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Feature requests: What do you know about Russian(or Soviet Union)'s mathematical education system?

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    I am not sure whether this question is appropriate for MO because what I want to ask is about "starting early in mathematics" But I saw there was one question about this was closed as" not real a question" and others did not like this question for they thought this kind of questions could discourage people who want to do mathematics.
    Nevertheless, I am really interested in this question.

    Why am I interested in this question? Last week ,when I was taking the lecturing course on noncommutative algebraic geometry by my advisor. We are required to do some exercises which looks very abstract(of course with rich meaning in representation theory but not easy to understand). Then my advisor told us that in the Kolmogorov' times. Teachers taught set theory in usual elementary school at first grade and Axiomatic geometry at second grade. I think what he talked about is something equivalent to "set theory", say taught students to do some set manipulating without telling them the precise definition.

    It seems that many Russian mathematicians began very early, my advisor told me that when they were 16, they could play algebraic geometry and attended Gelfand and Manin's seminar to learn mathematics. He also told me that it seems that there existed some special school called" secondary mathematical school" which was founded by Dynkin to cultivate mathematicians

    What do you know about the Russian(or Soviet Union)'s mathematical education system?

    I think I can tag "mathematical history" or"mathematical education"here, but I am really not sure whether this question is good for MO. It is just my own curiosity.
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    The former Soviet Union still has specialized secondary schools for mathematics and physics. I am personally aware of one such school in a town of population ~300K.
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    I would more inclined toward a question like "What are some good sources for learning about the Soviet Union's mathematics education system?" I think any question which starts "What do you know about...." is probably a bad fit for MO; what I know about the Russian education system is not what you want to know. Rather, what you should be looking for is books and articles about it.

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    Phrasing aside, it is certainly an interesting question and well worth asking.
    • CommentAuthorBen Webster
    • CommentTimeMay 2nd 2010 edited
     

    Certainly the history of Russian mathematics education is extremely interesting and appropriate for discussion on MathOverflow; I do think that historical questions on MO really should be a bit more focussed than what Shizhou wrote above (though the body of the question makes it a bit clearer than the title). In particular, there should be some clarity about whether one is looking for general sources, or the answer to a particular question. It looks like maybe what Shizhou really wants to know is about the introduction of concepts at a young age and whether that was effective; if that's really the question it should be indicated in the title.

    • CommentAuthorvoloch
    • CommentTimeMay 2nd 2010
     
    Some historical background on mathematics education of gifted students in the Soviet Union can be found in Masha Gessen's book "Perfect Rigor" (which is mostly about Perelman). I, personally, don't think this is a good question for MO.
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    I don't think that this is a good question for MO. At best, I would like to see it written as a "request for reference" question.

    • CommentAuthorfedja
    • CommentTimeMay 3rd 2010
     
    "What do you know about the Russian(or Soviet Union)'s mathematical education system?"

    Well, I went through it from elementary school to PhD in Leningrad, so I fancy I know quite a bit about what it used to be before "perestroika" and "democratization" that completely destroyed the country and are now threatening to destroy its education system as well. But I have no inclination to write a long manuscript that would be needed to answer the question as you posed it. Either ask in a much more specific way, or, indeed, read the books (I mean those written by real mathematicians who know what they are talking about, of course).

    "I think what he talked about is something equivalent to "set theory", say taught students to do some set manipulating without telling them the precise definition."

    That would be a typical idea of modern American educationists. We've never been taught to "manipulate" abstract objects without understanding what they are, neither at school, not at the university. There were many things in the old time Russian mathematical education. Some of them were good and some were bad from my perspective, but there was nothing that would be that nonsensical. If you want to know what really was in the school curriculum, just get some Soviet era math. textbooks.

    "It seems that many Russian mathematicians began very early, my advisor told me that when they were 16, they could play algebraic geometry and attended Gelfand and Manin's seminar to learn mathematics. He also told me that it seems that there existed some special school called" secondary mathematical school" which was founded by Dynkin to cultivate mathematicians"

    It seems like he got his education in Moscow in 60's. The Leningrad system in 70's was somewhat alike but also a bit different. We've got more problem solving than theory during school years. There were several special schools in Leningrad (30, 45, 239 were the best known ones but there were quite a few less known ones as well). Also there was a huge system of math. circles, regular math. competitions, etc. I personally wasn't able "to play algebraic geometry" at the age of 16 (i.e., in the 9th or 10th grade) but my command of analysis and algebra was fairly decent and, indeed, I did attend a couple of seminars during the last two years at school together with a couple of my schoolmates.

    "I am really not sure whether this question is good for MO"

    Probably, not in general. Certainly not as currently posed.
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    If you're really interested in digging in the topic, perhaps neither MO nor the meta is the right venue. Anyway, since you're asked, here are some factoids, Snopes-style. Also, I was educated in 90s, so that's my understanding of the history.

    The specific idea of a set theory being part of the elemetary school curriculum: not true. Kolmogorov (with the mandate from the Communist patry) attempted to reform the Soviet school system in 60-70s, creating innovative textbooks that taught set theory and axiomatic geometry. He, in fact, wanted to present some set constructions: certainly products of sets, the idea of function between the sets etc (although, no ZF axioms).

    Though I couldn't find the details right now, I think it was targeted at the ages 12-16, rather then elementary school. But the reforms were accepted neither by the society, nor by teachers, nor by the government, anyway, so this idea more-or-less fiddled.

    During the experiment, some teachers had pretend to teach set theory without really knowing it (remember, they themselves were educated earlier), thus leading to perception that the whole thing was about useless manipulation of symbols.

    It should be noted that Kolmogorov, while a highly talented person who studied math early in life, first seriously studied history before finally switching to mathmatics at the age of 17-18 years.

    The existence of many people in the Soviet Union who supplemented their education at school with more advanced mathematics: true. Starting in the 30s, but especially from 60s, many mathematically minded high school students in Moscow and often other cities could supplement their education with formal ("Small Mech-Math", specialized mathematics schools) and informal studies ("math circles", or if you just knew one of the professors, you could often study math by talking to people). Indeed, quite a lot of people in the 80s knew enough at the age of 16 to attend the famous Gelfand-Manin seminar and benefit from it.

    Although it's probably not the right idea to discuss possible reasons here, I think the facts are that the concentration of math talent in Moscow and St.Petersburg in the 80s was quite unprecendented in history. Many famous people from that period ended up in the US, impressing people with their genius and making people think that theirs is the typical level for Soviet Union's high schoolers and professors, while in fact those were the best of the best. That explains what you teacher told you: some mathematicians (which could be all ex-Soviet mathematicians he knew) were indeed extremely bright research-level mathematicians at high school.

    Now that I think about the culture of math schools in Moscow, to think about the high school being associated with only partying and not learning at all, is viewing education from an American point of view. Although I was celebrating my 16th birthday already being a university student, many other 16-year olds who still were at high schools studied harder then me and, in fact, took courses that were more advanced then the ones I took.

    More important, though, is what kinds of corollaries shall follow from this picture: for example, the fact that some people start early in math shouldn't blind our eyes to the fact that some other successful mathematicians started late and others started around the "typical" time (whatever you think it could be). So if you're feeling low because of the fact that somebody else knew infinitely more at your age, that's probably not the right thought to take out from a math course.

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