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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)

#291

Earlier quoted context omitted.

By CRT are you referring to Critical Race Theory? I'm sceptical that its both that influential, or that any good faith reading of CRT supports sacrificing accelerated programs. In particular CRT in education if anything pushes against reliance on standardized testing scores.

Yes, that’s what I meant (and I for intersectionality). Agreed that CRT/I would oppose standardized tests, but that’s only because CRT/I at its core opposes anything objective. And the philosophy of CRT/I has already made significant inroads in American culture. Witness all the accelerated programs that have been shut down, the many recent attacks on objective standards—all in the name of “equity” (which does not mea…

The thing is, if you accept the basic "liberal arts" idea of education that it's about creating a common culture, then a lot of the ideas coming from the social justice side of things actually make some sense. From the "liberal" point of view, one of the purposes of English lit class and education in general is to create a common background that people in professional settings can use in conversation - I can use my favourite Shakespearean metaphor to argue a point and I know that you, as an educated colleague, will understand what I mean. I could talk about CRT/I and say "something wicked this way comes" if I wanted to, and you could hopefully decode that. Otherwise I'd have the Herculean task of having to keep a database of which of my colleagues understand which kinds of analogies, or reduce all my communication to the lowest common denominator. For example, I'm assuming here that the expressions "Herculean" and "lowest common denominator" (as a figure of speech) mean something to readers on HN.

If you accept this point of view - and lots of educators past and present have done so, including white male ones - then the student slogan "Why is my curriculum white?" makes sense. Would a stock of common background knowledge (for want of a better word) be that much less effective if it included slightly less Hemingway and Twain and slightly more contributions from more diverse authors? So the argument goes, if (to simplofy a lot) white kids learn about white culture at home and black kids learn about black culture, but the test to get a good job includes the "culture fit" part of can we hold a conversation based on the kinds of analogies and forms of speech you learn at college, then it's (1) unfair if the thing you learn at college just happens to be "white culture" and (2) even more so if a more diverse college education would serve _exactly the same purpose_.

The million dollar question is whether (2) is true. I personally think it mostly is for "arts", mainly because there are different cultures with different languages even within "the west" and several of them seem to work about equally well.

But here's the rub: science doesn't work like that.

There's a philosophical argument that Twain _created_ Huck Finn, but Newton only _discovered_ the laws of motion - if Twain hadn't lived then we might have equally good literature, but it would not be the same. But if Newton hadn't lived, someone else would have discovered F=ma and the like by now, and the formula would be exactly the same.

My main worry is that if the US tries to turn science/tech into liberal arts and China doesn't, then we're creating a new kind of inequality: in a generation or two they will wipe the floor with us. But I'm happy to listen to any argument from the SJ/CRT/I side that doesn't imply us handing over our place in the world to a power who very much believes that all races are not equal.

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

#292
post #54

The linked article points to the fact that because the Soviets were resource-constrained, theory was more accessible than equipment which drove the education system to favor theoretical training. I wonder if there's a trade-off to this. On one hand you produce some really elite theoretical minds (Pontryagin, Lyapunov, Kolmogorov, etc.). But the counterfactual is that it excludes those with high IQ but are more practi…

Pontryagin is not simply an elite theoretical mind. On the contray, he illustrates in person the many aspects of the problem. During the fifties, he virtually vanished from public and came back years later with a Lenin prize and "The Mathematical Theory of Optimal Processes". Examples in there include 'two flying objects' and the task of an optimal solution for the problem to get them in close proximity... Obviously you don't receive a Lenin prize for pure mathematics.

The other part is content: Bellman dealt with the same problem. But Bellman equations are notoriously hardware-demanding. Pontryagin on the other hand gave necessary (and sufficient for some cases) conditions in a form much more accessible to pen and paper.

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

#293
post #271
post #115

Earlier quoted context omitted.

>University on the West gets its money directly from students so they motivated to attract and keep as many students as possible - so books are entry level to do not scare students. Barrier here is established from "paying user" side. I guess Western Europe isn't part of the West anymore.

In Denmark, universities (and possibly high schools too, I don't know for sure) get paid by the government based on the number of students passing exams every semester. I think this is part of what's called "new public management" where you attempt to bring market-like incentives to the public sector.

Attempting to force market-like incentives on the public sector often ends up working even worse than a purely public system, it seems to me. Use public or private, but mixing the two leads to odd incentive issues and bad outcomes.

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

#294
post #115

Earlier quoted context omitted.

>University on the West gets its money directly from students so they motivated to attract and keep as many students as possible - so books are entry level to do not scare students. Barrier here is established from "paying user" side. I guess Western Europe isn't part of the West anymore.

Yes, and actually Soviet/Russian education system has it roots in classic German one where Spießrutenlaufen ( https://en.wikipedia.org/wiki/Running_the_gauntlet ) was a great educational tool (see also: https://en.wikipedia.org/wiki/Birching#/media/File:Koerperst... ).

Rather than straw man the Prussian system you could iron man it.

Corporal punishment was common when the Prussian system was founded (1800s) across the world.

The system provided free education for the lowest rungs of society for the first time in Europe, that's a mighty achievement!

Pedagogically it is a hierarchical system with a strong focus on authority. It doesn't encourage questioning authority outside of the sciences which is a feature for the authoritarian societies deploying this educational model.

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

#295
post #88

Earlier quoted context omitted.

IMO, the point of textbooks is to educate people on some topic so making them as easy as possible seems like the correct choice. Outside of competitions, the value most people get from those courses is what them remember in 5+ years when their working not really the kind of symbol manipulation that makes can make things opaque. That said, soviet style education produced a lot of great mathematicians especially relati…

> point of textbooks is to educate people on some topic so making them as easy as possible seems like the correct choice It is not possible to “educate” someone about mathematics or math-heavy technical fields without convincing them to put in some serious time and effort thinking deeply about hard problems. Many US high school (and even undergraduate) textbooks are more or less analogous to taking a look-out-from-th…

I have actually learned an awful lot from assembling Ikea furniture. Some of those patterns make their way into my own little projects nowadays.

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

#296
post #289
post #276

Earlier quoted context omitted.

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.

> Kindergarten starts math education with set theory. Well what’s wrong with that?

Emphasis on 'theory', not 'set'.

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

#297
I still have my father’s MIR books and they seemed to me really practical and pragmatic.

Especially the Smirnov (iirc) ones about differential calculus, where he introduces it with a physics quantification problem.

You could then imagine objects moving around... etc.

Later on he introduces the formal definitions... informally (like “we discussed this and that, let’s call this concept and if you think about it if then “). It’s like a piece of literature or a correspondance.

Compared to that, Bourbakis feel like being lost in a desert without anything to drink nor eat but dry biscuits.

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

#298
post #239

Earlier quoted context omitted.

> And indeed 57 looks a bit prime for some psychological reason It tricked me, until I read the link.

No one taught me this in school, but if you add up the digits (5+7=12) and the result is divisible by 3, then so is the original number. It works recursively.

Yes, a simple consequence of e.g. 3-digit number being:

100x + 10y + z modulo 3

Removing 9y and 99x gives equivalence: x + y + z modulo 3

Now what’s left is induction with proper base (1-digit).

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

#299
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 o others, and shitty students went to shitty schools and other, non-general schools.

The biggest difference wasn't separating kids into math classes and language classes, but genrally separating them by "good" and "bad". Having a random mix of students, where some can barely read, and others read two books per week (or some can barely multiply, while others code math problems for fun), is a very hard job for the professor, because in the end, they have to lower their standards, expectations, and the quantity of material until most students scrape by. Having a group of students that are good at "school stuff", means the teachers are having very little problems with the basics and can continue faster and prepare students better for university and life. If we had separation for stem-talented students, and language-talented and *-talented, it would be even better.

So basically... group better students together, and you can do a lot more with them, if you don't have to pull the 'bad' students behind. I am aware that this is bad for 'bad' students, and that it should be fixable somehow (they should have options to move to better schools), but good students thrive without idiots in class.

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

#300

Earlier quoted context omitted.

Yeah please share the examples! What you write sounds plausible, but it also mirrors a lot of what we hear from the right that is at times overstated. I'd love to hear a set of sober examples- I don't have any connection to early education anymore and I'm really curious.

As someone that has been spending a lot of time around Higher Education over the past 7 years or so, I personally cannot think of a single University I have interacted that isn't making many of their decisions under the influence of the ideas described above. This is in the US/UK.

In the UK at least, the way I read the situation is that most of the Russell Group pays their bills off the fees they can charge international students - and compared to the income this gets us from China, other countries are a rounding error.

The problem is, these students are not coming here to learn how we're all equal, they're paying for a degree that proves they're very much not equal to about a billion people back home (compare the median wage in China with the cost of a one-year MSc in the UK for example).

That's also why most of our Covid-19 planning is around how do we deal with the income loss if 50% fewer international students enrol next year, the options seem to be government bailout or bust.

So there may be an unspoken rule in some places that you don't criticise the latest theories on diversity, but there's an even more unspoken rule that you don't publicly apply them to the situation in Tibet or Urumqi.

It will be extremely interesting to see how these two pressures interact over the coming decade.

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