The memories from before elementary school have grown too blurry; when I try to recall them, it feels as if I’m recounting someone else’s life.
When I was little, I changed kindergartens twice, but I hardly ever actually went—mostly I just hung around at home. I really was too spoiled rotten back then. Because I was overindulged, my health was terrible as a child; because my health was terrible, I was indulged even more…
At home, the division of labor was very clear when I was young: my father was responsible for earning money, my mother for my education, my grandmother for cooking, and my grandfather for taking care of me directly… The whole family revolved around me alone. Such an upbringing can easily produce an egocentric “little emperor,” but fortunately I somehow escaped that unhealthy path; instead, under all that pampering, I developed what I like to boast was a relatively independent personality and a fairly strong sense of responsibility. From a very early age I enjoyed enormous freedom. My parents never hit or scolded me, and rarely placed any restrictions on me. Anything I wanted to buy or do, so long as it was possible, would be satisfied. This made me realize very early on that I had to be responsible for my own behavior. Others never dictated my choices, so they would not be responsible for my mistakes either. Because everything was up to me, everything had to be borne by me. So, as long as I can remember, I seem to have been rather sensible.
Three scenes from childhood left especially deep impressions on me. One was riding on my grandfather’s head while strolling through Chenghuang Temple (my home was just across from Fuyou Road). Even from a young age I did not dislike places crowded with people…; the second was standing at the stair landing looking at that cat (a friend my age). I never thought of that cat as some kind of “pet”; she was more like a feral cat, very free, often running off for weeks or even more than a month, then coming back and having a litter of kittens, and so on. Cats are almost the only non-social animals that humans have domesticated. The reason people generally say that only social animals can be domesticated by humans is that social animals often have a “leader,” and the members of the group obey that leader absolutely; domesticated animals, in turn, regard the keeper as the leader. A dog’s loyalty comes precisely from the high degree of organization in a wild dog pack. But cats are solitary animals, and cat domestication is utterly different from dog domestication. The reason cats can be domesticated, I suspect, is that they are simply too “lazy.” If they have food and shelter, they accept you as their owner, but they can leave at any time, anywhere. My present understanding of the relation between humans and animals probably still bears the imprint of that cat from my childhood; the third was watching rainwater strike the eaves of the house across the street from the attic.
My mother took my education very seriously. When I was little I studied chess, Chinese painting, calligraphy—everything—but I’ve long since forgotten it all. Still, preschool education probably did me some good.
My first elementary school was Sichuan South Road Primary School in Shanghai’s Huangpu District. My family belonged to the Nanshi District, and we lived on the boundary line between Huangpu District and Nanshi District, so it wasn’t the nearest school to us. How I ended up entering Sannan seems to have involved many contingencies—for example, one school no longer admitted students; the principal of another school didn’t want me, and so on. In the end, after all kinds of effort (I only remember that the principal of Sannan gave me an interview, and seemed to ask some idiotically simple question like who was in your family… In any case I was too young then to remember much. All I know is that the final fact proved that entering Sannan was immensely beneficial! At the very least, the level of education in Huangpu District was worlds apart from that of Nanshi District just one road away. Now Huangpu District and Nanshi District have long since been merged; not to mention administrative integration, even educational integration reportedly has many difficulties…
Sannan’s first math Teacher Xi had a tremendous influence on me. I admired her greatly at the time, thought she was amazing, and believed her teaching was the best in the entire world (at least in all of Shanghai… let’s say all of Huangpu District…). Her teaching method really did have something special about it. One thing I still remember is that when she assigned homework, you not only had to write the standard format of “Solution: …; Answer: …” but also had to add a “Thinking:” before the “Solution” (that seems to have been the character), writing out the line of reasoning first. When doing math, a clear train of thought is the most important thing; a rigorous solution process comes second; the correct answer is the least important of all! I have always kept this notion in mind: the most important thing in mathematics is to grasp the problem, seize the essential point of the idea, think of the breakthrough in solving it, and then plan the strategy. Once these steps are completed in an orderly fashion, the problem will naturally be solved; and if you can’t sort out a clear line of thought, can’t write the “thinking,” then perhaps through repeated practice you can still master the methods of solving problems—because non-competition math problems in elementary and middle school are mechanical and formulaic, and as long as you proceed step by step and follow the rules, you can answer them—but in that case you will never truly grasp the intellectual essence of the math problem, and you will never improve your skill at genuinely “creative” problem solving! Math problems must be “thought” through—not merely in the sense of freewheeling imagination, but ultimately in the sense that one must be able to write down that thinking, to reach a level where the train of thought can be expressed and organized in words. “Thinking” is certainly not as rigorous as “solution,” much less as direct as “answer,” but learning to write the “thinking” is the first step toward deeply grasping the substance of the problem. This notion has guided me throughout my entire eleven-year “career” in Olympiad math, and even now, after I have read philosophy, it still continues:—first write down the “thinking”!
Teacher Xi emphasized not only reasoning, but also rigor. I remember once, when teaching how many rectangles could be counted in a grid of, say, 2 rows and 4 columns, Teacher Xi, in order to demonstrate the answer, actually drew all 30 figures on the blackboard. Then she had the entire class count aloud together: “one, two, three, … ten, eleven, twelve, … twenty-eight, twenty-nine, thirty!!” The answer checked out with absolute accuracy, and everyone was thrilled. But Teacher Xi’s rigor came out even more clearly afterward: she said our whole class was wrong! She told us to reflect on where we had gone wrong… It turned out the problem was that we had counted wrongly! What are “twenty-eight” and “twenty-nine”? They should be read as “twenty-eight” and “twenty-nine”! This really was too much detail—it’s a trivial matter, isn’t it? But mathematics is precisely such a discipline, so rigorous as to be exacting: how mathematical symbols are read, how they are written—none of it is casual, not a single character can be taken lightly!
Another influence Teacher Xi had on me was more direct—she was the first person to praise me without the slightest stinginess! I remember one lesson on the properties of “zero,” where Teacher Xi lectured for half the class period, then asked a student to repeat it. Apparently, I repeated it very clearly, and the teacher was extremely excited; in front of the whole class, and in front of my parents as well, she praised me without reservation. I believe the relationship between teacher and student is absolutely not an equal friendship, nor some kind of collegial academic exchange, but must be an asymmetric one. Especially when it comes to praise and criticism: when praise is due, it must be given; when criticism is due, even if conditions have to be created, praise should still be given! If one needs to remind a child that they have done something wrong, the teacher can do so by praising other students who have done well, and can even indirectly remind the child of their shortcomings by praising some other possible strengths of that student. Exactly what is worth praising, how to prevent a child from becoming complacent (for instance, one can control arrogance by praising other students), and so on—these are of course very hard to manage, which is why teaching requires “the art of praise.” But there is no such thing as an art of criticism—at least for small children, criticism, even when occasionally unavoidable, is absolutely not an art. Teacher Xi’s praise directly stimulated my interest in studying mathematics. Perhaps I did have a gift for math to begin with, and Teacher Xi noticed my potential; or perhaps I wasn’t anything special at all—after all, I just repeated something once… There is a story that psychologists conducted an experiment like this: in first grade, they administered some so-called intelligence test, then informed teachers, classmates, and parents that certain students were especially outstanding, though in fact this list of “outstanding” students had been chosen at random. When they came back to investigate in fourth or fifth grade, those students who had originally been declared outstanding often really did become excellent! It seems that the recognition of teachers, the recognition of others, and self-recognition are all forces that promote academic progress… Even today, although I am mature enough to sincerely welcome criticism, appropriate praise can still encourage me. Often I know full well that my actual ability falls far short of what the person praising me says, but I am willing to keep working tirelessly, striving to make those pleasing compliments “deserve their name.” On the other hand, what I dislike most is also praise—praise directed at things I myself regard as flaws leaves me between tears and laughter, and praise of this sort from friends especially troubles me…
Another lifelong gain from Sannan was “bead-and-brain mental arithmetic”—one of Sannan’s distinctive teaching methods. At the time, only those students who had done relatively well on the first-grade math exam were selected to participate. They had to train every day, morning, noon, and evening; it was very hard, but the benefits were truly enormous! Bead-and-brain mental arithmetic began with learning the abacus—using a modern version of the abacus, with one row of beads above and five rows below. It was also much more compact than the old-style abacus, a little narrower and longer than a typical pencil case, and operated with both hands. After hard practice, one could gradually do away with the physical abacus and keep it in one’s mind, so that one could use the abacus mentally at any time. Because it was entirely like manipulating a virtual image in the brain, there were no problems like slipping fingers, so calculation speed was faster than using a real abacus. Generally speaking, with a normal speaking pace, one could call out the answers to dozens of three- or four-digit additions and subtractions as one went along, much faster than an ordinary person using a calculator. Although the training was very hard at the time, once you had truly mastered it, it became like swimming or riding a bicycle—a skill you would never forget for life—because for me, even adding 5 + 7 was done on an abacus; I had already forgotten how to do addition and subtraction without bead-and-brain mental arithmetic… This skill was obviously beneficial for my later mathematics studies.
In second grade, I came into contact with “Olympiad mathematics”, which eventually became my bread and butter from elementary school through high school. At first it was at the Soong Ching Ling Children’s Library (something like that, I think…); then in third grade I tested into the math class at Huangpu District’s “Shaoke Station” (the Youth Science and Technology something-or-other station). The after-school time I had originally spent on abacus practice, as well as even more after-school time and even class time, was increasingly devoted to that thing! I could hardly have encountered Olympiad math at a more opportune moment. At that time, the Olympiad class was organized by Teacher Cao, with enthusiastic participation from a group of lovely parents led by my own mother, and with very little outside interference; it was run quite successfully! At least in Huangpu District, students of our generation were unprecedented and would not be equaled again. Of course, I can leave those matters for when I talk about my middle school days.
When I first tested into the Shaoke Station Olympiad class, it seems I was placed in Class B. After one semester, I was promoted to Class A as one of the four best students; after that, of course, I remained in Class A, and later on I heard that I had stabilized in the top ten, perhaps even the top six before I transferred schools in fourth grade. To be honest, I had absolutely no accurate sense of my own level at the time. Perhaps I was simply too dull to realize how outstanding I actually was!—I’m not boasting now; it’s just that I truly had no feeling for it then. At Sannan, I was in Class (4), and for a long time I believed that Class (1) was the best, that each class was better than the one before it, and in our own class there were also many classmates who seemed far, far more capable than me—one more impressive than the next… In any case, I just studied; Olympiad math and such were all arranged by my parents, and I simply studied without caring about rankings or anything. I feel that good parents and good teachers should above all help children find all kinds of suitable opportunities—for example, where there is an Olympiad class, which school and which teacher is better, and so on. How could small children possibly know? All this needs parents to help “reconnoiter.” Parents and teachers should encourage children to develop their potential and bring out their best; they must absolutely not teach children too early to compete with others, to compare rankings, to fight over who is better and who is worse—honestly, there’s no real point in that. Children are originally very simple; do not prematurely instill in them the adult mindset of mutual struggle, competitiveness, hierarchy, and so on. If the goal is to motivate good students, why not simply praise them generously? If you want to praise them, why not just say, “You did very well, wonderfully well; I’m proud of you”? Why insist on saying “You did better than him” to make it satisfying? Nowadays elementary education seems to have even more methods for comparing who is above and who is below than in my day—medals, little red stars, rank ordering of grades, and so on, lots of things like that. To my mind—why bother? Children originally do not care, and should not care. Comparing rankings and fighting over prestige is nothing but a boring adult game.
Another important ability I learned in elementary school was “slacking off”. This story is also one my mother likes to talk about endlessly (though of course she would never call it an ability to “slack off”): apparently I used to dawdle terribly with my homework. My mother always hoped that I would focus on study and not watch TV or play. But I always had so much homework that it could fill up that study time. So it seemed as though I was always doing homework, as if the homework could never be finished. Later, my mother allowed me to watch TV or play after finishing my homework, and then my homework efficiency suddenly took a leap forward in a very short time, improving greatly! After that, my mother stopped managing my schedule as well; everything was up to me. I always knew: as soon as the homework was done, I was free! So I learned to improve my study efficiency by any means possible, and as a result my mind became even more focused when studying. Of course, the success of this method may have been somewhat fortunate, but in any case, I never really experienced “stressful” studying from childhood through adulthood; I’ll talk more about that later.
Sannan also had one special feature: it used to be a Catholic school, and the campus was simultaneously a magnificent old Catholic church with a long history—the words “Catholic Church” hung directly above the school gate. Although I never once entered that church, for four years I always gazed at the church and did morning exercises beneath the cross, which counts as a rather special memory, I suppose. So although I was not religious and had no religious background, I nevertheless had a sense of closeness to religion from childhood, though that feeling did not become fully clear to me until college.
As a child I was extremely, extremely slow-witted—probably I’m still very slow-witted now, but compared with my Sannan days the distance is even more exaggerated than the gap between the educational levels of Huangpu District and Nanshi District. I studied at Sannan for more than three years, muddling through; even when I left, I still had not remembered all my classmates’ names, let alone now… Still, I think it’s not bad for children to be a little more closed off. During the period when my mind was least mature and most susceptible to the words and actions of others, I was excessively introverted, and my contact with other people was very limited. This helped me form a very independent personality and way of thinking. By the time I learned to communicate with others and understand what others thought, my own views and positions were no longer so easily disturbed. My personal thoughts and opinions matured within a relatively safe and independent environment, and even now I believe that while I am by no means resisting integration into this era, I can still keep a sufficiently clear distance from the restless, flashy, vulgar, and banal “trends” of the day. I never lose myself in a crowd. The closedness of childhood laid the foundation for independence in adulthood. Of course, if one stays closed off forever and never opens up, then there’s no point talking about independence or not—I’d be doomed. Fortunately, that situation changed in time.
In fourth grade, I seemed to be doing rather well at the Shaoke Station. At that time there was a competition called the “Singapore Elementary School Mathematics Olympiad,” and six students from fourth grade were selected to compete one grade level above us. Before the competition, there was a lot of time for special training together with the fifth graders. During that period I became fairly close with two classmates (who are now in the mathematics department at Peking University), and I learned that both of them had transferred into the legendary Cao Guangbiao Primary School. Cao Guangbiao Primary School had only been established for a couple of years at the time (it seems it had been formed by merging several schools), and Principal Jin had ambitions to make a real splash and achieve something astonishing. At that time he cooperated with Teacher Cao from the Shaoke Station to set up a math elite class—officially, of course, an “experimental class”—with just over thirty students. He was also preparing to “dig up” all the math talents in Huangpu at the time, and naturally I was among those being dug up.
I have long since forgotten exactly how I was “dug up” at the time. In any case, this decision was made under my own active desire rather than merely being arranged by my parents, and hindsight has proved that this choice was an important turning point.
——————————————（to be continued）——————————July 6, 2006
Latest comments
- veronique
2006-07-09 01:57:23 http://veronique945.spaces.msn.com/
Olympiad math… such a mysterious phrase. I’m always missing something when it comes to math; I revere those who are good at math as if they were gods. I once wanted to apply to the philosophy department, and for a time I was afraid that my logical and dialectical abilities in math weren’t up to par… My classmate is from Xuhui and went to middle school at Shanghai No. 4, a church school~
- Me
2006-07-09 02:17:28
From fourth grade through high school graduation, I was even more inseparable from olympiad mathematics. I’m continuing to write this after finishing the World Cup over the past couple of days.
Also, recently I’m planning to organize some of my own thoughts on learning mathematics, suitable for middle school students and even elementary school students. Please look forward to it~
I still occasionally talk about mathematics with elementary and middle school students now, and there is a huge difference between students who do olympiad math and those who do not. In general, when it comes to ordinary, non-olympiad-level mathematics, I feel I could teach it better than the vast majority of non-olympiad math teachers—my teaching method is not about quick fixes or short-term improvement, but about perhaps changing some students’ view of mathematics from the roots up and imparting the basic attitudes and methods for learning math. Especially for elementary and middle school students, as long as I prepare a little, I’m absolutely confident I can handle it~
Students who do olympiad math are stronger than ordinary math teachers—this is not only unsurprising, it is only natural. If you can’t even reach the level of an ordinary math teacher, then don’t even think about achieving much in olympiad math. Hehe, I’m kind of thinking that while I still haven’t forgotten all of olympiad math, I should tutor some students for fun and make some extra pocket money on the side. If interested, please contact me hahaha~~~ - unic
2007-02-06 16:47:23 Anonymous 222.82.78.24
……
- Suíyuán
2008-07-12 21:58:16 Anonymous 222.29.26.136
Hehe, a glorious history—watch how “steel” is forged! Once the master of Suixuan is forged into a great scholar, these materials can then be used to carry out a phenomenology analysis.
Translated from the Chinese original with AI assistance. The original text is authoritative.
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