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Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

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Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#301
post #263

Earlier quoted context omitted.

I wonder how much the respective cultures and politico-economic systems of those states play into that. My dad was similarly hyper-tracked: he entered grade school at 7 and graduated at 16 (he grew up in the Philippines, but as part of the expat Filipino-Chinese community, and went to Chinese schools). When my dad tried similarly hyper-tracking me academically (suburban Boston), I got beat up, physically, by my peers…

> I got beat up, physically, by my peers This is a problem. Regardless of whether hyper-tracking is beneficial, no kid should have to suffer from this kind of bullying. I don't know why bullying in the U.S. is (or seems to be) so much worse than other countries.

Teachers in American schools are usually shit-scared of their students, which is the exact opposite of how things are in Russia, China, or even India.

There are many reasons. Parents and students wield too much power in the American school system, and the idea of tying a school's funding to local property taxes makes this worse.

In addition, America lacks the cultural norms of respect and deference for education and educators that are present in more traditional societies like India or China.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#302
post #276

I can only assume but culture makes things very different. I often said that French abstract algebra books stopped me from learning for 10 years (after many serious attempts). One book from Garreth Williams unlocked 80% of my issues. The shocking part was the approach. It was very operational, you calculate, you manipulate concrete data. In French books it's all theorems and concepts. Learning curve to make a Haskell…

Bourbaki school of thought. Read Dieudonné - not a single( I think to remember) illustration. Kindergarten starts math education with set theory. This was the imaginated ideal.

Not a bad idea at all. You can have a separate class called “Arithmetic” and that can be used to learn arguably the most boring application of mathematics: operations on numbers. Maybe distinguishing mathematics from arithmetic will make people hate the subject less. Set theory alone you can get to continuum hypothesis. I’m sure children would find the idea that some infinite sets are bigger than other infinite sets quite fascinating.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#303
post #80

Disclaimer: I graduated from one of the top math high schools in Moscow in early 90s, I have MS in Math from Moscow State University, and a half finished PhD from the same place. I think on average the difference between a high school student from Russia and US is negligible. Either country doesn’t really require much to finish school and many kids just do the tests without understanding what is going on. What separa…

> I think on average the difference between a high school student from Russia and US is negligible I went to high school in Russia and then moved to Australia. The difference was immense. It felt like i just dropped 2 year levels. Even the accelerated programs were hopelessly behind the regular curriculum for my age group in Russia. AU/US high school students can't possibly compete against RU or CN high school studen…

There were other kinds of "anti" things in the USSR, like antisemitism. I think the whole of the Eastern block had a tendency to be better at mathematics since you only need your own mind and maybe a textbook and a mentor. South Africa was heading towards a very strong mathematics school and then this same kind of phenomenon whereby you discount mathematics starting happening.

Edit: I mean that in the Eastern block you were better off in mathematics than in things like physics and chemistry. This holds for countries with historically diverging cultures from the Russians too (like Poland and Hungary).

Edit 2: I think perhaps it is also worth mentioning that you have "hardcore" on the one side and then pure artistic poetry on the other side. I've heard that French mathematics is a pleasure to read as it is both hardcore mathematics and well written prose. Some of the limitations on the Russian texts was also imposed by other restrictions: For example, the articles often had to be shorter than the authors would have wanted.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#304
post #80

Disclaimer: I graduated from one of the top math high schools in Moscow in early 90s, I have MS in Math from Moscow State University, and a half finished PhD from the same place. I think on average the difference between a high school student from Russia and US is negligible. Either country doesn’t really require much to finish school and many kids just do the tests without understanding what is going on. What separa…

> I think on average the difference between a high school student from Russia and US is negligible I went to high school in Russia and then moved to Australia. The difference was immense. It felt like i just dropped 2 year levels. Even the accelerated programs were hopelessly behind the regular curriculum for my age group in Russia. AU/US high school students can't possibly compete against RU or CN high school studen…

FYI: Big Bang Theory is banned in China

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#305
post #260

Earlier quoted context omitted.

My maths teacher made me prove that, my first proof by induction. Try it. You know you want to procrastinate with a nice proof by induction now.

Induction seems like an odd way to prove this. Do you need to preform induction over all the numbers that are not multiples of three? The converse claim (every multiple of 3 has a digit sum that is a multiple of 3) is a more natural one for induction, though that's not the most standard proof there either.

If induction is the only tool you have then it’s ok. What you really want is modular arithmetic. If you don’t have modular arithmetic then pricing it directly is hard:

  n = Sum(d_k 10^k)
  Let S = sum of digits = Sum(d_k)
  n - S = Sum(d_k (10^k - 1))
  But (10^k - 1) = ((9 + 1)^k - 1) = ((1 + k*9 + (2 choose k)*9^2 + ... + 9^k) - 1)
  by binomial expansion so is divisible by 9.
  Therefore n - S is divisible by 9, so n is divisible by 9 iff S is.
  The same is true when you replace divisibility by 9 with divisibility by 3.
I remember being asked this in an interview for a place at university and I solved it by induction (which was all I had) and was then shown this direct proof.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#306
post #23

speaking from personal experience, the math I learned up to grade 4 in the Soviet Union was enough to glide through all of American high school math. And I wasn't in any way an advanced math student in the USSR. And I dont seem to recall any extensive, South Korean style homework.

You are probably really gifted. I don't think this is a typical experience, that a fourth grader in any country who doesn't do much homework knows most of US high school math.

In my Soviet school, we went up to Grade 10 US high school math and I have a clear memory when my old knowledge stopped and I had to actually learn. Up to that point it really did feel like just redoing old classes again.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#307
post #80

Disclaimer: I graduated from one of the top math high schools in Moscow in early 90s, I have MS in Math from Moscow State University, and a half finished PhD from the same place. I think on average the difference between a high school student from Russia and US is negligible. Either country doesn’t really require much to finish school and many kids just do the tests without understanding what is going on. What separa…

> I think on average the difference between a high school student from Russia and US is negligible I went to high school in Russia and then moved to Australia. The difference was immense. It felt like i just dropped 2 year levels. Even the accelerated programs were hopelessly behind the regular curriculum for my age group in Russia. AU/US high school students can't possibly compete against RU or CN high school studen…

> One of the major factors is this weird anti-intellectualism culture that just doesn't exist in Russia.

It was the same thing in Romania, at least in the '90s, when I went to school/high-school. It was always strange to me seeing all those American movies of the "nerds"/geeks getting persecuted by the "cool" kids, it certainly didn't happen to kids in my school and I'm pretty sure it generally didn't happen to kids generally around the country.

I know because I was a "nerd" guy but I also played sports and actively enjoyed doing that, was never made fun of by my high-school colleagues because of me studying/getting high grades, that would have been pretty awkward to hear.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#308
post #166

Earlier quoted context omitted.

There are now , not so much 40 years ago. Even today, a lot of the STEM enrichment programs in the US have roots in the USSR. Hell, a big fraction of the physics problems I assign when tutoring these days were written by Russians in the 80s, because they're just that good.

That's the opposite of what I've seen in California. There used to be a big focus on tracking, gifted programs and "accelerated math", but it is now perceived as inequitable. Gifted programs were cancelled, tracks eliminated, and accelerated math discouraged (you can skip a year if you study outside school, but it is discouraged). The focus is getting everyone to some minimal level, and no attention on the high perfo…

> There used to be a big focus on tracking, gifted programs and "accelerated math", but it is now perceived as inequitable.

That is exactly right. The other people commenting to the contrary don't seem to know what they're talking about. Even in public schools it was common across the US until the late 1990s to have separate programs and classes (almost always referred to as "gifted" in some regard) for superior students. It wasn't viewed as unfair either, it was common and it was a point of pride to be in those classes, to be selected as a higher tier student.

Something changed in the last 20 years where treating students differently became considered unfair. The everybody gets a trophy syndrome took over.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#309
post #80

Disclaimer: I graduated from one of the top math high schools in Moscow in early 90s, I have MS in Math from Moscow State University, and a half finished PhD from the same place. I think on average the difference between a high school student from Russia and US is negligible. Either country doesn’t really require much to finish school and many kids just do the tests without understanding what is going on. What separa…

I'm from slovenia, a small, former yugoslav country. We don't have special schools for math here, and elementary schools (7-15yo in my time) were the same for all, and you went to the closest school to your home... but our highschool ("gymnasiums" - 15-19) used the grades from elementary school + standardized testing scores to rank students, and somehow best students went to certain schools, 'the middle' got accepted…

We had that at my American high school. It’s called honors and AP classes. There are event “magnet“ high schools, or high schools dedicated to top artistic talent. They just aren’t uniformly available.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#310
I grew up in a former eastern block country.

There are many reasons for this:

In USSR and other communist countries, there was a pressure towards having more scientists, engineers and highly trained specialists. To achieve this, they had to foster excellence.

US educational system is optimized for inclusion, diversity and money making. This means technical and scientific subjects are watered down so nobody is left behind. USSR and eastern block educational systems were built to cater to the most gifted students and produce scientific excellence. That is also true for some parts of Europe today, China, India and South Korea and maybe some other asian countries.

There was also a lack of distractions so it was easier for the kids in schools and students in universities to concentrate on learning.

In general, kids were expected to do a lot of homework each day and during vacations - I remember doing tens of math exercises each day and hundreds in vacation.

There were special classes in high school for more talented kids - where they got to do more math, physics, chemistry than their peers. Those classes had the best teachers.

Best kids at math or other sciences had supplementary training, they stayed after hours and learned more advanced concepts often with University teachers.

The school books in secondary schools and high schools weren't authored by educators but by best scientist in their fields. Learning programs were unique and developed also by the best in their fields, not by educators.

Teachers followed very rigorous training in universities, so they were actually skilled in the field they taught.

Everything builds over notions taught in previous years. There's no shortcut, no constant remembering of elementary notions.

Everything was taught with proofs, in a logical manner. There was no "magic". No teacher said "this thing works this way, you have to trust me on this". Instead, all things were proofed and the students had to learn all the "whys" along with the "hows". If you were a high school student and forgot one more advanced integration or derivation formula, there's no problem in deducting it from more basic theory.

One could enroll in a technical Faculty at University only after a series of very difficult exams. Sometimes you had to fight with 30 - 40 others for a place.

Once students reached higher education, the mediocre were weed out, leaving University teacher concetrating on teaching most advanced concepts to the kind of people whou could grasp them and were interested.

Since any kind of education was free, and in many cases state provided free food and housing and many scholarship for many university students and some high school students, the state wanted to otimized their returns. That meant getting the most highly trained specialists they could for the resources they used in education.

Students were also motivated to learn, because a job as a scientist or engineer was deemed a much better career than working long shifts in cold factories.

To conclude: the communist regime had to compete with the West somehow, and in that competition they had to make learning a very competitive space.

US educational system lives from the money payd by students, or by funding based on the number of students, so on one hand it has to attract more and more students so it earns more money. US educational system is more and more impacted by ideology, and scientific education is more and more watered down, even at the best universities.[1]

For now, that impact on education is solved by bringing lots of people educated elsewhere. It will probably work this way as long as US has better standard of living. I think it is not a safe bet to rely in the long term, and since standard of living will constantly improve in other countries, US has to better its scientific and technical education, not worsen it.

[1] https://www.city-journal.org/html/how-identity-politics-harm...

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