example, Song Hao's own invention of various shape-based interpretations, "dropping M" is followed by continuous addition, and "π" is a continuous multiplication after straightening the two legs; The independent variable X in the function corresponds to the only dependent variable Y, "This is called 'monogamy', one X cannot correspond to multiple Y, because 'polygamy' is illegal." ”
Yao Shan, a first-year student in the computer science department of Shandong University of Finance and Economics, took Song Hao's "Linear Algebra" this semester, and last semester she was on another teacher, using PPT, the advantage is "clear and straightforward", but after listening to several sections, she was still at a loss. In Yao Shan's view, PPT is like piling up all the key points and building a magnificent mountain, but Mr. Song Hao's board book will tell you how this mountain of mathematics is built.
"Mathematics is very suitable for writing board books, suitable for writing out one stroke at a time, and every word written is a process." In Song Hao's view, the blackboard and chalk build an explanation platform, and in mathematical understanding, the process is indispensable, and with the derivation process of "left to right", thinking will develop, and students can keep up.
"To put it bluntly, it is to use the way of thinking of normal people and ordinary people." Song Hao believes that a good teacher should have the ability to tell difficult things in a simple way, "But whenever a teacher encounters a place and needs to use his brain, it may be a very difficult thing for students." ”
Putting himself in the same frequency position as students to talk about high numbers, being the leader of the classroom rather than the leader, Song Hao's teaching philosophy is not the way he understands it from the beginning.
Song Hao was born in a small mountain village in Wendeng County, Shandong Province, and completed his primary school to high school career in the small town. After completing his bachelor's and master's degrees at Shandong University, in 2007, Song Hao was admitted to the Chinese Academy of Sciences for a Ph.D. and studied under Hua Luogeng's students, in his words, Hua Luogeng's "apprentices".
Song Hao in the year of the college entrance examination
In fact, for most pure science majors, when a person has studied to a certain depth and height, it is possible to forget the difficulties they encountered when starting the basics. This "condescension" in professional density may appear in college teachers who have experienced long academic journeys such as masters and doctorates.
"A lot of teachers are miserable during class and think this place is not very simple? Do you still need me to talk about it? Don't you understand at a glance? "When he first became a teacher, Song Hao was also like this. He opened the freshman textbook he had just got and looked at it, confused, "Do you still need to learn this thing?" Isn't this as simple as eating and sleeping? ”
Later, he calmed down and pondered, and found that the current university textbook is actually very brief, "For example, talking about linear algebra, there may not be a single figure in the textbook, it is completely abstract, what is the relationship between vectors and linear space?" Completely difficult to explain. ”
Song Hao felt, "The process of class should be different from the textbook, the textbook may write the theorem first and then write the process, can the class be reversed?" Let's take one or two basic, small conclusions, and then derive the theorem. ”
Nowadays, the new mathematics teachers in the department will almost turn over Song Hao's video before taking the first class. In this sense, teachers may have to go through a process of "entering the university classroom" just like students.
02
"Good classroom, no walls"
Today, Song Hao carries nearly 20 pounds of backpack every day to class, and in addition to textbooks, it also includes a 4K Sony camera, a microphone, and a folding small tripod. Before each lesson, he had to arrive at the classroom at least fifteen minutes early, adjust the parameters, set up the tripod on the last row of tables, and the camera passed over the students and aimed at the lectern.
This has been the case almost every day for the past nine years.
Shooting, editing, compression, transcoding and uploading are all completed by Song Hao alone, "integrating collection, editing and broadcasting". Since I started recording classes in 2014, I have changed a total of 7 DVs, and there are 4 computers used to cut videos at home, which rotate 24 hours a day.
As he repeatedly emphasized in the interview, in fact, all actions and inquiries must come from the most primitive enthusiasm in the heart. When he was still studying, Song Hao loved photography, and when he graduated from his master's degree, he photographed, edited and produced the commemorative disc of the class alone.
Song Hao debugging camera before class / Shandong Education Satellite TV · Educating dream builders
In the second half of 2014, several students whom Song Hao had taught complained to him that they could not understand the new semester's "Linear Algebra" and asked if they could listen to his class.
But Song Hao took classes on another campus that semester, and it was troublesome to run around. It happened that he was also teaching that part of the course, and he came up with the idea of recording it and sending it to students to listen to alone.
Initially, I used a voice recorder, but there was no picture, and the effect was not good, so I spent 800 yuan to buy the first second-hand DV.
At first, only a few dozen familiar students circulated it privately, and a month or two later, Song Hao stumbled upon that the number of downloads had unknowingly reached thousands. Further back by leaps and bounds, from tens of thousands to hundreds of thousands of exponential growth.
Then, he began to upload video courseware to "Youku" and "Tudou" network, which was not yet 4K and the picture quality was touching. But a "first-generation student" of Song Hao recalled that since then, dormitories and libraries have been full of classmates holding computers to watch Song Hao.
Video of Song Hao at Station B in the early days
In the early years, Song Hao liked to let go of himself in class to tell his emotional history, but now he is a little embarrassed in retrospect, and his mouth is almost difficult to collect for a while, "How can I think that so many people (look) later?" As a result, countless students across the country knew: Song Hao of Shancai had waited for a girl in the snow for seven hours.
That was twenty years ago, and Song Hao was still in college. When the "first snow of 2002" swept the country, on a snowy winter night in Jinan, he ran to the door of the community where he liked the girl he liked to find her, and began a thirteen-year love run. The screen name "ice_mouse" that Song Hao has used to this day is also related to his memories of that youth.
"People are young." Twenty years later, Song Hao was a little shy to the students and the camera, "Now, there may be only one girl worth waiting for seven hours in the snow, and that is my daughter." ”
Almost all students also know that Teacher Song is a daughter slave. Whatever he says, he may drag his mind to his young daughter, who is still in preschool, and in class, he talks about the coordinates of the ball with his hands and feet and imitation robot, and he can't help but smile: "My daughter likes it the most."
"It's unrealistic to ask students to pay their full attention to a lesson of ninety minutes." So he occasionally nagged about his private life, and also tried to keep up with the trend of young people, such as the "current boyfriend" and "Di Li Gerba" in the entertainment industry.
For a long time, teaching and communication were not part of the same concept pool, and the "destiny-changing screen" only appeared for the first time in 2018, raising the spotlight on knowledge sharing. Today, only in the high number world, in addition to Song Hao, there are also millions of fans of the postgraduate examination master Li Yongle, Tang Jiafeng, high school mathematics Zhao Lixian, and so on.
In fact, Song Hao was ambitious about education from the beginning. When he first stood on the university podium, he was thinking, "The mathematics department of Peking University is good, the mathematics department of Tsinghua University is good, and the mathematics department of Shanhua University is good, but which mathematics teacher in Peking University and Tsinghua University knows the whole country about the lectures?" ”
After I started recording lessons, I became bolder in my idea: Sooner or later, I will have all the math students from all over the country watch my video. "Our Shancai may not be good in school, but it does not prevent our teachers from teaching this class well, and I want students all over the country to know that there is a teacher Song who talks about mathematics."
"Good universities don't have walls, and good courses should be." He thought that a university teacher could not only be trapped in the classroom, pat his ass and leave after class, but also use the Internet to extend the class.
Today, nine years later, Ye Hua of Shancai's 2022 School of Computer Science and Technology went to the school library for self-study and found that "three of the four who reviewed high numbers were watching Song Hao". This is not an exaggeration, because similar descriptions can be heard on various platforms, like a campus landscape.
In the first semester of his freshman year, Ye Hua met the rumored Song Hao in class for the first time. He looks taller than in the video, one meter eight, has more hair, and loves to laugh. In the first class, Song Hao half-jokingly told the students: "It doesn't matter if you don't listen to me, anyway, if you don't understand, you will turn over my video and watch it again." ”
Song Hao is called "high-count koi" by students
For his popularity, Song Hao is confident. In the past two years, he will embrace "traffic" with a positive and enthusiastic attitude. He advertises himself on Weibo, keeping in mind the number of fans and views of each platform, and he hopes to spread his courses as far as possible, as wide as possible.
"Isn't it nice that we have a place in the world of traffic, we also have a place in mathematics? Now some young people worship celebrities and Internet celebrities, why can't they also worship a person who spreads knowledge? ”
03
Mathematical castle with high mountains
"Advanced mathematics" is by definition separated from "elementary mathematics" in primary and secondary schools, but from a certain point of view, learning mathematics, whether in method or reason, is essentially no different between secondary school and university.
Liu Xuefeng, associate professor and doctoral supervisor of the School of Computer Science of Beihang University, and author of the 18th Wenjin Award recommended book "Knowing Numbers: Mathematical Thinking in Life", also believes that in higher education, the biggest feature of mathematics compared with other disciplines is "rigorous". And the more rigorous, the more we should pay attention to the basics.
"The so-called foundation is a mathematical concept one by one, and they continue to deduce, and the entire knowledge system is built. Just like the grapes, you have to pick them up in bunches, you can't scatter a handful of east and west. ”
Liu Xuefeng believes that "high-number knowledge points are built layer by layer, as long as a certain point is stuck in the middle, the entire chain may be broken, and the back will not be understood." "Therefore, the process is also particularly important.
Today's college mathematics textbooks are quite thin, in contrast, foreign textbooks are often thousands of pages, "because it tells you the truth and history of every concept, and when you know why you have these things, you know how to use them." ”
Multiple editions of the Advanced Mathematics textbook
How can you be sure you can grasp this concept? "You take it out alone and try to see if you can explain it in the language of life, and whether it can be combined with your own life." This way of understanding life also coincides with Song Hao.
To this day, the necessity of learning mathematics is still questioned, especially when students hang high on the "high number (tree)". In Liu Xuefeng's view, the development of mathematical value will not be immediate, and cultivating "mathematical thinking" through learning is a long-term spiritual investment.
A large number of professionals such as designers and engineers "need mathematical thinking ability to refine real problems into an abstract problem", and some cutting-edge technologies, such as the Shenzhou spacecraft launch that Liu Xuefeng participated in, "need to use mathematics in many tasks such as spacecraft navigation and control". ”
For most of the remaining ordinary students, "mathematics is also conducive to cultivating a set of useful ways of thinking for life, such as probability theory, which can help you use certain rationality to identify many rumors on the Internet now." ”
The ideal mathematics education also emphasizes the dynamic combination of thinking. Yau Chengtong once mentioned his views on mathematics education in his autobiography: "Most people engaged in mathematics education only study how to teach mathematics, and do not pay attention to the content, goals and meaning of mathematics. ”
Liu Xuefeng believes that in college, a mathematician is not necessarily a perfect mathematics teacher. "How to teach math in a way that is acceptable to all students, to articulate a difficult concept in the vernacular, is not just a technique, but an art. Or maybe it takes some talent. ”
Song Hao, who loves mathematics and education, obviously belongs to this list.
For Song Hao's "pro-student" Qi Sixian, the most difficult thing about high mathematics is its high abstraction, "and there is less time to brush questions in college, and many knowledge points are not proficient, and it feels very handy." ”
For example, the limit definition, after listening to it in class, Qi Sixian did not understand it at all, and later listened to Song Hao explain in a sentence: "When the independent variable approaches a certain value, the value of the function will approach a definite constant." Qi Sixian suddenly felt a bell ringing in his head, "It turns out that the essence of this concept is so simple and profound."
Song Hao's strength is not to turn mathematics into "flowers", but to have the patience and enthusiasm to cut the soil of mathematics. And this is absent in the college classroom that some students experience.
Li Huang, a first-year finance student who traveled south from Shenyang, Liaoning Province to Nanjing University, barely passed the line in linear algebra in the first semester, and he even felt, "If my high school math teacher came to teach me high numbers, he probably wouldn't have taken the test so low."
"The high school teacher will completely show you the reasoning process, tell us why we got to this step before we got to the next step, and why we thought about this deformation. (My) college teacher just moved the things in the textbook to the PowerPoint and kept only the key processes, and didn't tell you why they did it. ”
Li had to force himself to adapt to this method, and the result was: "I learned to memorize by rote and memorize those steps and formulas, but if I were to use and practice, it might not be very good." ”
After the course, the students brushed the screen to thank Teacher Song Hao. Song Hao can often explain complex knowledge in the vernacular that students can understand, which is why his classes are loved by so many students
In the current college education in the mainland, some specific objective environmental constraints have indeed opened a certain distance between the classroom and students. As Liu Xuefeng mentioned, "Teachers of public courses like high mathematics are mainly teaching, and do not do much scientific research; For teachers who are both shouldered by teaching and research, the pressure of scientific research will crowd out a lot of teaching time. Because for them, applying for projects, mentoring students, and publishing papers may be much more important to promotion and assessment than teaching. ”
Nanfeng Window interviewed several young teachers in 2021, among them, a teacher of the Information Management Department of a 985 university in Xi'an said that lesson preparation and class attendance actually only account for a very small part of work and life, and most of the time is filled with trivial matters such as administrative tasks and course activities; Another 30-year-old teacher said that under the "promotion or go" competition mechanism, whether teachers can finally pass the assessment, "the key is no longer teaching ability, but the number of scientific research results and papers published".
In today's universities, is high mathematics more used as a tool or a way of thinking, a common choice between educators and students, or a tool for each to achieve their goals? Liu Xuefeng also pointed out that "many freshmen and sophomores are not motivated by interest, but in GPA, whether the insurance research committee will add points, whether they can go abroad, and so on." ”
However, Song Hao, and more and more "Song Hao", let us see the good side: "There are more and more excellent teachers of high mathematics, more and more mathematicians are willing to spend time to study how to teach mathematics, and more and more students are beginning to take the initiative to find information, and the world of mathematics will become more and more broad." ”
The pictures in the article come from the Internet
Edit | Wu Qing
Typesetting | Sissy
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