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Lots of comments asking what is "Soviet/Russian Math" actually like, and how is it different. I was lucky to get an education in three systems (Soviet Math, Ro

• bordercases 5y ago
  What characterizes the French?
• horsawlarway 5y ago
  As an american who went through US-based curriculum in the 90s, this sounds FUCKING WONDERFUL. Basically - it seems like the approach above treats math as a conceptual playground, where you should develop intuition and understanding. Instead we seem to be going down the rote memorization route for most of our classes, where the goal was to apply an equation to some numbers and get the right answer, with little to no thought, and an emphasis on easy grading. ---- Our physics education seems quite similar, though - and I loved that.
  • BoxOfRain 5y ago
    My British state education really did feel like "memorise just enough to jump through these arbitrary hoops which keep the government off our backs" sometimes. It's very exam-driven rather than learning for its own sake and apparently it's got even worse since schools started transitioning to academies and Gove's reforms took effect.
    • cabalamat 5y ago
      One fix for this is to have exam questions such that you cannot pass them unless you have true understanding rather than rote memorisation.
      • nicoburns 5y ago
        That's one part of the equation, but it only works if you have teachers and a curriculum that are capable of imparting that understanding.
      • fiftyacorn 5y ago
        Normally the curriculum was split between knowledge and understanding, and problem solving. You could memorize the first part and not the second part. The problem solving sorted out who got the grades
  • selimnairb 5y ago
    I have always liked math, but have never been great or very good at it. I graduated from a US public school gifted program, and a top 30 US university. The biggest problem I always had with math education is they didn’t teach the “why” nearly enough. I was lousy at memorizing formulas/methods (esp. in calculus), so I often found myself dead in the water during exams.
    • zsmi 5y ago
      I used to suffer from the lack of "why" too until one day it dawned on me that there really isn't a why, or maybe, the why is always the same: for engineers doing classical physics solving problems by hand, it's convenient to define it that way. No more, no less. When I was a math tutor in school, everyone would complain about lack of why. This was my approach to address the issue. I would describe a problem relevant to the class, say something like find the angle between two vectors, and ask them to think of a general way to do it. Usually this require some help from me but the solution was always "theirs". Then we would play with their solution: find corner cases, figure out which operations broke, develop a couple of theorems with it. Then I would show them the dot product, and a couple of its tricks (a.k.a. theorems), and they would get a good appreciation for why the dot product works the ways it does. And that's the why and the reason it stuck. It's useful way to solve a common problem. There is no magic or deep philosophical truth. The problem is this teaching style works with a dialog to a few number of students. I am not sure how well it would work in a lecture setting. It was also not so easy on me as I would be the person who had to spot the problems in their definition, basically on the spot, and lead them to it on their own without revealing the answer. With basic things like a dot product it's pretty easy to know where to look (i.e. is their definition commutative, pretty much never) and finding issues and nudging them too it wasn't too hard. But it's likely hard to scale things like this on many metrics.
• sologoub 5y ago
  That’s very insightful - when I switched to US high school, the approach to math was baffling - everyone had programmable graphing calculators, whereas I wasn’t allowed any calculator at all, and took a lot longer to solve the most basic problems. Most questions were answered by the teacher as “it’s a formula, you follow it and memorize it” (which sounded ridiculous to me for the exact reasons above - I was taught to understand the basis first, then the applications).
  • starkd 5y ago
    I never understood why graphing calculators were required for basic calculus or math courses. Always wondered if it was part of a marketing deal with the company that manufactured them. The course is said to require a particular make and model of graphing calculator.
    • Isthatablackgsd 5y ago
      I believe it is more of a standardization of knowledge when picking the tool for mathematics. TI-83 calculator is common and easily to have all the students to use the same calculator and provides various approach of how to solve it. If one student is a outlier (like using HP calculator), then it could be an issue since the instructor only have the knowledge of using TI-83 (or its variants), the instructor couldn't help that student since HP and other graphic calculators have different inputs, layouts, etc. And not everyone is good at solving math alone without the aid of the calculator. Some people simply can't solve mathematics at all, maybe up to multiplication/division level is the best they can do. I am not good with mathematics myself and struggles with some advanced algebra. It is not the matter of trying to solve, it is matter of memorization of mathematics formula and equations that US Education drilled down so hard which is ironic when they said that calculators are forbidden to use during the exam while they are encouraging to use the calculators in class and homework... Their pedagogy is fucked and hypocritical.
      • sologoub 5y ago
        Sorry you had such an experience! There really is a lot to unpack here. As the article describes, memorization of “formulas” doesn’t actually work for my students and leaves those that it “worked” disadvantaged in future learning. My personal guess is the “not being good at math” originates from this, at least in part. It’s a confidence killer for sure that on one had you are being forced to do something unnatural (memorize weird looking formulas) and on the other give a somewhat easy, yet demeaning, way out by saying “it’s ok, you are just not good at math”. The calculator to study and no calculator for the test is even more ridiculous - students are put in a high pressure situation without the very tool/crutch they came to rely upon. If anything, the inverse might make more sense - homework you have a lot more time and less pressure, so try working it out on paper. Test is timed, so it’s ok to use a calculator aid, so long as you show your work.
• starkd 5y ago
  I've heard from many Russian immigrant friends who insist that Soviet education was one of the few areas that was done well in USSR. Particularly, mathematics, which, other than the obligatory Marx/Lenin quotes at the top of papers, tended to avoid ideological corruption.
  • smhost 5y ago
    What's funny is that the differences in pedagogy is probably a result of that "ideological corruption". Going through the American education system, it's clear to both professors and students alike that the system was designed on the assumption that there should be winners and losers, and that meaningful education is an afterthought. My math professors complained that the way the system worked made it impossible for a student to have continuity in their learning experience, and if you measure the number of A-students in one course who get an A in immedate next course, it's random. They weren't talking about courses that have large conceptual leaps between them. They were talking about first semester calculus vs second semester calculus.
  • culebron21 5y ago
    I studied in 1988-1999, and these stories may be true for Soviet elite education, but not for average Ivan. I personally studied at a school with advanced Physics and English (our teachers after graduating from uni went to Minneapolis for a year of practice). But maths had nothing close to what's described in the article or comments here. No witty simple problems, just boring theorems, then simple tasks to solve. I did see those witty nice problems in journals and special math tasks books, but that never appeared in our lessons. That was boring like hell. Well, ...at least it wasn't dumb, we did take logarithms, derivatives etc. But if you take an average Russian, they can't solve a simple proportion problem: say, income tax is 15%, you paid $450 of tax, how much net salary did you get? The answer is easy: 450/.15*.85 (then do it on calculator), but when I did this calculation with accountants from vocational college, they were stunned and didn't get how I did it. I'm not exaggerating a bit. So those people were either from elites, or nostalgic. On other courses in Soviet/Post-Soviet school. Russian language focused mostly on orthography, punctuation and participles. Like if British school focused on spelling "coloUr" or "emphasiSe". The examples of good style were only 19th century literature, especially Tolstoi's suffocating long sentences. Literature course is similar to what Paul Graham wrote about in his essays: old, boring and already unimportant literature, plus writing essays that must imitate literature critics. I think this was the most hated task at school, and it lasted all the way from 5th to 11th grade. Such essay writing is still obligatory till today in 2021, and I see consequences of it while teaching in a university: students write in unnatural high style, but have difficulties conveying their thoughts or selecting proper evidence (few can distinguish between facts and theories). And that's in a good university -- I'm scared to think what less smart people write. This is not a "degradation" of modern ages, it's almost unchanged since Soviet times. History course conveyed a Communist narrative, cherry picked facts and asked you not to analyze anything but to remember dates/years. E.g. a textbook on medieval history (6th grade), a paragraph on knights and their armor started with exactly this phrase: "It was not easy for peasants to fight even one feudal lord." (then it described the armor). The entire country of Grand Duchy of Lithuania (at the time it was also called Lithuanian Russia) was omitted, except for being shown on a map. Because it was embarassing to compare that country with Russia under Ivan the Terrible (who became an icon in Stalin's age). Geography was interesting to me, but when I got to Wikipedia in 2004 and started reading on languages and nations, I saw how much was missing from there. Biology was a simple and rather boring literature, and the home work was to read a paragraph and be ready to retell it. Most students would simply learn them. (Actually, with mediocre English teachers that was the case as well: read a text, called "topic" and retell -- and the teacher saw students telling the text learned by heard, but didn't care.) So, to conclude, math in Soviet elite education was good. Other courses were probably reasonably good, because those elite schools for talented also attracted good teachers. But the average school was of much lower quality.
• systemvoltage 5y ago
  Meanwhile in California: https://equitablemath.org/wp-content/uploads/sites/2/2020/11/1_STRIDE1.pdf https://equitablemath.org/wp-content/uploads/sites/2/2020/11...
  • primitivesuave 5y ago
    This is fascinating and I appreciate you linking it. I was mind-blown when I read page 8's claim that white supremacy manifests itself in mathematics education when "students are required to show their work in standardized, prescribed ways".
    • dharmab 5y ago
      For the curious: > The child of immigrants might have learned a different way to solve a problem because that’s how their parents were taught where they grew up. If we just tell that student their way is the wrong way, we risk turning them off to math for life. If we take the opportunity to explore why there are different ways to approach the same problem, it can be a learning moment for the entire class. I certainly had this experience in school! I did many math problems mentally, using the method taught in schools today where a problem like 23 x 7 is split into ((10 * 7) * 2) + (3 * 7). As a result, showing my work was challenging, because the teachers of my time wanted us to write out the long multiplication and I didn't know writing the above expansion was an option.
      • lotsofpulp 5y ago
        Part of schooling is learning and showing you can follow a specific set of instructions. As long as one was taught how to do long multiplication, I do not see the purpose of taking into account what every kids' parents taught them if the purpose of the exercise is to learn a certain method and then show that you learned that certain method by doing it.
        • TheGigaChad 5y ago
          Idiot.
• dartharva 5y ago
  That sounds wonderful! As a product of Indian education (that prioritizes rote learning), I wish I had been subjected to such a school, maybe then I (and majority of other kids) wouldn't have fallen out of learning math like we did.
• janeroe 5y ago
  I had a chance to compare the systems, too but my conclusions are completely different. Teachers at the physics/math lyceum I studied at were emotionally unstable psychopaths with mood swings. They could switch from calm "kids, if you don't understand something, please, don't hesitate to ask" to the screaming at the top of their lungs of "are you a stupid imbecile? what a moron you're to ask that" just a minute later. It was all about rote memorization. Rules, theorems, axioms. Not just the way to prove or principle behind, but the textual representation (to the teacher's liking) word-to-word. Of course, there was a division of students into multiple groups, and those with important parents had an easier time. Any of their bullshit was always graded as "A". But those actively disliked could get "F" for a perfect work. A dot at the end of the sentence is missing? "Go back to the kindergarten where you belong". Something is crossed? "What is it, a toilet paper? Go use it for wiping your ass" (they could tear it apart in front of you). So, the representation/look of the work always came first. A teacher was a lawyer, prosecutor, and a judge at the same time (just what some Americans wish to have as a state): you don't like something, go f___ yourself. The textbooks. If you compare the best Soviet ones with some average American, you can come to the conclusion that Soviet are so good ("exercises are something to behold", "high quality in their expression", etc). But the best American books wouldn't give a single chance to the Soviet ones. In fact, even some Russian Empire textbooks so much better than Soviet (not to mention Russian), they are getting popular among parents for homeschooling (schools can't use books unauthorized by the ministry of education). The best American and pre-Soviet textbooks are born out of lectures, author's personal experience with students. Soviet authors are disinterested observers who don't care. Textbooks, apparently, were the product of central planning like process (so they were getting worse and worse, the further they went from Russian Empire epoch). And finally, a thing that really deeply touched me at a western University. A teacher when asked a question once said "I don't know, I have to check it". Holly f... Someone who openly admitted they don't know something, no freaking way! Back at the lyceum it would be "Shut your mouth with your stupid question, we don't have time for that". Then she would find the answer and during the next class say something like "now when we have a few minutes, I'll do you a favor, here is the answer... What a moron you're not to be able to conceive this yourself".
  • filoleg 5y ago
    I was about to reply with something like this, so thank you for posting it. I don't know where the top level grandparent comment comes from, but your experience matches mine almost 1:1 (except I went to school in russia between 2001-2010, so hardly soviet anymore, and then finished up high school+college in the US). Something to keep in mind: my school in Russia wasn't just a random school, but a physics+math focused gymnasium, one of the best public schools in the city. I am shuddering to even think what it was like at less well off schools. Everything was about rote memorization, to the level i couldn't imagine in the US. Physics? Nope, memorize everything, you don't need to understand why or how formulas relate to each other or what they mean. Math? Nope, no need to understand logic behind anything, just memorize the formulas. Even with something like programming, we had to memorize bubble sort in TurboPascal, without the algorithm ever explained at a higher/pseudocode level (it was introduced in TurboPascal right off the bat and you had to memorize it line by line, I wish I was kidding; we were graded on how line-by-line it matched the given solution, not on whether the implementation actually worked/was valid). It was pain, I barely learned anything, and was convinced that I am destined to never do well in physics, thinking "this was just not for me, i am not smart enough to get it". Then we moved to the US, and I felt like my eyes were opened. Physics were explained from bottom up, from actual phenomena and how they worked, and formulas were just a glue connecting those phenomena and their interactions together. There was zero actual need to waste time memorizing those formulas, despite formula sheets not being allowed on the exams, because they actually explained the logic/reasoning behind it all, so it was no issue at all to simply derive those formulas on your own during the exam. Same happened with math and programming. I actually finally understood what I was doing, rather than robotically recalling appropriate strings to put on paper from memory. In the russian school I went to, logic didn't matter, only correct answers. For a specific example, in every single physics course I ever took in the Russia, if you got the calculation wrong for one small part of the problem (which propagated to the final answer being incorrect), but you got the rest of it right, you get 0% for that problem. While in the US high school/college, I could even omit a small part of the problem that I didn't know how to solve, put a placeholder number there, and then solve the rest of the problem correctly, and I will get points for the parts I got right. Which makes sense, because if I forgot how to solve one out of many subproblems, but know the rest perfectly, or if I miscalculated a single variable, i just lose points for that portion. It isn't "all or nothing, the only thing that matters is the final answer." I get part of the reason the "all or nothing" system was done in my russian school, it makes grading much easier. But it also introduces tons of both false positives and false negatives. You know how to solve everything, but screwed up one small calculation? No points for the problem. Oh, you got the right answer at the end and wrote a bunch of gibberish to "get" to that answer (because you just copied the answer from someone else without knowing how to solve it at all)? Well, you got the answer right, so we will give you almost all the points. Cheating was off the charts. And that is at one of the most "prestigious" and highly ranked specialized gymnasium schools. Of course, high school in the US still had plenty of memorization, but not even close to 100% like it was in Russia for me. And once US college hit me, it became even better. >A teacher when asked a question once said "I don't know, I have to check it". Holly f... Someone who openly admitted they don't know something, no freaking way! This, so much. Professors/teachers behaving like humans instead of "even if i was wrong, I am marking you down because you argued with the teacher, and the teacher is always right", that was incredible for me. P.S. sorry for the long rant, but it bottled up, especially after seeing comments proclaiming the exact opposite of what I, and every single person I know in real life who went to high school/university in Russia, have experienced. Oh, and no comment on "Russian schools in the US" (as I feel like they could indeed be great, but the "russian" part of them is imo just a marketing trick), as that's a very different beast that I have zero experience with. I was talking only about Russian schools in Russia.
• OnlyOneCannolo 5y ago
  Do you happen to remember any specific textbook? I'd be interested to see an example, assuming that they're still available in some format.
  • udev 5y ago
    See my reply to other similar question in this thread.
  • rramadass 5y ago
    Many of the Soviet-era textbooks (mainly by Mir Publishers) are now published by low-cost Indian publishers and available on Amazon.in. Just search Amazon.in for Piskunov, Irodov, Vygodsky etc.
• cabalamat 5y ago
  The focus on understanding rather than on rote memorization of methods, is paramount.
• filoleg 5y ago
  My take on your list of advantages of soviet math/physics approach is mixed. Fully agreed with you on the rigor regarding notation, really good progression of teaching (pacing and order in which the material is introduced), and soviet math textbook exercises being well thought-out and entertaining. Very much disagreed on the rest, as my main personal gripe with learning math+physics in Russia was that there was zero emphasis placed on understanding of principles and logic and 100% on memorization. I spent 3 years taking physics classes there, and I learned effectively nothing, having to relearn it from scratch in the US. And that was the moment where I truly felt I understood what was going on, instead of treating physics as just another memorization exercise for a variety of random unrelated formulas. Similar with math, but to a lesser degree, because with math I was personally invested and was trying to understand the material rather than memorize, despite it hurting my grades in Russia greatly.
  • portpecos 5y ago
    > - teachers are astute at spotting students who memorize blindly, and will intervene to correct that > 100% on memorization OP says it’s not 100% memorization and you say it’s 100% memorization. So which one is it?
    • filoleg 5y ago
      That's why I posted my previous reply, despite me being in strong opposition of the "argue anecdata with your own anecdata" approach in discussions. But I couldn't resist replying, because all of my 9 years of experience in Russian educational system were the opposite of what OP claims in terms of memorization, and so were those of every single person I know in real life who went through that system (in other schools in Russia, not just from mine, obviously). Coworkers of mine (who went to Soviet schools a decade or two before I was even born) echoed the same sentiment in discussions on the topic, with the halfway sad "some things never change there, huh" sentiment. Would have been less surprising if my school was doing poorly in rankings and such, but it was quite the opposite. Of course, all my claims here are anecdata, but it just feels like something is off when the fantastic utopian description of how "soviet math" education works just runs counter to every single lived experience I had, as well as that of everyone I know in real life. Especially given that experiences of some of those people in real life I mention were separated from mine by both decades and geography (some did school in Moscow, others in smaller towns, some in soviet ukraine, etc.).
• ksd482 5y ago
  As I was reading the summary, I was thinking "well, of course -- that makes sense. Any teaching curriculum has got to be like that so what is so special about Russian math curriculum?". Then I read in other comments about US math curriculum and I was shocked to learn that not only they were NOT doing this, but they didn't have a better alternative. This is mind boggling. It seems almost idiotic. My schooling was done in India. Our curriculum was quite well planned, but what is laid out here is the methodology of teaching in addition to the curriculum and textbooks. And that depended on teacher to teacher and school to school. But nonetheless, the textbooks were very well written so everyone got exposure to pretty much the same level of teaching styles, more or less. When I came to US in college, I was surprised to learn that people didn't know basic techniques and tricks for algebraic manipulations. Of course, we were taught the basics and whys behind every trick but emphasis was also given to internalizing these tricks for quick computation by hand. This, in my opinion, is important because these tricks also become your mental models when thinking about math. And quick tricks would lead to quick thinking, roughly speaking.
  • lumost 5y ago
    It wouldn’t be an exaggeration to state that most Americans experience k-12 math as an exercise in memorization. Even relatively simple algebraic manipulation such as quadratic equations are drilled for factorization first.
    • jdgoesmarching 5y ago
      Yep, it’s like teaching someone how to cook by quizzing them on recipes. I didn’t understand the purpose of calculus until grad school despite having “learned” it several times by that point.
      • jacobolus 5y ago
        If anyone wants a book focusing on the purpose of calculus, check out http://www.math.smith.edu/~callahan/intromine.html http://www.math.smith.edu/~callahan/intromine.html This is significantly different style from Russian textbooks. If you want a nice one of those translated into English (albeit not the easiest to find a paper copy of), I like Piskunov’s book. https://archive.org/details/n.-piskunov-differential-and-integral-calculus-mir-1969 https://archive.org/details/n.-piskunov-differential-and-int...
• ilikeatari 5y ago
  I also had a similar experience both on the US and Polish side. The US math exercises that I experienced through my niece were really much more focused on reading comprehension, but almost hoping that the student trips up. Maybe its because I am not a native speaker, but this seemed to be not constructive to the task at hand.
• bulka 5y ago
  Anecdotal, but still: What you have described might have been the case in a handful of top schools, mostly at metropolitan areas. The key difference for the "rest of us" was a high school theacher who would pick top 1-2 pupils after couple of lessons and teach at their pace for the rest of the year. This is my case and the story that was confirmed by dozens of people in my university.
• tjchear 5y ago
  Any books you can recommend that are similar to the Soviet Math textbooks you talked about?
  • udev 5y ago
    A book that appeared previously on Hackernews is Lev Tarasov's "The world is built on probability". This is not striclty a textbook, but it is translated in English in a way that preserves a lot of the feel of the original: https://archive.org/details/TheWorldIsBuiltOnProbability https://archive.org/details/TheWorldIsBuiltOnProbability For examples of beautifully crafted exercises see this: https://www.imaginary.org/sites/default/files/taskbook_arnold_en_0.pdf https://www.imaginary.org/sites/default/files/taskbook_arnol... There are plenty of books in Western literature where exercises are also very good, and not only in math, but other fields too. One that comes to mind is Jon Bentley's "Programming Pearls", which has very well chosen exercises.
  • kevinkeller 5y ago
    "Mathematics: Its Contents, Methods, And Meaning" https://archive.org/details/MathematicsItsContentsMethodsAndMeaningVol3 https://archive.org/details/MathematicsItsContentsMethodsAnd...
• onecool 5y ago
  A Russian mathematics professor of mine in graduate school was a student under Kolmogorov. He taught information theory and algebraic combinatorics and helped develop a number of systems for the Soviets. He was extremely challenging, but he cared less about the grades and more that you were understanding the material. He would say at the beginning of the semester: "You must learn to build the castles in your mind." The visualization of the constructions really helps to understand how to apply the concepts in different contexts. The Polish professor would hand out chocolate to every student before every test, so that your mind was more relaxed.
• yhoneycomb 5y ago
  This is probably a dumb question, but I'm guessing all the textbooks are in Russian? I really would be interested in seeing this: > - the old soviet textbooks are generally less verbose than North American ones (less fancy), but high quality in their expression, typesetting, and ESPECIALLY (!!!) the quality of the exercises but sadly it would be no use to me if it's not in English