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 separates Soviet Union (and now Russian) system is the practice of selecting kids with interest in mathematics / physics into special classes or schools for gifted kids. This government program feeds the mathematics and physics departments in the universities and allows kids who go through this program to get a very early start in mathematics. This is very similar to government sponsored sports programs with talented kids getting help with summer camps, or even all year round training schools.
> 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 students. The gap only begins closing around year 11/12, sometimes not until tertiary education.
One of the major factors is this weird anti-intellectualism culture that just doesn't exist in Russia. Doing well at your subjects in Russia put you in the cool group. Doing well at your subjects in AU got you labelled as a nerd. This permeates western culture across the board, hence domestically popular tv shows like Big Bang Theory which have 0 audience in countries that value intellect. I hear the culture of marginalising smart kids is somewhat changing lately though.
The other factor is that westerners really love to coddle and infantalise their children. A 12 year old in Russia is basically treated as a small adult with the associated respect and responsibilities. A 12 year old here is treated (and behaves) like a large baby.
Not the same, but I went from the Polish education system to a British university, and it also felt like it was a massive downgrade.
What really surprised me was the core principle at British unversities - "don't assume prior knowledge of anything". It basically meant that on a CS course, they teach you basic level maths, basic programming skills, you spend the entire 1st year of university learning what we learnt in school around age 15-16. A Polish university absolutely won't be teaching you basic algebra,statistics or core concepts of programing on a CS course - you are simply required to know these things, otherwise wtf are you doing on a CS course.
Also in general, I find the elective system of subjects in British schools to be.....poor. As in, I was(and am) surrounded by perfectly normal adults who are good in certain subjects(the ones they picked) and who have zero knowledge in others(the ones they didn't pick). I feel like my own Polish education has given me a very broad understanding of a lot of different subjects even if I wasn't personally interested in them. Like, even though I went to a school with a "maths and CS focus"(which just meant these two subjects had 2x the number of lessons each week), we still had lessons in history, physics, chemistry, biology, Polish literature.....all of it was mandatory, you couldn't just decide to skip it. At the time, I thought it was useless, but in hindsight I am very grateful for it because it has given me at least basic level of knowledge in many different subjects, whereas my British peers just can't even have a conversation about basic chemistry for instance, since they never took it as a subject.
> What really surprised me was the core principle at British unversities - "don't assume prior knowledge of anything".
The rationale is that you want to give 18 year olds the opportunity to pick a field of study that they're excited about now rather than forcing them to choose something based on what kind of education their parents thought proper for them six years ago. If a single "intro to programming" course and a slightly easier first math course can onboard smart students who otherwise would be hopelessly lost, and the only downside is that a couple of better-prepared students feel a bit bored, that's a small price to pay.
That is just an excuse. You could easily take an "intro to programming" before trying to get into the school. All it does is lower the bar of entry and you can only teach so much in the time given so it will ultimately take time away in the other end.
UC Berkeley (where I did my CS degree) follows this model after admission. There's CS61A, an introductory class for people with some math/computers background, and CS3, an introduction for people coming in with no background. Successful and interested CS3 students are then funnelled into CS61A.
Yes but minus the math; what math there was in 61A was easy. 61A didn't really expect much prerequisite either, but then it took off quickly. A lot of work but not intellectually very hard. It was then taught in Scheme which no one knew. Scheme is an elegant language which we never used again. SICP was the course text which no one ever read.
What I really remember was EE40 taking like a week to explain Ohm's Law. I thought, Ok, I think I've got this class. But then it just went exponential and then the prof just dumped a bunch of chapters on us at the end that he didn't cover and said that'll be on the final. EE40 covered about a third of 105. EE40 just had an insane amount of material and labs. FWIW, I think 16A+B covers better material than EE40 did although I have a soft spot in my heart for what was EE20.
BTW, Calculus 1A at Berkeley, if you didn't take AP Calculus in high school, was brutal. Pointlessly so, since most math in non-math courses was pretty straightforward.
But all the freshman courses at Berkeley were hard. You either got up to speed or you got out. Upper division was even harder, but you were prepared by then.
61A was easy in terms of math, but hard in terms of everything else. Every student I met who had never programmed before taking 61A found it intellectually quite challenging, both before and after the switch to Python; even without math, thinking in terms of computation and execution is not natural.
Given that second-hand experience, I found the excision of all of SICP's math from the curriculum to be quite a good choice, as adding advanced math as another prerequisite would have raised the barrier to entry even higher.
(Side note: your description of EE40 sounds like a professor who didn't schedule well, not intentional difficulty.)
(As you know) most of the lower div EECS courses inherit slide decks and the coverage is set by the department. CS70 has a wonderful set of notes which should be a book. I regularly go through the CS61C, CS152 and CS252 decks; those are great Berkeley classes. CS162 has a good set and then Kubi has his which even better. Hilfinger's CS61A notes were quite good. The deck the EE40 prof used was based on a previous semester and it was pretty good. It's just that the class is an insane amount of material and work.
There was an intent behind the work. All of the lower div classes are hard with a massive amount of content. But you can show up a Berkeley from a substandard high school on the wrong side of the tracks and blow it out of the water; a buddy of mine was like that and went to Columbia for his PhD. It's very simple. You just have to work. Immediately. Day one. I don't think Berkeley EECS rewards creativity. Indeed I think EECS punishes creativity. But EECS teaches its students to work their asses off, regardless of whether they came from Lick Wilmerding or Skyline.
Don't know if the workload was all that hard compared to, say, the experience of my MIT friends, but the level of intellectual rigor and methodical thought was high.
What's wrong with a low bar to tertiary education? It lets disadvantaged kids get in and catch up. As long as the standards are high by the end everything is fine right?
In practice, some see the fact many tech employers give coding tests to people with CS degrees as a sign the standards at the end aren't as consistently high as one might hope.
This is a stupid argument. Is one to suppose that the brain teasers that were popular in interviews 15 years ago implied that universities weren’t teaching people to be clever or something?
I think a lot of interviewing style is fashion driven.
Also computer science isn’t necessarily about actually coding anyway. It’s mostly about algorithms and structure and complexity. Similarly, anyone who knows anything about university mathematics courses does not expect fresh graduates to be particularly good at arithmetic
The difference is that programming is an essential craft. Algorithms are fundamental here, but it seems like teaching „structure and complexity“ equals to teaching paradigms that where en vogue a generation ago. This kind of knowledge is distracting, pretentious and even harmful.
On the other hand, I find it hard to imagine you can make a multiple year degree out of just programming. Hence why the best courses will have a mix of both practical and theory.
It works in practice as well. That is what junior college is all about. About a third of Berkeley graduates came from JCs. Transferring in at the JC level is competitive and hard and getting out is always hard.
I also studied CS on polish university and I feel we had the best of both worlds:
Initial programming courses were electives, where you could choose between more basic or more advanced "intro to programming" course. Basic had python, while advanced had c and c++.
Similarly logic classes were in basic and advanced groups and it was easy to choose the group you want and switch groups during course.
In fact, I was the guy who came for CS degree after never doing great at math or CS in high school and it reaaaaaally helped me to get up to speed with the others.
If those people who do not waste time are so smart why they have to be hold by the hand and given curriculum? (tuition fees you can count as means for getting a diploma, but also if someone is soo smart, why does he need a diploma anyway?)
What I imagine really smart person would do is: go to people giving the course for additional work or talk with them to show where they are at. Skip classes, read something else while in a class. Take advantage of knowledge to not care about the course curriculum and do his own research.
But that is my idea and maybe people who think their time is wasted could be a bit more humble and learn to work with other people.
In principle, yeah. Read something else in class -- better to just skip it then. It is not uncommon for people to skip lectures and just do the exam.
>If those people who do not waste time are so smart why they have to be hold by the hand and given curriculum?
There's a culture of "rules apply to everyone" and people are not used to asking for special treatment. So if you don't make it super obvious, people will assume they can't ask for adjustments. Also, no tuition so weaker incentive to get your money's worth.
> go to people giving the course for additional work
Always seems to be the solution. It doesn't scale, even if you know how to make a PCB or a cupboard (for example), it doesn't take 0 time. That extra work would be extra time spent, which is nonsense if the goal is to demonstrate competency and reduce wasting time.
Does not scale in what way? Exceptional people are rare, just as I wrote if someone is really exceptional he will blow through all this with no issues and minimal time. There is loads of people who just think are exceptional just like all those people on Instagram.
Does not scale in the way that the day has limited hours, extra work might be okay for a few courses, but not for more because you simply run out of time. There's also the issue that that extra work is given the same grade in the end, but you've spent more time. And no, knowledge doesn't make things take zero time.
Plus, the extra work is still about the same course material - instead of one hello world you write two. It's not hard, it becomes depressing and demoralizing.
In my experience, it's like being sabotaged. If one has a previous interest in the subject but is forced to complete all the same courses it gets very very tedious. Akin to being forced to fill middle school worksheets - you can do it, but it takes time and is just mind-numbing.
I think US universities are forced to cover things again due to a failure in the K-12 system of schooling that precedes it, and the lack of adequate testing to weed out ill prepared individuals.
In many countries, these kids would probably not get into college in the first place due to failing preparatory tests. In the US there are many financial incentives to pull in as many kids as possible and that may cause a lowering of barriers.
An observation in the maths, many countries in Asia cover calculus at the middle school level and continue into high school, in the US I noticed many public schools categorize calculus as an advanced (sometimes elective) high school subject.
The total amount of a study program is limited, if you spend a year on repeating the basic concepts, that's a huge part of your "learning time budget" that you're not not able to devote on learning more advanced topics.
Let's say lowering the bar has the result of making two courses absolutely useless for you, because you've already mastered everything there is to know about them. And let's say your typical bachelor's degree includes 30 or more courses. The time "taken away" from you is around 5%. Time that surely you could spend by studying for the other courses a little bit more diligently, by solving all the optional homework exercises, by going the extra mile for projects.
That said, if after your undergraduate degree you are unsatisfied by the amount of stuff you've learned thus far, there's an easy solution: continue on and pursue a master's degree.
In my opinion, British universities focus less on technical skills/knowledge, but more on research skills. Initiative is encouraged. You come out knowing more useful things, with experience in independent work/research, and with more confidence in yourself.
A Russian university would absolutely hammer you with technical knowledge (including in many irrelevant subjects), but when it comes to actually doing an independent research project plagiarism is rampant. As a student, you are belittled at every step. You are unlikely to get involved in any independent research, initiative is discouraged, you learn a lot of things that are not useful.
However, I agree with other posters that British universities bizarrely seem to often reward/celebrate athletics more than academic achievements. Somehow, the top of the social hierarchy are the kids that are good at team sports. In a Russian university, how you do at sports is for the most part irrelevant and if you are not involved in the sport yourself, you will likely never hear about someone's sporting achievements. That makes for a healthier social environment, I think.
> British universities bizarrely seem to often reward/celebrate athletics more than academic achievements.
I'm not sure how you get that impression.
American universities do this, but (with a couple of famous exceptions, like the traditional boat race between Oxford and Cambridge) British universities don't care about sport.
The social hierarchy was just separate, and had no bearing on anything academic. I didn't care for a second what the rugby team were doing (generally drinking themselves into a stupor), and they didn't care about me. That's just a reflection on British culture in general.
At Oxford, for instance, social life mostly happens at colleges. The way things are set up, you simply do not get to spend that much time with your course-mates - you do not interact with them during lectures, and then everyone goes back to their colleges.
And social life in colleges is (sadly) dominated by drinking at the college bar, drinking in clubs, and dinners in the dining hall, where everyone seems to sit according to some unofficial hierarchy (with being in the top sports team in a popular sport seemingly correlated with being near the top of that hierarchy). Inter-college and Oxford vs Cambridge competitions in all kinds of sports (but primarily rowing) are a massive part of college life. The university rewards athletes with awards of blues and half-blues, drawings on college walls celebrating sports victories, prominent mentions in college publications etc. Academics, on the other hand, are not given nearly as much attention - you would almost never know how good someone is doing in their studies, especially since they are probably studying a completely different subject to you.
It would be common to go and support your college sports team in, say, rowing; whereas nobody really cared so much about academic competition between colleges. Those academic victories were never really mentioned or celebrated.
I went to a mid-ranked UK university and while social life is definitely drinking and partying heavy, sports played basically no role in it at all, like not even a bit. I don't remember a single sports match even being advertised let alone having a major spectator turnout.
This is an American perspective but I think this could be an Anglo phenomenon so let me take a crack at it.
When I was brought up, the image of what a successful student was, was a very well rounded one. The perfect student was a diligent worker in all courses and always an athlete. Athletics was very very tied to the image of being a proper student because basically athletics = team and team = learning to work with others to overcome challenges and work towards a goal + being physically fit.
This is the gist of it, it's a bit hard to explain without living it. Also there is a religious aspect thrown in because America.
This was the image of the perfect young adult given to me by Boy Scouts and the image my private school friends were given by their schools. At my public school though everything was a bit watered down as we got far less development attention than private school kids would get.
For non-Americans reading: private school = good, public school = bad, in terms of education in the US(usually). I know this is flipped in some places.
> when I was brought up, the image of what a successful student was, was a very well rounded one.
I think this idea is dead, or close to it. Almost all the people I knew in college were there for a simple reason: to get a piece of paper that says they can now participate in the work force. Being educated was more of a side effect.
Plenty of people complain about gen eds or other requirements for degrees that are not explicitly related to the major.
> For non-Americans reading: private school = good, public school = bad,
This really depends on the university, the professors there, and the field. My school (USC, no, the other one) is #1 for international business, etc.
Athletics is extremely emphasized, though. I understand that colleges have to discriminate somehow to give people scholarships, and that sports make an insane amount of money for colleges, but it always struck me as odd that getting a full ride for being excellent at a sport is even a thing.
To me, that seems like an odd culture for universities to encourage/perpetuate, given that most top professors at top universities are unlikely to be particularly athletic, and the word "intellectual" is often used as almost an antonym of "athlete".
I do think it's worth adding, though, that from what I've heard (and given my own experiences), the culture in Oxford/Cambridge is not at all representative of University culture generally in British Universities.
True, yet they are some of the best universities not only in Britain, but in Europe and the world. So they are highly relevant in this discussion as we are talking about the top maths/physics education in each country for top students. E.g. when Russian universities/schools are mentioned here, it is usually Moscow State University or another top university or school that is assumed.
And in many ways, e.g. when it comes to drinking and partying, I would guess the culture in other British universities is even worse. In a top Russian university you simply would not have the time, and they would not hesitate to kick you out; graduating from university can be more difficult than getting into one.
The criticism, then, should be directed at Oxbridge, and not at [almost] all other British universities which don't do this.
I went to Imperial College. "Work hard, play hard" was some kind of motto. Most people followed the first part, the second part was optional. There was more "play" at weekends, and less during the week, compared with my friends at other universities. Mostly, it meant focussing on work during the week to leave time at the weekend.
I remember two mentions of sport: when a friend turned out to be on the hockey C team, and when the student newspaper announced that we'd lost some traditional cup [1]. You can see just how little attention was given to the game by the number of spectators [2].
(It would help the UK if the drinking age for beer and wine were reduced to 16. People can then get too drunk and do silly stuff with some oversight from their parents, and be a bit more mature about it at university. See Denmark for a similar Northern European country with this.)
The minimum purchasing/public drinking age is 18 (other than a single pint with a meal), but there's no practical restriction on parents letting their kids drink in private. My parents encouraged me once I was around 16 to join in with the adults whilst they had drinks. This led to me getting silly drunk a couple of times but with proper supervision. Same thing with going to some college house parties with 6th form friends - their parents knew that at the end of the night all the kids we're being picked up by their family.
The problem is if parents don't consider this and just ban drinking for kids up until they leave the house and aren't under their control any more. That's what causes people to go out of control at Uni since it might be literally their first experience with alcohol, or at least more than "1 glass with a meal" etc.
In MSU of early 00's most students drank a lot. I certainly did, mostly with other people from schools #2 and #57 already mentioned in this thread. But there was another company with a reputation of "real crazy drunkards". They were from another excellent high school, distinct from the Konstantinov lineage: the Kolmogorov's boarding school. Most of them left parents' house at age of 15.
My sister was at a private school in the UK and they were given drinks(a single glass of champagne) at certain events even before they turned 18, with permission from parents. Like you said, it's only illegal to buy alcohol under 18, but there's no problem with consumption itself.
I was given Buck's Fizz (Champagne and orange juice) when I was 5, at the birthday party of a super-posh boy who lived in the village. His grandfather didn't even ask my mum first. Upper class people apparently have different rules.
At Imperial, when the Google London office was new, the feedback from staff for why so few students hung around at their recruitment event was the lack of alcohol. Overturning this HQ-imposed very American policy apparently took significant effort.
In a top Russian university you simply would not have the time, and they would not hesitate to kick you out; graduating from university can be more difficult than getting into one.
Are you sure? I studied math in MSU in early 00's. Most of my coursemates drank a lot. I took some silly pride in drinking a lot and still learning enough to get good grades, but a lot of us just weren't bothered by getting worse grades. You had to be exceptionally and repeatedly bad at the exams to be kicked out.
It varies by course and college. My college had a relatively small number of maths students and would give a prize to the top performers each year. We all knew who got the prize and what grade everyone got. Some of my friends were top athletes in niche sports, but none of us really cared about the boat race, varsity rugby, or anything like that. Social life was centred much more around drinking than sport. I don't think our dining hall arrangement had anything to do with sports teams, official or otherwise.
Possibly relevant quote from Stephen Hawking, Brief Answers to the Big Questions (talking about the early '60s):
"The prevailing attitude at Oxford at that time was very anti-work. You were supposed to be brilliant without effort, or to accept your limitations and get a fourth-class degree. I took this as an invitation to do very little. I’m not proud of this, I’m just describing my attitude at the time, shared by most of my fellow students."
> What really surprised me was the core principle at British unversities - "don't assume prior knowledge of anything"...
I think it is a good thing. There is a big difference between doing well on a test and understanding the subject. You may think you know basic algebra because you can find the correct value for x, but chances are that you don't really know what you are doing. So having a refresher course telling you what you are actually doing when solving an equation, and how it fits in the big picture is valuable.
The thing is: when you relearn these basic subjects, you do it with a wider field of view. For example, when I first learned derivatives, I knew it had was about rate of change, and I knew the formulas, but I didn't quite get the relationship between slopes and derivatives. It came back later, as I was more familiar with things like linear interpolation and how to manipulate curves in general.
Yeah, I'm not saying that it's a bad thing, just that I was really surprised by it. In the entirety of my Polish education it was drilled into our heads that we had to be super good at algebra for example, because "no one at university will wait for you to learn, you have to know it before you start" - and then I went to a British uni, and well, people did wait for us to catch up, which lead to me having a very relaxed 1st year, while I know from my friends that at Polish unis the 1st year is actually the worst one as that's where a lot of people get kicked out for failing exams and there is a lot of catching up to do. In a British uni it was the opposite - I have no idea what you'd need to do to get kicked out of the course in 1st year, I've never heard about that happening to anyone, while in some Polish courses the attrition rate is above 50% in the first year.
UK universities generally have a low attrition rate (at least to failing exams). If you struggle with the subject you may wind up dropping out on your own due to stress, but if you stick with it you'll probably still technically get a degree, just a third or an 'ordinary' (which is basically a fail: I don't know many employers which will count it as a degree).
Also, the way mathematics is taught at high school might not prepare you well for the way you use it at university.
Maths in high school focuses more on applying methods (taking a derivative etc.); maths at university (even on a CS course) is more about constructing mathematical models and arguments.
It can almost feel like a completely different subject.
It is interesting that you say that because I had huge variations in my test results, dropping from top of my class to the bottom in an instant, then back to the average.
At one point I met a guy who was working on ways for computers to solve math problems. He told me that early college level problems are actually easier to solve than high school problems for his algorithms. The reason is that while college problems have more steps, and are therefore harder for students, you essentially just need to string theorems together. High school level problems are simpler (less steps) but require significantly more intuition.
And that's what I think happened with my grades: I was never good at math, but I had good intuition. And the switch from using intuition to using actual rigorous mathematical thinking killed me. It was like a completely different subject, and it took me years to catch up.
I wouldn't say if was it was different when it comes to applying methods vs constructing models.
I also moved from the Polish to British system and I do agree with your first point, but not really with the second one. I really welcomed the ability to focus more (but not only) on things I was more into.
A major difference for me was the approach to grading. In Poland, you might attempt to pass an exam until you do pass it. In Britain, you take an exam and you either pass or not. You can even pass the year if you fail an entire subject. Universities specifically want a certain % of people passing so they do doctor the numbers.
The most important thing is the end result. And here, I believe, the UK universities are better: they actually give you way more practical skills, while Polish unis give you more knowledge. If you want to be a scientist you might prefer #2, but for having a good job #1 is way better.
One thing Polish education teaches is how to remember 100 random facts in 2 days and forget them immediately after the exam. This really trains short-term memory, but I don't think it's worth training it for 8+4+5=17 years so much :)
Also it teaches you that if you don't cheat the system on the subjects that doesn't matter to you - you will have worse grades than people who have the common sense to focus on a few subjects and cheat on everything else.
I guess it instills some healthy scepticism and antisystem attitude, but it can't be good for society if everybody first instinct is "is that rule for real, or bullshit like most of them?"
I noticed this when comparing American vs British degrees that the British ones seemed much much more focused on a topic.
American 4 year degrees require you getting a reasonably well rounded education.
I have a 4 year degree in comp sci but I was required to learn state history, Biology, Chemistry, Geology, Art, Communications, and probably some other things off the top of my head that I've forgotten.
My issue with the US system is that the universities in general are pretty good, but before university the education is garbage. All of these "well rounded" things I just mentioned they could have easily taught me in high school instead of wasting so much time on random things or reteaching the same things over and over.
Essentially because of the cost of US uni they wasted my money making me have to pay for my well rounded education and now upon writing this I just realized that despite the downgrade so to speak I would prefer a British degree as I think theyre shorter and if I'm to pay I just want to get what I came for which is CS skills.
I believe British kids(non-Scottish ones) have to pay some amount for Uni right? Do you pay in Poland? This could be part of the reason for the difference.
Polish universities are completely free. And yes, British universities are not free, they have recently gotten pretty expensive(£9000/year), with the exception of Scottish ones which have different rules.
"Pretty expensive" is a relative term. For comparison, one year's cost of tuition at Boston University is $53,000, plus $16,000 housing, plus $1,000 for books and supplies.
Don't forget parking. My university realized they could charge upwards of $400/semester for a spot in one of the few garages. With all the housing being built now I imagine in a few years it'll be $600+.
I appreciate general knowledge and wide interest Polish shools can give you, especially after I worked with people from UK, and I noticed I knew more about their history than they did, despite graduating computer science :).
But one effect the Polish education system has is rampant cheating. It was expected (if officialy discouraged) that kids good at "hard sciences" will cheat on "humanities". Kids who were good at biology and wanted to become doctors were supposed to care about math and language less, etc. But they still had to have good average grades, so they were cheating on everything that wasn't on the entrance exams for medical schools (nowadays there's final exam at school instead of entrance exams at universities, but it changes nothing - there's still a few subjects you have to be good at and everything else you just have to have good grades in).
In effect adults are saying "this you should really know if you want to be X, and everything else you should somehow have good grades in, I don't care how".
So kids cheated on the subjects they weren't considering important for their future. I had wide interests and treated most subjects seriously but still I cheated on some geography tests because they were absurd - teacher expected us to remember top 5 exporters and importers of each of like 30 different resources and foods. And to remember how many tons of X each produced...
It was literally remembering tables of hundreds of numbers for 1 test and then forgetting them immediately. And that test was the same every year (data was from like 10 years ago :) ), and we had the test and the answers from the previous year. I'm sure the teacher knew it, but making a new one was too much hassle. It was basically an exerise in cheating the system and showing kids how absurd it is and how dumb you have to be to follow the rules.
And then there were subjects that were unimportant for everybody (no entrance exams depended on them), so even teachers teaching them expected everybody to cheat. And that was like 30% of all the subjects in high school - stuff like economy, plastic art, music, philosophy, religion, ethics, defense training, politics and society knowledge, even computer science (because computer science entrance exams were all about math, and computer science in high school was mostly microsoft office tutorial and playing games while teacher pretends to teach).
This culture of the top hard sciences students cheating & not caring about the required humanities classes happens in the US too, at least at top universities/colleges that are heavily focused on match/science.
It was definitely a thing where I went to college. The humanities classes were very easy compared to the engineering/science/math classes. The school required them to try and round people out. But the humanities teachers were lazy or unskilled enough that it became exceedingly easy for people to cheat.
The canonical example is the humanities teacher who gives the exact same tests every time he/she teaches the class for 20 years. After a couple years every fraternity & sorority had a file in their study room that had every assignment & test problem that professor ever gave. So you'd have one student from the fraternity/sorority who was low on the totem pole go to class to collect the homework/requirements. Everyone else would just look at the test files to get the answers and then show up for the tests. Generally everyone would get an A, including the students who never went to class except on test days.
This was partly evil, but it was also partly students prioritizing their work hours on the vastly harder courses they were taking in their fields of study, namely the courses that were important to doing well in their field.
I graduated with a 3.7, I didn't really cheat like this, but I did put lower priority on getting top marks in the humanities class. If I got a B in a humanities class in order to allow myself to spend more time on a Computer Science class so that I could get an A in the CS class instead of a B or C that was fine with me.
At the high school level in the US everything is bifurcated into a two tier system.. one tier for the serious students who want to do well and go to college. Another tier that is state sponsored baby sitting for the students who don't want to do well and whose parents don't care.
I went to a state university in the US, my science classes were pretty rigorous, with professors saying "you have 1 week to know everything up to Chapter 6, if you didn't get this in high school, tough".
In STEM curriculums, you have to choose an interdisciplinary science track, I chose Biology and Ecology because I thought it would be easier than Chemisty. It was much more complex than anything I was ever exposed to in High School and then spent 0 time on catching anyone up.
Yes. It is odd that in the British system at age 16 you can choose to study mathematics and physics and literally nothing else. (I blame this for my poor history knowledge.)
Well in the UK the subjects you select is very closely tied to which University you can go to. Some universities require maths and will not accept people who haven't done it (sometimes even more advanced maths is required).
Some universities don't require maths and so will teach it to everyone who's applied. Some don't require it but force you to take a year of it if you haven't done it. and others require it and reject you if you haven't done it.
I'm not sure what you mean by "never took it as a subject". In the UK you study Biologly, Chemistry and Physics up to and including year 11 (16 years old). I don't believe you can opt out of those, along with English and Mathematics.
I wouldn't be surprised, however, to hear that what we did learn in those years was behind a lot of Europe/USA.
Right,ok, I wasn't aware of that. I'm just basing this on the experience with my own sister, who went to a British school at the age of 15 and immediately picked only the few subjects that interested her and didn't have to do anything else. By age 18 when taking her A-levels the school actually limited her to only taking subjects where she had a high chance of getting a good grade as to not accidentally lower the average for the school. So in her final year at school she only had like 3 subjects, where I at the same point at a Polish school had like 10 subjects.
Normally, people choose around 10 GCSEs (taken in the school year they turn 16, the school year starts on 1 September). They choose 3-5 subjects for A level.
For GCSE, "minor" subjects can be abandoned -- I stopped studying art, "technology" (design/engineering) and German (since I continued with French). At A level, the majority of students focus on closely related subjects (e.g. maths and science), which I think is the weakness of this system.
Harry Potter has essentially the same system (GCSEs = OWLs, A levels = NEWTs), this isn't something J K Rowling invented.
It's unfortunate your sister couldn't study more subjects. Parents who knew the system might have been able to push the school to allow her to study more, but I can't find anything online where parents/students are grumbling about this. (Again, Harry Potter has the same situation -- Prof. Snape says he only takes the best students into his NEWT class.)
This was not my experience with university education in the uk. I studied mathematics and we had perhaps two lectures of recap of the “further maths” A-level. One reason is that not all schools could provide all of this course so it wasn’t a hard requirement; another reason was to introduce consistent notation that would be used in the rest of the degree.
Similarly in the uk mathematics curriculum there are a bunch of “applied” modules and schools choose which to teach. Some students would have only done mechanics and some only statistics, for example, so the corresponding university courses would have to start at what might be already known for some students.
Probably this depends on the university, what they look for in students, and more generally the strength of the students they do get. There are a lot of university students in the uk but obviously some will be stronger than others and the distribution varies by university.
One part of this doesn't make sense to me. Can only talk about German universities, and I started in 2003, but...
They will start with math you already know, but only in the first semester, so from October until Christmas, from then on everything is mostly new. But... to be eligible to study you kind of have to have had math on that level at school. with no exceptions.
But for anything programming related? In the late 90s/early 00s there was ZERO mandatory programming in school, and if you were really, really lucky if there was any graded course. We had some elective courses but they were not really awesome and only there because one teacher wanted to do them.
So, I'm also against rehashing stuff you should know, but if you can't know it from school, why wouldn't they start at the beginning?
That's precisely the case with British schools/universities too. I know now that programming has been added to the curriculum, so in years time these intro courses might no longer be necessary, but the opportunity for prior CS/programming education depended heavily on which school you went to and that's a massive red flag for trying to enable people from all backgrounds to be able to study.
> What really surprised me was the core principle at British unversities - "don't assume prior knowledge of anything".
My experience was that even if all of the students prior to university studied maths A-Levels, we all studied different topics. Before those two year A-Levels, we all studied different topics in GCSEs. There is so much time wasted giving everyone the same knowledge because of how our system is set up with different exam boards.
I don't know if this is the case in other countries.
You don't get to choose different maths A-levels in Russia. There is one state standard that every school and every student has to stick to. You can have accelerated or deeper "special schools" but you can't evade the state standard on maths or you won't get you high school diploma.
There is a state standard in England and Wales (and another standard in Scotland). It's called the National Curriculum, although I'm not sure if it has a different name for A-levels.
There are multiple implementations of that standard, in the form of exams that meet the standards. The government checks the exams satisfy their standards.
For example, an exam on history might by on the 20th century Britain, and a different one might use 19th century Europe.
Everyone in England also has to know logarithms and derivatives. There's much less flexibility for maths.
For history, the government requires that they:
• develop and extend their knowledge and understanding of specified key events, periods and societies in local, British, and wider world history; and of the wide diversity of human experience
• engage in historical enquiry to develop as independent learners and as critical and reflective thinkers
• develop the ability to ask relevant questions about the past, to investigate issues critically and to make valid historical claims by using a range of sources in their historical context
• develop an awareness of why people, events and developments have been accorded historical significance and how and why different interpretations have been constructed about them
• organise and communicate their historical knowledge and understanding in different ways and reach substantiated conclusions
The topics should be:
• from three eras: Medieval (500-1500), Early Modern (1450-1750) and Modern (1700-present day)
• on three time scales: short (depth study), medium (period study) and long (thematic study)
• on three geographical contexts: a locality (the historic environment); British; and European and / or wider world settings
and "British history must form a minimum of 40% of the assessed content over the full course."
Beyond that, it's up to the people making the exams.
I think this is great -- everyone should learn the techniques ("to investigate issues critically" etc) but the school, teacher and student have some flexibility in their learning. At university or in life, it hardly matters whether I focussed on Roman Britain or European WWII history to achieve this.
> There are multiple implementations of that standard, in the form of exams that meet the standards. The government checks the exams satisfy their standards.
In other countries, all students get the exact same exam.
Different exam boards is not the reason -- a single exam board can (and does) offer the flexibility of topic in areas the National Curriculum allows this, and sticks to what's prescribed elsewhere.
I think if you feel time is wasted for something like history, geography etc that people have uneven knowledge of, that's because they've failed to learn the techniques or fundamentals, and can only apply what they've learned to a single topic. There's little difference to everyone having to study WWII at GCSE, then only knowing what (not why) at A-level.
I'm not sure why the reason for superior performance matters. Genetics are just one tiny factor. Good parenting and nutrition are often more important.
> 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.
It even went further: in Romania, there was a popular movie in the 80s where the main plot is a high school student going to the math olympiad and his classmates cheering for him (with additional romantic threads of course).
Obviously all culture, and certainly mass culture in the Soviet bloc was controlled for "proper social message". I don't suppose Romania was more lax in respect to that?
A movie cheering for, or even trivializing anti-social behaviors would find it difficult to go past censorship (not to mention - to be conceived in the first place...)
It's for the same reason that you'd be hard-pressed to find a pre-1989 Central/Eastern European movie depicting any subcultures (like punks or hippies) sympathetically.
Yes, that's a good point, and it was a positive side-effect of Soviet times that intellectual pursuits were valued/supported, especially those that were "pure" enough (math, chess, etc.) to be harmless to the regime.
Based on my experience (Poland) bullying typically targets social ineptitude and sycophantism towards teachers, which tends to be somewhat correlated with good performance at school. But I've never really seen anyone being persecuted for good grades as such.
I wouldn't assume that's the case in American schools, though - not based on movies, at least. Could be just a convenient stereotype peddled by "college comedies", not a genre I'd take as valid social commentary
> But I've never really seen anyone being persecuted for good grades as such.
As someone who went through the US public education system in a lower-class neighborhood in the 2000s, I can't speak for wealthier neighborhoods [1], but people are definitely persecuted solely for their grades.
[1] One of the most interesting things about American culture is the dichotomy we have due to the large population and inequality (meaning there's ~no group overlap prior to college) - educational experiences had been so vastly different for many I met in college, and we were shocked at hearing the other side's experiences.
I don't know if it's a class thing so much as an aspiration thing. In my diverse community, which could be broadly characterized as "middle -class/upper middle class black, lower-middle class/middle class white," it was the people who put on airs who had the biggest problems with me getting higher marks than them. There was also a transition; when I was younger, I got the most guff from the ghetto-fabulous black kids and got along relatively well with the white kids. Starting in middle school and intensifying in high school, the black kids seemed to chill and the hostility and ostracization from the white kids grew. I attribute this to the changing social dynamics: while the black kids who weren't getting the best-of-the-best scores had already been tracked into standard classes and could read the writing on the wall in terms of how academia was going to treat them going forward, the mediocre, insecure, and would-be upwardly-mobile white kids were becoming aware of the precariousness of their situation. They'd been boosted beyond their natural ability by savvy parents and a system set up to do so. An aloof black kid waltzing into class and getting by with little effort was threatening. God forbid he learn to study.
There is also this often link-to essay by Paul Graham, called "revenge of the nerds" [1], that was also one of the reasons why I wrote about the situation in US high-schools (of which I have no direct experience).
In Romania in high school (Sf. Sava) being good at math and physics made you automatically very popular, everyone wanted to sit near you whenever you had written exams :) In any case, smart people were appreciated, there were no "nerds".
A Sava person in the wild :) My significant other went to Lazar and I wasn't aware of the rivalry between the two high-schools until I met her, I personally grew up in a small-to-medium town where these school rivalries were pretty much absent.
It's also sociologically interesting because Sava/Lazar/Vianu people (or, generally speaking, people who went to good Bucharest high-schools, it's probably the same for other big-ish Romanian cities like Cluj or Timisoara) are more "aware" of the high-school they went to and they generally tend to keep friends with their high-school colleagues for way longer (my so's boss went to Sava and he's still active friends with his former Sava colleagues 25+ years after finishing high-school). Like I said, we don't have that thing in small-ish cities.
I say it's interesting because I kind of noticed the same thing in this thread with people who went to prestigious schools in Moscow (#57, #2), they tend to remember fondly said schools and some of them kept closely in touch with their former colleagues.
I keep in touch with former colleagues from high school, nobody from college, if that tells anything. The problem is that all these people live abroad, I am the only one living in Romania.
There was no rivalry between Sava and Lazar 30 years ago, except for the Cismigiu park. They were in the top 5 schools in Bucharest, but there was no direct competition, they were all considered good places to study and kids used to choose based on the location and other preferences. Lazar had easier access to Cismigiu and lower admission grades, Sava was in a strange neighborhood but a nice, larger building, MF1 (Vianu) was smaller and harder to reach from some places, etc. They all had good teachers back then, no longer these days.
> Like I said, we don't have that thing in small-ish cities.
It's definitely a thing even in smaller cities with good highschools. Reunions for 10,20,30,40 years are very common and attended by all, including teachers still alive, etc.
We all have reunions, but I was saying that apart from them we don't keep that well in touch and we don't seem to show that 'esprit de corps' showed for example by OP (who mentioned his high-school) and by other people who went to prestigious high-schools from bigger cities.
Oh in small towns there is definitely some of that too, as in former classmates doing favors to each other, doing business together, as a miniature cartel running towns -- what I noticed to change in the past ~20years is that a good part of the elite left the country, so these local groups fell apart.
To add more color, the top few high schools in Bucharest at the time were all highly competitive, with low % admission rates. So the student body was naturally skewed towards more academically inclined students. In a sense, if you made it in you were more or less a "nerd" compared to the general population.
I was the nerd in my class and I was bullied at primary school in Poland in 90s, but that's because I had lots of pretty obvious sicknesses (asthma, skin allergies, half the time I was going to school with my arms bandaged, I wasn't participating in sports, etc.).
Being good at everything was actually cooler than being bad, especially if you were pretending you're naturally smart and didn't have to work to achieve that. I never understood how come kids in American TV are bullied for being smarter than the others, usually being smart is an advantage. On the other hand if you worked hard for grades or (even worse) were a favorite of some teacher and sucked up to her - you were a "kujon" and that was very uncool.
So everybody pretended they are brilliant and never study for even 10 minutes just know everything :)
It's not that way anymore. That's even "propagated" to movies (see the scene in 21 Jump Street where they go back to high school and unsuccessfully try to persecute smart kids).
But as an American someone in their mid-40s...can anecdotally say it was definitely true in the 80s-90s.
It's a senseless/strange phenomenon that definitely existed but seems to have naturally died off. Guessing it's related to the increasing amount of tech-billionaires during this time. In general in American society, people with money are considered "cool".
Idk. I graduated in the past decade. My school had a pretty expansive program of advanced classes and not advanced classes, which resulted in basically isolating the smart kids from the not so smart kids. Because of this, it was fine to be nerdy and smart. Yet in senior year there was an unexpected sort of social war when the not so smart kids wanted to control things like prom, and were unhappy when the rest of the school, who were never seen in their social circles, also had a voice. Got quite nasty. My area was relatively wealthy, and people probably had generally good lives. I think it would have been very unpleasant if it were a poor area with no separation of classes and more frequent trouble at home situations.
At the end of the day, if kids are struggling, they're going to feel frustrated. And they're going to take it out on the physically weakest kids and the ones who are most making them look bad by being good at school if they're not separated, protected, or somehow made mutually engaged (all of which are expensive things to implement). I don't think it has anything to do with anti intellectualism personally.
Would you mind linking to the 21 Jump Street scene? I'm very curious. As an American nerd in my late 30s, I definitely recall being relentlessly teased as a kid. I don't have kids of my own now and so I don't really know how and if things have changed, but if true this would be a very positive development!
Not sure I can link it but I can definitely describe it. To be clear I'm referring to the 2012 film not the original show. The scene though is sortof referencing the original series because if memory serves it was sortof how they would have done "high school undercover" in the 80s.
Basically the adult cops undercover as high school students try to make a first day impression and they sortof trash academics and try to intimidate kids interested in studying etc. So they try to be stereotypical 80s/90s popular kids. It spectacularly backfires and they have to change their approach. It's actually a surprisingly insightful scene in the context of this discussion.
All out kids are relentless teased by the popular ones. You have observer bias to what you were teased about, but if you look you will see many out groups teased about different things. You will often find kids in the in group not teased despite having the same characteristics.
But I think you are wrong on "nerd" thing. Which doesn't mean technical excellence or excellence on a particular subject. "Nerd" means being weird while somehow interested in some technical matters.
There were a lot of "cool" kids doing great at math, physics or programming.
According to Mirriam-Webster, a nerd is "an unstylish, unattractive, or socially inept person".
Yeah, didn't know how to best translate "tocilar" into English, I guess it's a combination between geek and nerd? Couldn't tell.
> an unstylish, unattractive, or socially inept person
I was definitely unstylish, that's for sure, and I was no Adonis, that was also certain, but the good thing is that back in the day that didn't matter, how you looked and dressed as a kid didn't matter. I only had 2 pairs of jeans for my 4 years of high-school because that was all my parents could afford to buy me back then, but to be honest I wasn't aware of that back then. I'm afraid nowadays things are completely opposite.
> 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.
In the United State there is an extreme anti-intellectual bias among conservative middle and lower class whites.
While I don't necessarily love the show, I've known many PHD students from China, Taiwan, and Korea that absolutely love the show. Hardly from countries that "don't value intellect".
"This permeates western culture across the board,"
I can't speak for Australia, but I went to high school in the US during the 90s. The 'cool' kids weren't necessarily anti-intellectual, they were just more social and were well versed in the ability to make friends. Most were in the top 10 in terms of grades at our school and I didn't go to a specialized or private school.
The 'nerds' and unpopular kids weren't necessarily smart either. Many had Aspergers or were on the autism spectrum, which means they most likely won't do well in social situations and most likely won't ever be popular.
Others were just anti-social or were just never taught how to make friends or be a friend.
Sheldon from the Big Bang Theory is supposed to depict someone like this.
It's easy to say we aren't popular because we are smarter than everyone else, but the actual reasons are much more nuanced.
"The other factor is that westerners really love to coddle and infantalise their children. A 12 year old in Russia is basically treated as a small adult with the associated respect and responsibilities. A 12 year old here is treated (and behaves) like a large baby."
I suppose this is just the result of living in a stable and safe country. 12 year olds aren't adults and shouldn't take on adult responsibilities. It's sad to me that there are children out there that can't actually be kids for awhile, which is something you can never get back as an adult.
Simplifying what the other person said, what is social status a function of? You say having friends and being popular is all about being able to make friends, which is only partially true. Social status is also a function of being good at what your peers consider important.
Anecdotally, and based on depictions in movies and TV, status for American kids is directly related to how well they do at sports. Doing well in your subjects and "trying" in class can either lead to ostracisation at worst or at best doesn't make a difference to your social status.
Whereas in other places, such as where I grew up, kids who tried hard and did well in their subjects had the highest social status. They were the "coolest", in the eyes of their peers. Rewards in status meant that such effort was positively reinforced.
You know how Hermione Granger is thought to be a know-it-all and insufferable? I could never understand that. Where I grew up she'd have been the most popular kid. Most other kids would have wished they could be more like her.
> It's shown in 180 countries worldwide and very popular internationally (Including Russia)
If you pick 10 random people in Russia and ask them about this show, all 10 will either not have heard of it or react with disdain. I have no idea where you get the notion that it's popular in Russia.
> It's easy to say we aren't popular because we are smarter than everyone else
I was popular in Russia. Then I had difficulty fitting in at the Australian school until I learned to act like an idiot and not reveal my 'nerdy' (a word that doesn't even have an equivalent in Russian) hobbies and interests outside of select circles. The same hobbies and interests that were perfectly average in Russia - electronics, astronomy, chess, that kind of thing. After that I fit in again. It's pretty hard to interpret this as some sort of social issues like you claim. I think you lack perspective on this. This is also the same culture that teaches teenage girls to act dumb in order to appear more attractive, which is pretty well studied at this point and will hopefully die now that it's in the public eye.
> It's sad to me that there are children out there that can't actually be kids for awhile
As one of the kids who would match your label, I think it's sad that children here are artificially held back from their natural maturation in order for the parents to selfishly extend the baby phase for their own enjoyment. Nor does this coddling have anything to do with stability. Plenty of stable countries across Europe where kids are allowed to grow at their natural pace, including several first-hand accounts in the comments section here. This is also why you'll find significantly lower age limits for things like consumption of alcohol, drugs, sexual activity in those same countries.
Coming back to the OP topic, soviet textbooks are 'hardcore' because the pupils are 2-4 years more mentally mature than their western counterparts due to cultural and education system differences. It's as simple as that.
> 'nerdy' (a word that doesn't even have an equivalent in Russian)
I wonder how many languages actually do have an equivalent. Maybe English is the only one?
When I translate something to Slovak, I also struggle with the word 'nerd'. We do not have a word for this concept. A close one is "bifľoš", which means a person who puts a lot of effort into memorizing school material, but it is implied that the person does not truly understand it. Another one is "kockáč", which means a math-oriented person. But we do not have a word that means: a weird person, because they actually study and understand something.
To me it seems that America is like "no child left behind", while Russia and Eastern Europe are like "if a child gets behind, wolves will eat them, who cares, at least it motivates others to run faster". :D
> If you pick 10 random people in Russia and ask them about this show, all 10 will either not have heard of it or react with disdain. I have no idea where you get the notion that it's popular in Russia.
And that's why it has 8.6 on Kinopoisk? I don't like it either, but imaginary statistic is not a statistic and your social circle is not the whole country.
> I learned to act like an idiot and not reveal my 'nerdy' (a word that doesn't even have an equivalent in Russian)
Of course it does have an equivalent, it's "задрот" if you're being mean or "ботан" you're old enough to actually have used that.
> 2 year olds aren't adults and shouldn't take on adult responsibilities.
While this is true, I think we often don't give kids enough credit either. Around that age they can be quite capable.
I think we've gone too far the other way and just don't push kids whatsoever, so now most 18 year olds are completely clueless as they head into college. This is compounded by USA's growing anti-intellectualism where we're proud to be bad at math, argue about having to study literature, and so on.
> It's shown in 180 countries worldwide and very popular internationally (Including Russia):
I can make this same argument about a Korean tv show called Running Man, which is indeed popular abroad... to niche audiences, like me. :-) I probably wouldn't argue with a Russian person about what shows are popular in their country, though.
I have not-so-fond memories of being bullied for being clever while growing up in the UK. I was placed in all the accelerated programmes and bumped up a year in some cases, which resulted in the odd situation where you were bullied for being a nerd, but also relied upon by the same bullies when they needed help with their tests.
I landed on my feet as a programmer, thankfully, but not until the depression set in and my performance in sixth form and university utterly plummetted. Impossible expectations, zero family support (never good enough and never doing the right thing _for them_).
Hearing stories about the different priorities in Russia and Latvia, from my various friends who came frmo there, made me feel quite envious, although I only heard the good parts of it (like learning multiple languages from a young age).
It's definitely not just the education system that's to blame (although the repeated hammering it takes from successive governments is an issue), there's definitely a wider cultural issue where it's almost cooler to be ignorant.
The USSR coasted its first half of existence milking Tsarist legacy of science and engineering, then the other half copying the intellectual fruits of supposedly dumb Western jocks.
Modern Russia isn't even half of that.
Precious little to show for all the cheek puffing and talent grooming.
Pre-1943 USSR was very much into violently rejecting anything Tsarist. Ioffe, Kapitsa and others survived only as pragmatic accessories to weapons and industrialization programmes.
Post-Stalin they had an opportunity to develop their schools of science but it's only so much a few, even dedicated, individuals can do. By 1990 these efforts largely fizzed out.
> Doing well at your subjects in AU got you labelled as a nerd.
As a Chinese student who studied in Australia for a few years I think you just misunderstand the culture.
Most of the popular kids got good grades and were not labelled as nerds. And the nerd kids didn’t really get good grades either.
I think Australians are very practical focused (maybe this is what you mean by anti-intellectual?).
For example the friends I know who wanted to do medicine and law - and are now successful doctors and lawyers - stopped focusing on maths at the end of grade 10.
This would put them way behind in math than an equivalent Chinese student who also wanted to be a doctor or lawyer but as far as I can tell it hasn’t had any negative impact on their careers.
Not being profound at statistics should be a strict no-go for anyone practicing medicine.
Many great discoveries come from linking different disciplines. I hope there is more to live than just a career. I am very grateful for the broad spectrum I've been given.
I need my doctor to have a basic understanding of statistics. I don't need them to have a profound knowledge of anything except their professional specialty.
Chances are they took a basic Epidemiology class -- or a class that had it as a component -- and covered "Stat for medical workers." And that should be enough.
I disagree. Accurate reasoning under uncertainty is highly non-trivial (as current events with covid-19 are making clear) and is I suspect one of the most important skills a clinician could have for making rational diagnoses and treatment decisions.
Whether currently available statistics training is even adequate to the task of teaching this skill is a separate question, the answer to which is unclear to me.
My family is from Serbia (my parents were both mathematics teachers in Serbia) and I was raised here in Australia. It's definitely true that the curriculum is many years behind even relatively poor and corrupt countries (like Serbia). As a toy example, my parents taught me how to solve simultaneous equations in year 4 (when they'd have taught it in Serbia) while everyone else had to wait until year 9 to learn it in school.
I had friends who came to Australia after starting their education in Singapore, and they were continually shocked how far behind we were. It's honestly gob-smacking how little is being done about this, we're doing a massive disservice to our young people which they will have to overcome for the rest of their lives.
> we're doing a massive disservice to our young people which they will have to overcome for the rest of their lives.
Is this actually the case? Much of the most useful science & software comes from people educated in the Americas and Western Europe. I think that non-western schooling methodologies under-value problem solving and overvalue "raw" knowledge.
One other thing that i have noticed, is that in "rich" countries, knowledge of trivial and basic stuff are celebrated in the name of "positive reinforcement". This gives students the false idea that they have "mastered" something while they have just started learning. IMO, this is extremely harmful to the student's psychology.
Can agree with similar comparison - when studying at the end of 90s on high school, one student from our central/eastern european class spent 1 year in US. After he came back, he'd tell us how in math they were several years behind for same age group (ie we were running derivations and integrals and they were more on end-of-secondary school level). He was average back home, stellar math student there.
Of course, case point 1, comparing 'gymnasium' (more theoretical study-focused high school instead of say practical crafts, good preparation for university) with some US public high school.
Schools back home have gone 'softer' on students since we studied (don't all complain at some point about that?), so maybe now its more comparable.
The thing is, hardcore math skills apparently don't have that high impact on overall functioning economy. More open society, freedom to pursue ones dreams, freedom to try your own business idea (and fail hard if stars don't align) make overall a better functioning economy.
My (slightly more recent) US high school experience had nearly all students cover the calculus you described by the end of high school, and about 1/5 of the students got fast-tracked to the point that they studied linear algebra and multivariable calc by the end of high school.
I talked to a couple of friends about this, and about 1/2 had similar course offerings.
Your last paragraph makes a valid point. The question then is whether when the schools became “softer”, they replaced the math and sciences curiculums with something else (politics, economy, governance) or whether the kids themselves started doing something more meaningful. If not, it sounds like a wasted opportunity
Anecdotally, a I know some people that grew up in Europe and then went to America/American schools and they did way better there because it was way easier. I also remember something on 60 minutes a long time ago where they had some some Dutch students take some advanced American test and the lowest score in a test not their native language the lowest score was like 92 I think...
> 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.
I know nothing about your history, but usually moving to a new country means you are now an immigrant and by definition have less privilege than before, even if you can't immediately notice it.
Another hypothesis is that you left an elitist good school in russia and joined a not-so elite school in Australia. You could have done the same in Russia just by moving to a slightly cheaper neighborhood. Confirming the parent poster you were replying to.
Absolutely. There are plenty places in Russia where you totally going to be bullied for academic performance. Also the plagiarism/cheat culture is rampant throughout the country, from elementary and up to postgrad.
> AU/US high school students can't possibly compete against RU or CN high school students.
Can anyone comment on how this translates into results in adulthood, in the current age?
Do we see more discoveries in fundamental science, more inventions, better medical care, or better-run businesses?
As I don't speak Russian or Chinese, I don't really have a fair view and it would be easy for me to mistakenly under-estimate what the graduates of these schools get up to.
There's also something else. The best and brightest from these countries are rarely (if ever) retained in their homelands and end up migrating to one of the western nations.
Ultimately, regardless of how the high school education level might be, these countries win out.
Pretty much my experience as well moving from Russia to the US. Team sports and social deviance seem to dominate the popularity hierarchies of American schools (as of 2003). In Russia being the top student is respected instead.
US has American Football, jocks, and cheerleaders. This is something notably absent elsewhere. When you watch a hollywood high school move, this strange obsession jumps at you. In Poland the word "nerd" is difficult to translate. It has no direct equivalent.
Don't mix up movies and reality. They are often based in reality, but movies exist for entertainment and that often means exaggeration of the truth for effect.
But there is an insidious mental effect on students growing up in such an environment unable to discriminate between the two. They learn not to value "knowledge" and "learning".
While there is no direct equivalent, kujon seem to be pretty similar. (For non-Polish people, kujon is a derogative term for someone having good grades, coming with a stereotype that such person spends all their time learning, not doing any fun stuff)
kujon is probably the closest, but it means a person who gets good grades because he works on them very hard, especially by rote memorization and repeating. His method to learn anything is brute force. You never call someone who asks great questions a 'kujon'.
Nerd is different in that it's more about interests. If you're interested in any kind of science, biology, history, literature you're a nerd. Anime nerd is also a valid combination but it wouldn't work for 'kujon' because there's no repetition.
In Russia it used to be pretty common to see chess players in a park or train. Books readers were also more common in public spaces than in Poland. Russia has many problems for sure, but it has certain respect for intellectuals, composers etc.
Level of school while it is supposed to be same is night and day. The special Math/Physics school is one thing, but under that there are “good” schools in the city, ok, shitty then you have countryside etc
Same thing applies to other countries. Depending on where you went to school in same city you experience can be vastly different. Some school in let’s say Toronto have A- Math in high school average, other 20mins by bicycle can be C-. In Moscow you can have an awesome school, take metro for 30 mins and only thing you are learning is how to not get shit beaten out of you during a class break.
I went to a very good city school in Kyiv till grade 8, then specialized Math/Physics school from then on(I was bottom of the barrel at the new school in Math ouch). I used to come to my old school sometimes to hangout, level was absolutely different as in nobody there could solve a single problem in my home work. University exam at KGU in physics I took 1 hours instead of 3. But this is a trick. Once you get in second round of weeding out starts, I remember the breakdown people had after first couple tests. People who had 5 on all subjects their whole life, but they went to normal school. I think more then half of them did not make it through first semester.
I then left to Canada and went to middle of the road University there for Comp Sci. Honestly I liked it far more. It was more fun and flexible in terms of what you could take and learn, I could do a minor in Economics half way through because I liked it. I could work as research assistant in later and actually get my name on a paper and then go to a conference in Vegas :)
One thing I noticed in the US is that there seems to be many wasted years in mathematics education. Between learning long division (maybe 4th grade ?) and algebra which I didn't get until the first year in high school (9th grade) I don't think I really learned or was taught anything of significance.
EDIT: My recollection is poor, long division and the associated concepts like fractions and decimals may have been later and spread out over more years, but I'm sure there were at least 2 to 3 wasted years in my mathematics education.
You are confusing American media with American culture. In American movies of the past the smart "nerds" were bullied. In reality, at least in my experience as someone who was bullied a decent bit, this is actually conflating two separate, but overlapping, groups. This isn't surprising since most foreigners understanding of our culture comes from our media.
In my experience (left high school in the early 2000s), the kids who were bullied were the kids regarded as "weird", smart kids were mostly left alone or blended into popular groups. The "weird" kids were mostly kids with obvious issue. Social maladjustment, visible poverty, autism spectrum disorders, or just being unkempt. There is some overlap here with smart kids, largely due to autism.
The reason this narrative exists is that a lot of the children with issues told themselves they were bullied because they were smarter than everyone else, even though that wasn't the reality. I don't know if this was them internalizing the hollywood stereotype, or hollywood playing to an existing narrative. It's perhaps more tragic that kids who were already at a disadvantage were the ones who were bullied, but it makes more sense and is the actual reality as I experienced it.
Anti-intellectualism isn’t the same thing as anti-nerdism. People respect originality and innovation, but who really is going to respect those who shut themselves away to cram their heads with facts, to please their teachers and get good grades, when they could be out having fun and mixing with their peers. And for what? A higher salary band? Four star hotels during summer vacation rather than three star?
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.
In my family some – during their high school years – managed to move from Eastern Germany (GDR) to Western Germany (FRG): They unanimously state the same thing as you did.
My speculation: This hasn't anything to do with the "eastern-ness" of a countries culture – but rather the ROI for education / medicine, which looks quite different under a communist economy, under which so many other endeavours scale so much worse.
>but rather the ROI for education / medicine, which looks quite different under a communist economy, under which so many other endeavours scale so much worse.
Great point! I might add that this is also true of many "third world" countries even without Communism.
In Australia, a few of the top private schools as well as government schools in demographic areas with a high Chinese student population do have an intellectual culture.
A few of my family members are teachers (in both private and government schools) and from what I hear there is not yet much of a shift away from the anti-intellectual culture.
> Doing well at your subjects in Russia put you in the cool group. Doing well at your subjects in AU got you labelled as a nerd.
Seems a bit exaggerated to me. At my high school (in the US) the cool kids were just the more socially outgoing kids. Some of them had great grades and others not so much. It was the same in the 'nerds' group.
From my experience academic achievement didn't really have any bearing at all on the social group you fell into.
But I guess experiences will vary....there are pretty huge differences in public school quality across the US and even within one local school district.
The Russians have it wrong. Their model of government and socializing obviously failed the process of economic selection. Kids are not coddled here and they grow up just fine. I would pit American Scientists against Russian Scientists any day of the week. The same with your Average American Adult vs Average Russian Adult.
There is a big difference between high schools in different ares in both Russia and US. I don't think you will argue that a person from a country school in the middle of nowhere in Russia with one teacher for all subjects will be able to do better in a top-level school in NYC.
On the anti-intellectualism and bullying of nerds, how do we fix this? (I'm American.) I'm not a parent myself, but my brothers and sister are. Should I suggest to them that they home-school their kids to shield them from this toxic culture?
I think it's changing quickly. Not sure if you remember the movie 22 Jump Street? The old guys show up at a high school to be "undercover" high school students and it turns out that the "cool" kids are who used to be the nerds. They are vegan, don't make fun of gay kids, stand up to bullies...and wear backpacks with two straps (lol).
I think that image of high school has some truth to it, as I graduated high school a couple years before the movie came out and it was already beginning to change. Kids playing pokemon at lunch were the same kids on the varsity sports teams. It was okay to like video games, and to be upset about getting a C on a test. The image of bullies as "cool kids" was changing to "kids whose parents probably never told them they love them" - and everybody knew it. The cool kids are nice now. Not totally sure if the shift has continued in the last 7 years, but it is definitely happening.
I always had the impression that Russians are more serious. Also Americans have developed tons of expressions for every nuance of greasing the wheels for business and relationships. Russians are more straightforward.
So it is with the kids. I don’t think there was a lot of “participation trophies” and idea that “you’re a winner just for trying”. It was realistic. Women in Russia are told to look beautiful by their mothers, for example, and they are expected wear makeup and heels just going out to the store or to work. Imagine a US mother saying that.
STEM in Russia and China’s schools is wayyy more advanced than USA.
Not just in Moscow but every city center in every former Soviet republic. It’s one of the things the Communists really instilled early on after taking over backwaters (at the time) like Uzbekistan (along with equal rights for women, 95% literacy and electricity). Compare that to pre-revolutionary Cuba or Hawaii, for instance, that USA took over.
I think right around Sputnik time and the cold war, the US had a major STEM crisis and started trying to teach math more. But really, most of our brightest students are just imported - and they’re happy to come.
Gonna drop this one in there, from Dr Kaku, on a panel discussing this exact question:
> Doing well at your subjects in AU got you labelled as a nerd.
As an Australian nerd who got higher than average grades, it's not accurate in the slightest to generalize your experiences to my entire country and I haven't seen the anti-intellectualism you claim is there.
When I was in high school I was very much a nerd. Good grades, tried to win the approval of teachers, head in a book, never played sports, interested in chess and video games.
I definitely did not fit in. Making friends was difficult, I was teased and all the things I gather you had issues with.
However I also had a close friend who despite sharing my interests and grades, was also much more outgoing, participated in sports and was generally well-liked. He had no troubles at all fitting in.
To strengthen the counter-example even more, in grade 9, all of the highest academic achievers got put in the same class. These people did not have issues.
So intelligence clearly wasn't the problem. What I think the problem was is that I was quiet, shunned sports, kept to myself and occasionally saw my brains as making me better than other people. That's what led to the ostracizm that might be misinterpreted as anti-intellectualism.
Also, all traces of this were well and truly gone by years 11 and 12. At this point everyone is doing what they can to get into their chosen university so they can't criticize you for doing the same.
> A 12 year old in Russia is basically treated as a small adult with the associated respect and responsibilities. A 12 year old here is treated (and behaves) like a large baby.
I'm married to a Russian and my mother in law is a high school English teacher in Russia. I think you're very much overgeneralizing in these cases too.
Perhaps in some cities and families 12 year-olds are expected to behave the way you claim but it's definitely not universal. There are plenty of 12 year-olds who are allowed to be children in Russia.
> > Even the accelerated programs were hopelessly behind the regular curriculum for my age group in Russia.
Which curriculum? They vary by state. I believe the curriculum for maths and sciences in Victoria (my state) was very similar to the International Baccalaureate (I compared topics with students in that program).
If you want to point at an area in which Russia is significantly different, I'd point at the arts. In Russia children are expected to study and learn poetry and read literature from a very early age all the way through high school. It's not at all frowned upon. Boys choosing to learn "feminine" things like ballroom dancing also seems to be well accepted from what I've seen.
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.
This is one school of education. The other is the Finnish model, with no separation. I am yet to see some comprehensive multinational study that would suggest which is better. (Better for the students, or society as a whole?) It’s probably impossible to do objectively. I also feel there is probably quite a difference between these two systems in the effects on the, say, top 0.2%, 2%, and 20% of the students.
Seems to me that the Finnish model is better for an average student (guessing by their PISA test results) and worse for a talented student (guessing by their math olympiad results).
Anecdotally, a Finnish friend told me that if you excel at one subject, you are encouraged by teachers to stop doing it, and instead spend more time learning the other subjects.
I spent 6 years in one of those highly selective schools, and I have mixed feelings about this.
One problem is that Small-fish-in-big-pond-effect, a good chunk of us realized there that we weren't special anymore, there wasn't the honor and praise for being top- and consequently that drive was lost.
Plus, once some schools become well established and start to attract highly talented kids- kind of kids who can do well by themselves without much external help, the school itself, I mean teachers and administrators, doesn't have to be very good. Their success starts to depend more on their ability to attract talent, and less on actually nurturing and developing them. Past success bring more success- a sort of virtuous cycle.
I dont know about the second part... but i'm sure glad I didn't jave illiterate trouble-causers in my class (as i did in elementary school (7-15yo)).
One such disrupter can take away easilly 10 minutes of a class hour, and 1/3 of the class not understanding basics, means the teacher has to try again and again to teach them the things they should already know, while the rest of tle class stagnates.
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.
In the early 90s, I lived in a US apartment complex and went to schools with a lot of recent Russian migrants.
Three times a week all the Russian kids were rounded up for "Russian Math," taught by, Arkady... my friend Mike's Dad. They followed the Russian/Soviet curriculum, which was 2-3 years ahead of the school's.
I think we focus a lot of educational systems, because these are matters of policy which can be critiqued and maybe changed. But, I think culture plays a big role.
My mother has PHD in physics, so its not like I'm from an anti-math culture. But, the Russian take was a different level. Being mathematical was very important to them, and they made it happen.
A good example for this is language learning. In some schools/places/countries/communities, language learning is culturally important and culturally supported. In those places schooling works, and kids graduate with strong language abilities. In other places, it isn't, and kids generally don't progress regardless of what classes they are in.
Europe is like a lab for this. Most Dutch kids graduate with native-level english, and often a 3rd and 4th language. In Italy, kids have almost no english. Modern young-people Dutch borrows a lot of English. They watch English TV. English is part of the culture, so the schooling works.
I moved from post-Soviet Ukraine to Alabama in 1999 and started school in grade 6 in the US. For the first 3 years or so my entire math class seemed like just a rehash of things we had already learned in Ukraine.
I failed in taking math study seriously at that point as everything was so easy. When things did get hard at some point in high school and I had to learn new things, I no longer had the discipline to really commit. Also there was no strict grandmother to make me study math for hours after school or on Saturdays anymore. I really regret not having the foresight to stay committed to it now. I did end up taking "advanced" math classes through high school, but my level of commitment and understanding was never what it could have been.
> I failed in taking math study seriously at that point as everything was so easy. When things did get hard at some point in high school and I had to learn new things, I no longer had the discipline to really commit.
oh god.. I failed because of this too. By the time I got to college I was so weak I sunk to the bottom in less than 3 weeks. An .. interesting experience.
"I think on average the difference between a high school student from Russia and US is negligible." That's difficult to believe. I went to comparable level early education schools in Russia and the US and observed stark differences in the quality of math education. Math culture is a thing, and it varies between countries, affecting the education system on the whole as well.
I think OP's comment focuses on the average outcome and your comment is about the education process. I think both are right. While there are stark differences in the process, the average outcome is probably not much different. Students not in the US can do harder problems in their final exams but how much of that comes from actual understanding of math. How much is retained a day or a month after the exams? This is about the average student, mind you. From my short talks with math educators in the US and in a Soviet-like system, I got the impression that the average math student is a mess in math in both cases.
There are probably more people on the long tail of math talent here so it's understandable their impressions on the two systems are much different. OP's comment also talked about the pipeline for gifted kids and he concurred that the Soviet style is effective for training those students.
I remember reading about the Soviet physicist Landau and I believe they made the argument that the difference between the US and the USSR is the US tried to bring every student to as high a level in math as they could, whereas the USSR was more interested in just selecting the best math students and didn't worry so much about the rest.
Curious, what do you and your peers that were feed into a well defined path so early make of it now understanding that is not how all children reach advanced skills in mathematics?
In iirc 8th grade, I've placed high in the final round of a Moscow-wide physics competition, incidentally hosted by MSU. My classmate, who placed even higher, and myself have received an invitation to enroll in the MSU-affiliated maths/physics focused school (#2, the schools in Moscow are all numbered semi arbitrarily).
As far as I recall, every time I'd go to one of those competitions bulk of the people in later rounds were from #2 and #57, another math-focused school. The kids from other schools who did well were, I assume, largely scooped up by those targeted schools.
EDIT:
Oh, and the maths/physics/etc. competitions started at neighborhood level, so every school would typically send at least a few kids, and encourage the kids who were better at the subjects to do well. I went to neighborhood biology/history/etc. competitions too, but never did very well. I assume whoever did well in those and went into next rounds could go on to enroll into a different set of specialized schools :)
Also, some parents did enroll their kids straight into those schools, but I dunno how prevalent that is. They are very ability focused, unlike US private schools that I've heard of where money and helicopter parenting seem to be a major factor.
As a side note, my friend did enroll into #2, and I didn't go because was too lazy to commute 40mins one way when my own school was a 3-minute walk (it was a subway trip for him as is, so I'd like to think that was the difference ;)). We've both done well for ourselves but he's definitely much better at math now.
Yep, can confirm, such system existed in other large Soviet cites as well. I also graduated from one such maths and physics oriented school. Compared to regular public schools the education level was much higher, and not only in those subjects. The studying there was extremely intense, 6-day week (which was standard in USSR at that time), long hours, and tons of homework to keep you busy late at nights and weekends (read: Sunday). Best graduates were expected to go further study in MSU or other top universities. The rest of us who went to local universities found themselves bored in the first years of their studies.
Now, living in a western European country I found in a hard way that the key to a better education for your talented kid hides in your bank account.
Don't get me wrong, I in no way support Soviet system, but this was one of the things they did good.
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.
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.
Odd if you're looking for the simplest way to prove that. Less odd, perhaps, if you're looking for something that can be proved simply using induction, in order to make students do their first proof by induction.
I don't remember precisely what it was we were asked to prove. It may have been the converse.
As dan-robertson mentioned in another branch, you don't even need induction - you can sidestep it by writing X = sum_i x_i 10^i and noticing that all the 10^i are 1 modulo 9 (and therefore modulo 3).
"What is Mathematics" by Courant and Robbins teaches some more divisibility tricks, might be useful sometimes. btw, we learned divisibility by 3 in 5th or 6th grade (not the proof, of course)
> and I didn't go because was too lazy to commute 40mins one way when my own school was a 3-minute walk
Hah, that mirrors my wife’s experience in Riga - she came second and first in national physics competitions for two years, and was twice invited to enroll in a different school - but she stayed put, because she didn’t want to have to change trams twice, rather than a direct trolley bus. She’s happy with her choice.
Went to #548 from elementary to middle, tried to transfer to #57 but failed interviews (I think I went up to round 8), spent one year at #1523 and then successfully got into #57 the next year.
I think that I was very lucky to get in and it was the most valuable part of my overall education. It taught me many things. That there are other people who are much smarter than me and it's OK (and may be I'm not smart enough to do math as a science for a living). A lot of mathematical intuition, about very non-mathematical things, all the way to poetry. How to structure your thought, attack your own arguments and prove something - or discover that the proposition you were trying to prove was false to begin with. (Apart from state-mandated math program, we had our own, with special lessons, where we wouldn't need to calculate or find anything. The only activity was to try and prove theorems and lemmas that you didn't know the proofs of.) That despite years of experience of being a weirdo and a nerd I can finally find a social circle where I can feel normal and accepted. In fact, 15 years after graduation we still have an active Discord server where 8 people were streaming some video games and chilled in voice chat just last night.
So, I think that when you filter kids not only by some "IQ-by-proxy" tests but also by what later get the name "culture fit", and let them coexist together for a few years, it can be a very powerful and life-changing thing. Not everyone such a good experience, of course - but a lot of us did.
I suspect that there's much more of us here in the comments in general than you would recognize. As well as all other post-soviet math-schoolers. It's exactly the kind of education and attitude that makes a career of a senior engineer at FAANG or CTO at a VC-backed startup not only easy in a technical sense, but also a perfect cultural fit.
I liked to read and found (and understood) my farther’s calculus books while in elementary school ;) I was honestly bored in math classes through elementary and middle school. Teachers preferred to ignore me and especially my questions. I got through some math competitions with average success, then got invite to a qualification testing into a couple math high schools. Was selected in the last round of testing to the one I liked the most, and then graduated at the top of my year ;)
Edit: btw, I don’t know how I actually got these invites. Either from math competitions, or through my math teachers who found a way to get rid of me ;)
> btw, I don’t know how I actually got these invites. Either from math competitions, or through my math teachers who found a way to get rid of me ;)
Almost certainly from the math competitions. Nikolay Konstantinov [1] had his apartment full of boxes of punched cards with data on every high school student who produced at least a partial solution to any of the advanced problems at those competitions.
Most of the children don't want, don't care or just plain stupid to be able to grasp the subjects.
It makes sense to isolate together those who can. The special schools don't do anything special, they just cut down the distractions, shift 0.5-2 university years into the school and spice things up with some competitive math/physics/programming/chemistry/biology/geography/etc.
Im crap at math, but annoyed at why. Read about math teaching, and what I found was that there's nothing that correlates with math ability except interest and encouragement (and general iq). There's no genes, brain scans, blood tests, or behavioral signs at preschool age that can predict math success. Teacher ability and enthusiasm likely plays a role.
I believe the opposite when it comes to 'behavioral signs at preschool age' .. I think a child natural inclination towards 'math like' sciences is visible very early
I don't believe there is anything as too stupid child. Not even a stupid child. They become stupid adults, often because of school and people there treating them as stupid children when in fact it's a problem with the socioeconomical/family situation.
When you're in such a school you can really feel what's up, especially in Soviet/post-Soviet case: the socioeconomical situation is exactly the same (because communism), and you usually know the families of other pupils. Then you see the ones who try hard but still can't get it, you also see the lazy smarts.
I am a kid from a post-communist state. What I saw was that abused children had it very rough even though they were very bright, and the lazy smarts generally had perfect conditions at home with loving parents ready to help at any time - and I don't mean with homework itself. You wouldn't believe what sense of not being loved and stress does to a child.
> the socioeconomical situation is exactly the same (because communism)
Not true at all. It might look that way to an american, but there are things like social capital, and it's not even true for financial capital. From USA perspective we were all equally poor, but from our perspective and "in our world", 300 vs 900 usd monthly wage is (was) a huuuuuge difference.
You have to consider that my parents and parents of my former classmates were raised during actual communism. Do you know how they raised children during communism? They beat them, because disobedience could mean death or lifelong prison or being sent to uranium mines - for the whole family. One bad word was all it took. And many parents haven't yet realized, even today's, that this is not the correct way. On top of that, during the 90's, rampant corruption has emerged, then the economical crisis, etc.
And then of course the teachers - their role during communism was different that what it should really be today, and many have not realized yet.
The "social capital" was based on the proximity to the ruling minority. The power was greatly centralized so there weren't many of those type of families. Majority had all same: same stuff like photocopied all over the place.
About the beatings: it's more about the Russian culture, it's even kinda normal for the husband-wife relationships in some regions. To the West there was less of it.
> The "social capital" was based on the proximity to the ruling minority. The power was greatly centralized so there weren't many of those type of families. Majority had all same: same stuff like photocopied all over the place.
Sounds like something from a school history textbook. It was way more complicated than that; the "ruling minority" or proximity to it was nearly irrelevant to most people (and also a direct threat - you stayed away from these people and their 'friends' as much as you could), what mattered more was your street's communist committee, the teachers at schools, if you wanted to have nicer (or any at all) stuff, then you had to know the shopkeepers, if you wanted your child to go to a high school, you had to know the principal, if you wanted your child to go to university, then the whole family had to have a clean and pro-communist record, if you wanted to visit a doctor, you had to know them or bring something (not necessarily money - money was not that useful), if you wanted to have a okay-ish workplace then... (I could go on forever)
In my previous comments, I was talking mainly about the 90's and early 00's - post-communism. I'm also not a Russian, I'm as west as communism got.
Well, you were apparently too far from that ruling minority. At the level of the shopkeepers/teachers/etc.
For the positions like for example even drivers for the high party members it starts getting unequal.
And about the nineties: inequality in the nineties is weird because very large amount of the criminals who got rich didn't bother to educate their children. Of course, some part of them opted for expensive teachers/schools or for sending children to the Western schools, but the "getting by force" attitude of the parents didn't really mesh well with learning.
Everyone was "too far" and no one wanted to be close, it was more of a death sentence than anything else, not a good price for not that much better life. You're talking at most about hundreds of people - out of hundreds of millions (in the Eastern Bloc as a whole).
There will always be stupid kids in a world where intelligence levels vary.
In the 80s and 90s some attempts were made to try to escape this reality by changing the question. Multiple-factor intelligence models were proposed and widely accepted by pop-psychology, but most academics acknowledge now that there is some general intelligence level, a "g-factor".
Anecdotal - I always remember my aunt who was a literature teacher. She always stuck to those ideas and told me that it's obvious that there are different types of talents, because there are people that are good at maths, but do a lousy job in her classes. What she did acknowledge once though, was that people that were good at maths were also the ones that have been writing the best essays from all of her students. There was something that underpined their skills in both areas, but since they knew that they can achive something real in maths they probably did not try so hard to "pick the right key" in interpretive literature tasks. On the other hand for those students that were a bit slower literature was the only field that thay could perform well. Good literature students did not have any particular field in maths that they could perform well in. They stuck to literature, because they could memorize all the important answers and boast that they poses some innate talent.
Anecdotal 2 - Sure, there are some kids that could perform in one area better than in the other, but in my experience this variance is overshadowed by the difference between kids that can do ALL things well and kids that can do NO things well.
EDIT: A nice example of the multi-factor intelligence "scam" are the books from D. Goleman in "Emotional Intelligence" series. They were mostly targeted for middle management people and were very in line with the whole trend. The main motive is that emotional intelligence is a much bigger factor than general intelligence in the context of career progression and overall success in life. What was not made obvious is that the comparisons were done in environments of people that were already successful. If you take a group of people that have a high iq level, then it's very possible that the most successful will be the ones that can work with people a little better. Unfortunately it's not sufficient to be a peoples person to achieve high efficiency in such environments. The "hidden" conclusion was: GI + EI > GI; EI < GI; GI + GI < GI + EI (at least to some degree). There were also some unresolved questions - can you really possess EI without a sufficient level of GI? Isn't EI just a form of GI? In summary there was a lot more of nitpicking of definitions than actual science. It all felt like p-value hacking on language level.
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 performers.
It’s not just California. The combination of “no child left behind” legislation, combined with modern political movements (CRT/I in particular), has rendered large swaths of American public education devoted to bringing everyone up to a minimum standard (not necessarily a bad thing in itself, mind you), but all the while sacrificing the potential of gifted students by not placing everyone into separate (and significantly varying) tracks according to their varying abilities.
In addition, schools are funded based on standardized test scores, which encourages many schools, especially in poorer areas, to teach to the tests—instead of teaching students to think.
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 mean equality of value, treatment, or opportunity—it means creating equal outcomes by whatever means is available —consider the implications carefully).
Universities are being forced to grapple with these ideas, with the core question being “does our university still value the pursuit of truth, critical thinking, and free inquiry above all else, or will we acknowledge that ‘people from oppressed classes have a truth unto themselves that cannot be taught but must be respected, and all opposing viewpoints must be shut down’?”
If this movement hasn’t yet affected you, it will soon. It’s ripping apart social groups all over the place.
(I can give examples of all I’ve described in the morning if you’re interested. I’m just tapping this out before bed.)
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.
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.
Johnathan Haidt has some good talks on youtube about this sort of stuff. I think he mentioned Chicago University being one that is pushing for "truth" over "social justice".
Sorry these are coming a whole day later. Here we go:
New York City has (or had?) an active effort in place to cancel/dismantle "gifted" programs in primary and secondary education. Here's the PDF released by their committed last August: https://docs.wixstatic.com/ugd/1c478c_f14e1d13df45444c883bbf... . There are lots of other examples of this phenomenon around the country... I doubt I need to come up with more examples now.
Here's a good introduction to many of the practical, everyday consequences of CRT/I's influence in American culture. It's an interview with Peter Boghossian and James Lindsay (this is part 1, and I think there are 3 or 4 parts in total): https://youtu.be/YDFL3xwEEG8
-- that last one in particular, if you watch the whole thing, is chock full of great examples.
Hope that's helpful. That's all I was able to find in the time I had.
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.
SJ/CRT movement is devouring itself. The more and more it will affect sciences, technology and other critical economic areas, the more US economy will suffer. That will mean US will be less capable on exporting those ideologies into other countries.
Meanwhile, countries which no such handicap will rise economically and be able to export more of their own ideologies.
> 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?
In practice it hasn’t worked out that way.
Instead it has:
1) Created a cultural barrier between the average Joe and the “liberal elite”.
It turns out that Twain etc are approachable to the average high school diploma American in a way the replacements texts are not.
2) Created a clear divide between minorities who study at elite US universities and the rest of us.
For example there is a level of alienation between Chinese tech workers who went to college in the US vs other Chinese tech workers here.
3) Created a group of “liberal elite” who think they can speak on behalf of, and even lead, other cultural groups when what they have learned isn’t representative of those cultures at all.
Its hard to take these assertions seriously while they are so vague, especially as they seem to be respins of the idea that education, and higher education in particular, is taking liberalism/anti-racism/feminism "too far".
My understanding is that you're saying there is a causal link between admission programs being shutdown and CRT/I, and that the particular aspect of CRT/I that causes this is an insistence on equal outcomes across social groups. I'd be interested to first establish what the actual statistics are wrt gifted and talented student programs - are the closing faster than they opening? Are they shrinking or expanding? Where approaches have changed, are the outcomes definitely worse? etc.
Does this mean we are discounting material possibilities, such as just not having enough money or changing demands/restrictions on expenditure? Accelerated programs sound a lot like arts programs - easy to cut with minimal blowback. Are we also discounting that providing fair access to accelerated programs turned out to be far more complicated than we originally thought and that the choice has been to cut rather than spend money on extra tests and more qualified staff? CRT/I [aren't the only academic source](https://sci-hub.tw/10.1080/02783190609554382) of critique these programs receive.
I'd also contest your definition of equity in CRT/I as an overriding principle ('equality of outcomes by whatever means available' and implicitly, regardless of the consequences). CRT/I uses the principle of equity - that outcomes should be proportionate across social groups and that unequal outcomes must be accounted for. The vast majority of CRT/I scholarship explicitly focuses on 'leveling-up' outcomes, and where this focus is not explicit it is normally implicit (in that the paper would not otherwise make much sense, or the prospect of reducing everyone's outcomes to the lowest common denominator is a rhetorical tool).
‘people from oppressed classes have a truth unto themselves that cannot be taught but must be respected, and all opposing viewpoints must be shut down’: This is a misreading of CRT/I, and one that I suggest highlights its value. CRT/I asserts that everybody has a point of view and way of seeing the world that is affected by their various interlocking identities and experience. There are plenty of aspects of life were we generally accept the necessity and uniqueness of experience as a kind of knowledge - jobs, parenting, relationships, etc. Why should race, gender or class be different? However I'd argue that this assertion gets us closer to the truth. Accounting for bias in science and acknowledging how fundamental it is to people and instruments gets us better science, not worse, even if its harder. "all opposing viewpoints must be shutdown", seems to be a strawman: No reading of CRT/I demands this, in fact most of the literature consists of patient, often quantitative, critiques of systems (law, education, science, public health, etc). So if anything, CRT/I furthers the ideals you see it as threatening.
CRT is postmodernism, witch is basically what depressed Communists came up with to continue to hope they get communism. The amount of inroads stuff like this has made, specially in universities is beyond sad.
Wow. By that argument, one could just as easily label top universities with high scholastic admissions requirements to be “inequitable”, and thus unacceptable.
Equal opportunity does not imply equal outcome—even for a perfectly fair school. Quite the opposite! In fact, I’m glad I got rejected from several schools... their high bar helped guide me to something that worked better for me anyway.
I think people do say that. The notion is that when you look at the people attending Harvard and Mit, for instance, their parents tend to be much more wealthy than the students at Bunker Hill Community College. You're right! That isn't an excuse to shut them down but it might be a reason to think of the system a inequitable. It may be that similar parallels exist in K-12. Then if you're middle class or poor, you have to wonder, "Why am I paying taxes for an elite school that my kid likely won't attend? Can't the rich kids' parents pay for the elite school themselves?" That may be short term thinking or kind of defeatist but it is reasonable.
> That may be short term thinking or kind of defeatist but it is reasonable.
I think this is exactly the wrong thinking about taxes. And it's abused by pundits and politicians by making people spend the same money many times in their head. I mean, you can't be simultaneously outraged that "your tax money" supports elite schools and abortion clinics and the military; you don't pay that much of a tax. In fact, an average taxpayer's contribution would amount to buying some office supplies for one, small government building.
Money is fungible, and by the time enough is collected to fund a school, there's no "my money" in there anymore, much like if you take a fistful of sand from your yard and throw it on a beach nearby, there is no more "your sand".
People who believe in this nonsense are essentially communists. The people who came up with it, clearly were and they were quite explicite about this.
They don't want equal opportunity, they reject that something like that even exists as opportunity is always unequal. Only transformation of society to communism in the end will 'solve' those problems.
So yes, in their opinion all of this stuff is evil and bad and should be replaced with ... something better. Of course they couldn't really tell you how that would look like.
These programs exist, but are generally separated from the ordinary high school system. For example, right here in the Bay area there's Proof School, a private school founded precisely "for kids who love math", AoPS Academy, for extracurricular challenging math classes, and powerhouse public schools like Lynbrook, where gigantic student-run clubs aimed at competitions provide exactly this kind of education.
Comparing the Bay to the American education system as a whole is unfair. In the more rural part of California I grew up we had no options available to us at all. There was the high school, and the more trade-focused high school that only existed as somewhere to put kids who had been expelled from the normal high school.
People do that with Soviet system too. In the 1980s, a disproportionate number of top scientific cadre were born and raised in Moscow and went through the few focused schools there.
Born gifted in Govneevka, Kirov obl., pop. 20,000? Good luck.
The system was absolutely flawed, still is, but still good enough to encourage the highly skilled.
Our (Romania's) education system was (is) the same, if you were GOOD at something there were plenty of paths that teachers would generally push you towards, special clubs for maths, languages, art (less common). Or schools who would try to group together highly skilled students.
System (after communism) has the same flaw, most rural areas have worse access to education, or better said, much worse quality of education.
Yup, when I went through school the gifted program was cancelled at around the same time as the recession and never brought back, and students would skip a year or two in math. Now trying to skip two is much, much harder.
> 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.
He wanted poorer, minority kids to have a chance at a good education and high standards as well? Wasn't very shocking, though the title was incendiary.
I transcribed the clip, and I don't see where he's "dragging people down". My guess is that you're reacting to "as a white male in society I'm given a lot of privilege that I didn't earn" and "I think it's really important those kids learn how to read just as well as I had the opportunity to learn how to read." It sounds to me exactly like he's trying to "elevate people", but you're reading it as "drag people down". Why? This is confusing to me.
First person) Every teacher who's using it basically is saying this is inspiring a closer and more engaged student body. So the people that are actually using it like it. And again in terms of the local control, you still have local control. So if you want higher standards, if that's really, if that is your genuine point, then you can go ahead and do it. You can do the higher standard. And the process was indeed totally transparent. And when [garbled] we'll move on to David and Bill.
Second person) Um, I'm not paid to be here either. I'm just an interested teacher who helped write the standards. And the reason why I helped write the standards and the reason why I am here today is that as a white male in society I'm given a lot of privilege that I didn't earn. And as a result ... [scattered boos from the audience] ... I think it's really important that all kids have an equal opportunity to learn how to read. I think I had a set of advantages as a result of who I was, not ???. And when I walk into places like Roberto Clemente high school on ??? side of Chicago, I think it's really important those kids learn how to read just as well as I had the opportunity to learn how to read. And ??? created an equitable education opportunity for all kids. I think this is actually the greatest lesson we can teach our kids.
I don’t see the issue. The internet exists now and you can access a world of content in seconds. I didn’t get any of this, ever in my mediocre education - I don’t see why so much focus should be placed on these elites at the expense of everyone else.
> I don’t see why so much focus should be placed on these elites at the expense of everyone else.
Because the big breakthroughs and innovations in math and science are achieved by the elites and not by the mediocre masses.
This doesn't mean that we should neglect the mediocre masses (I'm one of them, by the way), they do good, important work. But they're are not sufficient.
The term "elites" in this thread does not refer to the aristocracy or the financial 0.1%. It refers to the high-achievers in math and science, and they have to work for their income just like everybody else (and from what I've ready about postgrads and PhD students in the US, they have to work their asses off).
Sounds like hagiography to me. There were lots of ordinary, non-prodigies that built ARPANet, TCP/IP, the Unix/Windows network stack and HTTP. Plenty work at companies that build the network planes, like Cisco and AWS and Microsoft.
Policies can't be decided based on your insecurities. You don't want anyone to be better perceived than you even when they may be objectively better. All your elitism comments say the same thing.
For one your comprehension. I said may. Give me a case by case study and I can give my opinion. Are you saying all software engineers are equal or you are better than everyone out there ? If not why don't the better ones deserve more pay / prestige etc.
I don't know you or your work. I have no qualms in saying most likely there is someone better than you. I have no qualms in saying that about 99% of the people I know because it's statistically true. To say that others don't deserve more pay or prestige is akin to saying "I will feel bad so don't pay someone better more".
40 years ago is 1980, so that seems consistent with his comment. Also consistent is that Thomas Jefferson High School for Science and Technology in Virginia, which has been ranked #1 and is generally in the top ten US high schools, was founded in 1985.
Not at that level, I have 3 kids of various ages from elementary school to college ;) There is a HUGE difference in the programs from who is selected into the program to program goals.
For the sake of example, how was Soviet Science high school different from Stuyvesant/Brooklyn Tech/Bronx school of Science? (Just to name the ones I know of).
I am not very familiar with these schools, I am in CA. I think the biggest factor for me during my high school years was several hours per week of 1-1 discussions with currently active mathematicians and grad students. While formal math is really hard to read, a lot of ideas are very elegant and actually simple. It’s hard to find these ideas in a formal math text, but you can explain a lot of things in 1-1 setting while still allow student to “discover” core concepts on their own. Mathematics is not about solving 100 problems of one type ;)
This is what infuriates me about college level mathematics from about 12 years ago at least. Why can't they also explain it like they do in those 1-1 sessions instead of making calculus textbooks that assume you know set theory before set theory is taught in some of the worst most obtuse writing there is.
There are good reasons why formal texts are important but I can’t agree more that this is not a good way to teach math if there is nothing else available. But you also need to learn how to read these texts at the end because this is the way mathematicians communicate to each other ;)
Re 1-1: the biggest advantage is that students can rediscover things. It’s one experience to read or listen to a proof, and it is completely different experience when you discover it yourself with small hints from the teacher.
I don't think formal texts should go away, just things equivalent to those well done, plain spoken, 1-1 explanations need to be right beside them in the textbooks. They often are not.
Also math tends to have a documentation problem that could learn a lot from software engineering. Single letter variables are not acceptable in most coding for a simple example.
And another point, high school and college level math is coming from the 18th and early 19th centuries. All of it can be explained without formalization from 1920-30 and students for non-mathematical degrees will understand it much better. I can explain sets to elementary school kids in 10 minutes ;)
The very point of 1-1 sessions is to start with an awareness of your existing knowledge background (set theory or not?) and to aim for real mastery in the most effective way. Unfortunately 1-1 sessions don't scale, while at least khan academy does.
I know lots of UC math/cs profs who meet 1-1 with high school students every week. Currently, the process is pretty informal, where local high school students just knock on the doors of professors until one agrees to regular meetings. UC Riverside is in the process of opening up a high school directly on the campus grounds to make the process more formal.
I'm not familiar with Stuyvesant, TJHSST and the like. The best Russian schools follow the Konstantinov [1] tradition of "listki" (handouts), where each student is essentially guided to re-invent the math curriculum by solving problems. There're no textbooks or lectures. You solve problems from the handouts at your own pace and discuss them with a TA when ready (typically volunteers from among former graduates of the same school).
And another factor, also coming from 1-1 tutoring, is that nobody waits for others. You can move ahead as fast as you can and actually you get more attention if you are ahead of class. As the result, while everyone knows the same fundamental theorems, some students have a chance to learn A LOT more.
Only in some very limited areas. I guess private programs exist too, but your parents would have to have knowledge of them plus the time, money, and wherewithal.
I am absolutely certain nothing like this was available to any kid in my schools growing up.
I'm not sure the total scope or worth really of the program in Los Angeles, but there are requirements just to apply (1), and slots at the highest scoring schools appear pretty limited (2).
It's also not an automatic thing, so a parent will have to be informed about the program and have the time to fill out the paperwork, and these schools are also at specific location, so if you live far away you might not be able to get there without difficulty and stress.
All of this puts filters on who gets to go, rather than just making space for everyone who shows interest in certain areas and puts forth effort. It also removes successful students from local schools, the proportion of academically inclined peers goes down, the proportion of bad influences goes up, and the entire school system suffers as a consequence. Ideally these programs should exist in house, expanded or contracted to fit the number of kids scoring >x% on whatever measure.
My kid is in one of these LAUSD magnets. It’s a public school. The gifted magnets are open to anyone who tests into a certain percentile. The test is given to everyone so it’s quite transparent.
To get into the highly gifted magnet, you have to request a subsequent test, which the district administers. You have to score above the 99.5 percentile.
But they are not on the federal level, with the benefits and disadvantages of this. The benefit is that they don't get dragged into partisan politics and have their agendas changed every four years. The disadvantage is in reach and scale. In some countries they can get the top 2000 middle school math students across the country into the same campus. In the US it's more like the Top 100 students in Virginia, which is a different experience.
AP classes aren't really close to the same in my experience. They may technically be on par with entry level college courses but none of the content is so difficult than anyone else couldn't do it. If anything we just have low expectations and do very little to foster any critical thinking skills in most students. You could be below average in terms of natural ability and not have a problem with AP classes just by actually giving a shit.
My AP history teacher read us historical documents and wanted us to "take notes" by writing them down and then tested us on random parts of the document. I wish I took a lower-level history class. Such a waste of time.
I'd argue you could do the same without even trying, either. AP classes aren't really significantly more difficult than a regular class; they just have more focus on content covered on the AP exam.
My feeling is that the students in Eastern Europe (where I'm from) and very likely the Soviet Union, are very bimodal. Some are brilliant, some barely make it. If, for whatever reasons, early in your education you find yourself in the upper hump of the distribution, then it's a virtuous cycle. If not, not.
In America, it feels to me ,there are plenty of programs to help the students who don't perform that well. Brilliant kids, outside of various gifted/talented programs, are left unchallenged. My son just qualified to an online math olympiad, and he told his teacher and peers about that (over a zoom meeting, obviously). The teacher was impressed, and commended him, but that's it. He will not give my son any more challenging problems, or give him any extra attention. If he does well in that olympiad, he'll congratulate my son once more, if not, he couldn't care less.
When I was a kid growing up, math/physics olympiads was what I was living for. Here most teachers are not even aware they exist.
Overall though, I'll go against the popular opinion, and state that I consider the school system in America (or at least in NYC) better than the one in Eastern Europe. Sure, some could point out at the ridiculous budget that schools have here ($25k per pupil in NYC [1]). But all in all, I feel my son's school experience is better than mine 35 years ago.
Yes! I was about to say something similar about China as well. In China, and maybe other former Communist countries as well, kids with talents or what seems like talents are identified very early on and only those with such aptitudes are given the resources and put on a track to nurture those talents. Same thing with sports too! My guess is that China probably borrowed a lot from the USSR in their programs and philosophy.
I went to a top university in the US and there were definitely kids who arrived being much more advanced in certain areas such as mathematics than the rest of us. Maybe it is not as regimented in the US but there are definitely highly talented kids who take much more advanced STEM classes than the average student.
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. Having been traumatized into becoming a terrible student, I later found out I did much better economically than many of my more academically-diligent college classmates that ended up getting physics Ph.Ds.
The U.S. is fundamentally an exchange economy: you succeed based on how well you can make other people happy. That privileges EQ and social intelligence over IQ and academic intelligence. The USSR was a command economy, and China was an export economy until very recently. Both of those privilege having specific technical skills in areas that are particularly useful to the state, many of which have mathematics and science as a precursor. It wouldn't surprise me if China starts devaluing academic achievement as it transitions from an export economy to an exchange economy. We're already starting to see it with the fuerdai, the children of the new Chinese rich.
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.
Well there's also the whole "school shooting epidemic" thing. But sure, the 3 billion people in those three countries are all fairly comparable.
China:1.4 B
India:1.35 B
US:0.3 B
In socialist Hungary the experience was more nuanced.
There were programs after hours for gifted students but for the first eight years normal hours you were locked in with the other animals there wasn't anything special and it was living hell. Don't think I call my young peers animals for nothing, I do not only carry the emotional scars but also the physical: more than thirty years later it's visible where one of them has bitten my shoulder at the age of 13. I ran away from the school very early once and my father practically dragged me back and I was contemplating suicide when I was 9.
Doing a lot of those after hour programs and an ungodly amount of luck and goodwill made me pass the admittance exam of the best special maths high school class in Hungary. You know those question where they ask what you would do differently in your life if you could do it again? Well, I would tell 13.5 yrs old me to do the goddamned homework for the preparation course! One of the homework questions was the entrance exam and I mostly fubbed it and as I learned much later one of the two teachers didn't want to admit me while the other saw something... It makes me shudder to think of my life if I hadn't gotten in that class...
This happens in America; the difference is that there is an expectation that parental means play a role in success (both in the way the system is oriented and on the part of parents themselves). Most, though not all, of the time, those with clear and high aptitude are "tracked" into gifted programs and magnet schools (though the efficacy varies based on local conditions, re: school funding models in the US). For those with moderate or middling aptitude, it's up to the parents to support and advocate for their child; there is an ostensible cut-off, but it's blurred by the degree of access to tutors or coaches and by the parents' savvy with navigating qualification procedures (often including places where subjectivity can sneak in, like interviews). This, of course, favors the children of wealthy and well-educated parents.
This runs through to post-secondary education. America's college admissions system is legendarily rife with corruption, even into its basic structure; you think it starts there?
I suspect there's a huge variation within the US; Chicago area public schools do what you described in Russia, or did anyway.
When relocating years later to California for work, locals seemed to have had access to far fewer opportunities in school.
Besides math, as in the OP's observations, foreign language options seemed to only include Spanish, whereas Chicagoland had French, German, Spanish, Latin, and that included some ancient Greek.
>I think on average the difference between a high school student from Russia and US is negligible
I don't think so, compared to the difference between the US and my country (which is western but closer to USSR/Russia regarding math curriculum). I think you overestimate what the average US high school student learns...
I traveled a lot and studied in international schools, embassy sf schools and schools in USSR as well as US. I was born in USSR so I mainly studied there between my travels, and everything that I saw and experienced came no where close to the curriculum that I had in motherland. So I have to disagree with you.
i agree overall, there are also high schools for 'talented' kids who can take exams/ or private schools in the US/ of course not all is available everywhere
Such a program will never happen in America again because some people will complain about privilege-this and equity-that. America is basically living Vonnegut’s Harrison Bergeron already and dooming itself to mediocrity if is doesn’t realize the damage being done and correct things.
What happened with NYC’s gifted and talented programs was a perfect example of this idiocy.
Unfortunately, our systems must reflect the fact that our "reluctance" to provide truly equal opportunity in early learning and grade school precludes any claim to meritocracy. We have hobbled ourselves, but not in the way you seem to be imagining: saddled with poverty and anxiety, history and double consciousness, our Harrison Bergerons don't trouble the children of parents terrified of a truly level playing field.
To have true equality we will need to bring genetic engineering to the masses. Human genetic augmentation seems criminally underfunded and over-restricted to me.
Everyone wants to not forget genetics. No one wants to admit the inadequacy of their models of heritability of cognitive function in explaining disparities in educational outcome. Should we continue to judge the entire country solely on studies that claim 60-70% genetic influence (on cohorts of exceedingly similar European-descended subjects)? Twin studies that fail to consider epigenetic influence, widespread psychological effects, etc.? Studies that cannot take into account disparities in environmental effects, because they were unknown or exceedingly difficult to quantify?
If we find that there are significant, genetically-controlled disparities, how do you suppose we go about treatment? We can't even treat SNP-based disorders yet. Cognitive function is controlled by the complex interaction of multiple genes.
I'm sorry for the cynical response. I'm just annoyed that this approach seems to come up constantly, despite the problem being unproven and the solution not efficacious. As a society, provide people with safe, stable homes and communities, their children with equal education and development-centered nutrition and activity, and keep going for a generation or two while we increase our sophistication with genetic and heritability science. Then we can talk about where differences may lie and how, if at all, to treat them.
Obviously heritability figures are time-and-place specific and safe and stable homes (with good nutrition) are vital for success.
But even if the IQ (yes, I can hear the collective groan, but keep reading) difference between a Nigerian and a South Korean is 0% genetic, the within-group differences are still a good 20 points, half of which a genetic engineering program might be able to fix.
We're a long way from being able to do this admittedly, which is why funding and less restrictions would help, but I believe the QALY gains from success would be huge.
Btw: If it does turn out that womb environment is the killer app, the government should try and encourage a massive surrogacy campaign (allowing payment if it doesn't already).
When I was in elementary school probably a decade ago we all had to take a math placement test (not the standardized test, a different one) to determine what math class we'd be in middle school.
Tons of privilege-this and that (this is normal in the bay area, pretty sure a lot more schools have similar systems) but at the end of the day kids (like me) studied extremely hard for these placement tests.
At my school in England, once or twice a year the best/worst students in each class were swapped with the class above/below, based on the teachers' decisions. I had this for maths and French.
I completely messed up a French test on purpose, so the teacher had an excuse to put me in the class below. We really didn't like each other, and I did much better being in the top 25% of the middle class, rather than the bottom 25% of the top class.
British teachers call splitting up a year by ability for all subjects "streaming", and just for some classes "setting", and searching with both terms shows there's plenty of debate on the merits of each (or neither) method at all ages. Since I left the UK, it looks like politicians have been trying to get involved.
Yeah maybe it was just me but I was predicting what the day would be, how many questions, difficulty, etc.
Ended up failing the elementary school test and was 1 out of 4 in the district who aced the middle school placement test to skip prealgebra (math 6 to algebra directly). Much of this can't be done nowadays because of common core.
By the time I went through precalc and calc at MV I realized maybe I should've taken a slower math sequence XD
I was comparing my math books (from Soviet university, Physics and Applied Math) and my son's from Canadian university (CS).
Huge difference to be honest. Canadian ones (same as in US I think) were more like belletristic texts written with the goal to give basics without too much thought needed by the reader.
In contrast you cannot approach Soviet text math book without serious thinking effort. You need to overcome some mental barrier to get into. If you cannot do that then this is not yours - choose something else.
I believe that is because of different motivations of high-school systems. 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.
In USSR universities were getting money from state/society as education was free so they must maintain those barriers so only those who went through were there. Barrier here is from "service provider" side.
>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.
Interesting, universities in Czech republic went through a simmilar scheme, but they'd get disproportionately more funds per head-count of first-year students (on-boarding, I guess?)
Several universities switched from entrance exams to a system of "Everybody gets in, it is the first semester that will probably kill you" :-)
Same in Poland for more than a decade. It's an open secret here that universities admit many more students than they can handle in order to capture extra funding, and then get rid of the excess after the first year.
On my first year, the amount of students was 2x the actual capacity. The first semester was very math-heavy, and everyone knew we had the toughest and CS-unrelated subjects delivered up front in order to weed out half of the year.
On the other hand, I have seen a prof. literaly say something along the lines "Dear students, my purpose here is not to teach you anything, just weed out 50% of you"
That actually sounds like it might work. I know a lot of people who just scraped through exams but excelled in University as well as a number who aced their exams but struggled and/or dropped out in University (admittedly this was more due to picking easy subjects in High School).
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.
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.
I think, he is confusing the figurative meaning with the real punishment. The former is not un-common in Germany even today. And yes, it has - or had - some relation to a certain concept of pedagogy. Cruel, but at times also positively personality-forming.
Depends. It seems to me that in general, post-USSR, school textbooks went through a nosedive in quality. I was educated in the 90s and 2000s in Poland, and experienced the modern, "capitalist" textbooks. At the same time, my grandfather showed me books from 60s-80s period. World of a difference.
What I remember the most was the contrast between the English language textbooks from ~80s vs. the ones I had in school. The modern ones basically exist for both publishers and schools to milk parents. They come in three or four pieces - a book and an exercise book for students, and then an exercise book with answers and some compendium for teachers. That's four books, structured in a way that necessitates attending (and paying for) classes. Meanwhile, the 60s-80s era English books were structured for self-learning. You could work through them with the help of a teacher, or you could do it alone.
(Note that while being self-contained, they've also managed to be smaller. That's because they were free of space fillers. Being set on something one step up from a typewriter limited the amount of bullshit designers could include to zero.)
By the time I was finishing high school in 2007, the regular public school's textbooks for subjects like Polish, math and physics have suffered from the same disease English language books did - they've been split into several pieces, refreshed yearly (ensuring there's almost no second-hand market for them), and structured in such a way you couldn't learn on your own.
I have a few of my grandfather's English books in my basement somewhere; I decided to keep them for my children, so that they have a quality textbook to learn from.
I'm in Western Europe. University courses get funding based on how many students are in the class. It links directly so "bums on seats" = €€. This money comes from the state but it has the same effect.
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 relative to population sizes. But it’s not clear to me if that’s an outgrowth of better education or economic forces.
Somewhat cynically, I think the point of many textbooks is to make money for the authors.
There is no reason why a calculus book needs to cost $200 (in the 1990’s) and get refreshed every 2-3 years. That subject has been known for hundreds of years and they rob poor engineering and science student of that $200.
Sorry, I just have a bad taste in my mouth from crap like that in undergrad. Not saying you’re wrong, just think it’s more greed oriented than we’d like to think.
No, almost nothing of the $200 actually goes to the author. A typical share goes like this: (concrete numbers for Germany) 50% of the sticker price goes to the book seller, 7% to tax, the remainder to printing, typesetting, logistics, the publishing house etc.
A typical author would get somewhere between 4-7% of the net sales. Most books, especially advanced science books, on the market (not your College 101, not NYT bestsellers) sell only in the order of hundreds, maybe a few thousand copies. The vast majority of books doesn't even earn the advance back. The reason why they are often not good, is that it takes months to write 500 pages of well-thought out, well-delivered material, and the incentive to do that for $5000 is relatively low.
1,000 students per semester times $10 bucks is money I wouldn’t mind having.
Professors write tons of pages on various topics as part of their job. We call that “research”. Not sure why contributing to a book effort should be looked at any differently than research papers.
Plus, from an economic sense, when you lower the price of a compliment, your demand g or price ) goes up. So it’s actually in a university’s interest to provide books for free (or very low cost).
The few thousand copies is over the _entire_ lifetime of a book, not meant per year. Again, your College 101 book in Physics or Calculus will be used in large courses and thus sell a large volume, if it is being that used that is. There are also many competitors in the market, and yours might not see significant pickup.
So, let's suppose that you indeed sell 1,000 copies at $150 a piece. Your share is 6% of the net sales, so $8370. From this you need to pay services such as the person making the index, or pay royalty for pictures (yes, many publishing houses deduct this from the author's earnings).
Let's say your book has 700 pages, which is pretty normal volume size, and after you paid for additional services and expenses you are left with $7000. You are a good writer, so planning the book, writing it, creating examples, copy-editing and rewriting it, making reference solutions, etc. and you only spend on average 4h per page. You have made $2.50 / hour before tax. And you probably have a PhD in that topic.
Not only that, but the books are horrible! Authors are incentivized to throw as much verbiage as possible, and this makes students' lives more difficult. It is much preferable to have a more concise book that goes to the core of what you need to learn.
I've heard about this, it seems to be an American phenomenon. I taught applied mathematics at a UK Russel group university for 10 years, I started each course with "You do not need any books for this course, the lectures suffice; if you want to read around the subject I would recommend [2 or 3 Dover editions at £10-15] or [a couple of classics I was sure were in the library]". Most other lecturers did the same.
Books form an interesting part of this HN posting anyway: I'm from East Germany and at that time I got much of the mathematical scientific literature as quite cheap (regarded to money, even workmanship, but not to content) russian translations from the Soviet Union. They were also quite fast in producing these, very close to the original publication (*).
The pricing model of the current locked-in science publication sector is completely ridiculous, counter-productive and even unjustified (research in many countries is supported by taxes, than the result should be free to the public). But luckily this changes with open access - legal and not yet legal.
edit: and not to forget, in some areas the soviet school of mathematics (meant as specific incarnation of mathematics as a discipline in the country) was excellent in itself.
> 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-the-bus tour of rock climbing sites, or maybe like teaching an advanced wood shop class by making students assemble IKEA furniture.
Textbooks should be exciting and fun, but “as easy as possible” is a terrible goal.
I think they mean "as easy as possible," in the sense of Einstein(?;) - 'An explanation should be as easy as /possible/, but not easier;' or something like that. - (?)
In Canadian universities you typically have 3 to 5 levels of mathematics courses for students specializing in something other than math. The highest level of rigour would only be found in the courses for mathematicians, with physics, engineering and computer science students studying many of the same concepts but less rigorously and with comparatively little attention to deriving results from first principles. Was the approach the same in the USSR?
First 3 years all students of all Sciences (Math included) and all Engineering specialties were getting the same (mandatory) set of courses. Only rest 2 or 3 years were variable.
As of Canadian Universities. UBC in particular.
Anecdotical evidence, but still.
Friend of mine, owner of small factory here in Vancouver, asked me once to assemble him software department specifically from Eastern Europe people. On question "why?" he answered - they are engineers first and programmers only second, and UBC makes CS people.
No? If we interpret his intentions generously, he didn't say he only wanted to hire people of Eastern European descent, but people who went through their education system. This can include people from any ethnic group that happens to have people living there. That's like saying it's racial discrimination to only hire people who went to MIT.
That's an even more interesting thought when you apply it to one-man bands. If the only employment is someone self-employing, then presumable the client can discriminate in such ways.
I suppose if you try to do it at scale though there are other mechanisms for calling you out on deliberately circumventing the spirit of the law.
Doesn't matter from the pov of the university. The GP's point was that 'money source' and 'educational facility' are the same in USSR, but not in the West.
Read, then reread, and still do not understand your point.
Are you saying that in Russia, since the education was free that the goal of the textbooks was to make it hard to want to stay in school, if so, to me, seems like it’s unlikely, but possible.
Putting aside non-Russian textbooks, what are you saying the intended reasoning of the textbook form was as it relates to Russian culture?
Yes, basically it's sort of a filter to get the people who coast mostly out. Free college means everybody goes to college for bad reasons, or no reason at all, just because everybody else does. I mean, some people openly told me they joined the CS program because they wanted to avoid the draft - a total waste of education.
So, for example the first ~2.5 years (out of 5.5) of my CS degree were mostly about some pretty brutal math units, each with an exam. There was also other stuff from entry level CS to physics to some token humanity courses but that was easy for most.
If you were inclined/smart/persistent enough to master the math (or, sadly, as some did that being Russia - not sure how prevalent that was in the USSR - bribe your way when you failed), you could continue to the easier more fun later years where you actually studied some CS. A considerable number of people transferred or dropped out.
I don't think the books were made hard intentionally.
From what I understand, in the US, the same course on, say, Introduction to Calculus, can be attended by people who are learning to be MDs, chemical engineers, accountants and mathematicians because there is no fixed curriculum and everyone can pick up that course. So the textbooks and courses need to be as accessible as possible to accommodate a wide range of aptitudes.
In Russia/USSR, at least till 90s (don't know if it's still true since there had been a movement to "westernize" education) you enrolled into a major, not a school, and the whole class had the same curriculum for the first two years with some specialization starting on the third year (the whole program is 5-6 years). So students with the same major go to the same courses, which are not shared with any other majors. In this system Introduction to Calculus for mathematicians will be very different from the course with the same name for sociologists and does not have to be as accessible for people who do not really care about strictness of proofs, structure and other "mathy" stuff.
>Are you saying that in Russia, since the education was free that the goal of the textbooks was to make it hard to want to stay in school, if so, to me, seems like it’s unlikely,
in publicly funded systems students cost money, so there's an incentive to control cost. In privately-funded systems, students make money (in particular with universal loans), so everyone's a paying customer and nobody turns those away.
Germany has roughly half the university graduation rate compared to the US, and this is the same reason why the US gives you 8 late-stage cancer treatments and the NHS gives you 2, or why sometimes you don't get the super expensive medicine you want.
No. Because education was free, they could make the books harder. They didn't depend on students pumping money into schools. Didn't have to pretend to be "nice".
(I grew up and went to college in the Eastern Bloc.)
USSR needed X engineers per year. The universities had to set their entry requirements high/low enough to only allow X*1.0X to enroll.
Once enrolled, they were ambitious enough to only allow the best to survive. They watched their bell curves and adjusted accordingly. I'm almost sure the Ministry of Higher Education would publish the guidelines on how to achieve that.
I think the reasoning is that the incentives are flipped. Capitalist school gets more money the more you stick around. Communist school spends more money the more you stick around. One has a perverse incentive to get as many people to pass as possible. The other has a perverse incentive to get as many people to fail as possible.
One would think Russia would have demand for strong advanced mathematics professionals, so unclear how failing students might help that. Missing something in the reasoning though, since I get that if you’re giving away something for free, you want to maximize the yield it returns, but still, it does not add up to me.
Further, reasoning that American schools get money might hold true for tuition based schools, but my understanding is that large percentage of pre-university mathematics courses are taught for free. So again, doesn’t make sense to me, because if that was the case, all schools would charge and majority of students would finish university to maximize the profits, and again, this does not match my understanding of how things work.
I think the point is that Russia's programs isolated those who had a talent/passion for math as opposed to just trying to bring every student to a basic level of understanding. If a student doesn't have the drive/talent/passion for a field, it follows that they will not perform as well in the workforce as their driven/talented/enthusiastic peers.
Au contraire, they’re some of the best textbooks I’ve had the fortune of reading! :-)
They make the student work (participate actively in your own education), which I’ve noticed that American textbooks (at least modern high school & college textbooks) seem loath to do. I don’t know why — you don’t develop what you don’t exercise!
If you open any soviet textbook you will see the following text on title page: (loosely translated) "Supplementary reading for students of xx specialties higher education" it can school level or college level. But in essence those books are an addition to the course which is mainly delivered by lectures. You can study by yourself but it will be hard and you will need extra material to replace lectures.
Same situation in Romania, some of the best math problem books I found were a bunch of books printed before 1980's. The problems were just wonderful. I was desperately searching for them for my kids through my father's library.
In 1990's after the revolution we got humanitarian aid from Western Europe, including some French math textbooks. They were so low level (simple) I was in disbelief. Useless.
I had the same reaction in Poland, when my grandfather gave me some textbooks from his collection. They were an order of magnitude better than what I was using at school.
and, somehow, the economic and social system in France is much better than the one in Romania
my take is that the western-style school focuses on getting students life skills, while the eastern-Europe one focuses on cramming knowledge in the brain
Maybe it's also the context, the gradual buildup France had over Romania at the time and now. Romania endured the communist regime for many decades and was very much isolated.
The ones I spent most time with were volumes titled (translated) "Selected problems in higher mathematics." I worked out of a German translation for one volume while I learned a smattering of Russian and then the Russian for a second one. This was to fill in assumed background in things like integration that was assumed by Landau & Lifshitz.
It's been long enough where I have no idea of the author.
Here is an interesting paper [1](PDF) by a Russian mathematician who has taught mathematics in Russia, USA and Brazil. He compares the "very successful usage of word problems in Russia and contradictory, inefficient and often immature
treatment of word problems in USA."
Wow, this is a great read! I'm on page 18 so far. It's been discussing how "word problems" are key to developing critical thinking skills, and how far behind the US seems to be in them. One point made: the idea that word problems can wait till algebra, which gives a universal method for solution, totally misses that they develop logic skills and practice with problem solving, which makes learning algebra so much easier.
Finished it - there is uneven editing in the second half: some passages reappear in multiple places, some thoughts are unfinished. Still found it well worth the read.
Huh. That doesn't really match my American experience at all.
True, in elementary school I don't recall any word problems -- because everything was practical arithmetic through sixth grade. I think sixth grade was long division?
But seventh grade was algebra, and all the Russian examples of word problems look like the stuff we got all the time, seventh grade through eleventh grade. Twelfth grade was calculus, and I seem to recall word problems mostly disappearing then, since everything was just graphs and derivatives and integrals.
Granted I was in honors classes and also did extra-credit "Mathcounts" and "Mathletics" after school, where we definitely got more of that stuff too. But that was just a difference of difficulty and, well, even more practice.
Now obviously different countries have different math standards and different cultural attitudes towards the value of math.
But the difference the author is describing doesn't resonate at all with what I learned growing up in a small town in upstate New York.
[1] has some word problem examples for every year of primary school in England. Year 1 is age 5-6:
"Chris is going to buy a cake for his mum which costs 80p. How many 20p coins would he need to do this?"
I remember lots of these "coin problems" when I was 5 or 6, since we had plastic money to help understanding, but I don't remember other problems.
If I'm equating the grades correctly, the Russian problems appear to be about 1-2 years "harder" than the English problems, at least around age 9-10 (Russian grade 4, English year 5).
That is what I am noticing with my son's maths lessons. He is in year 5 at a British curriculum international school. The word problems seem a bit too easy, in my opinion.
I don't see a conflict - what you're describing is very consistent with the paper. No problem-solving until algebra starts, then focusing on using algebra to solve 'word problems'.
I've noticed that a lot of students seem to have issues with "word problems"–as in, they have difficulty translating the problem into its mathematical form–and it's often treated as an entirely separate class of problem that you can be bad at. I guess that there's a lack of early training (it doesn't even have to be that much) to do this conversion?
I remember I had issues with word problems in primary school, main issue being I hated them. Trying to recall the specifics, I think they just didn't resonate with me - I've seen them as some weird tales of people I don't care about doing nonsensical things, that you then had to translate into numbers and equations while minding the non-obvious caveats, or that real-life intuition didn't apply.
Singapore's maths curriculum for primary-level students is full of word problems. It may be confusing at first but it lets students get good with interpretation of the situation and derive the essence of the problem from the scenario which is a useful skill irrespective of level.
Yes. The paper includes a number of examples of word problems from Singapore primary maths and the author says "the Russian and Singapore programs go roughly hand in hand in style and difficulty of arithmetical problems."
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 Haskeller faint. And that book is not the only instance, Gilbert Strang lectures on youtube are also similar in style. It also correlates with the pragmatic engineering of US history (electricity comes to mind).
I feel like it's worth pointing out here, for Americans who don't know better (no blame implied), that the French have one of the best mathematical pipelines in the world. They have almost as many Nobels (13 vs. 11) despite having 1/5 the population. Guardian article about them here:
So please don't think France is a backwater that just doesn't know how to do math - on the contrary, it may be the best country in the world to be born into, if you want to be a mathematician.
For what it's worth, I'm an American who honestly is pretty bad at math, but I try to keep learning, though I'm past an age where it will matter in college or higher education.
A paraphrased anecdote I heard about French math education:
"In America, they start by teaching you how to add two numbers, then once you've mastered that you learn to subtract, then once you've got that down you learn to multiply and divide and so forth. In France they tell you: this is an arithmetic object. The operations on it are add, subtract, multiply, and divide. It's simple!
It's a good way of cranking out a bunch of Fields medalists, while everyone else has no idea what's going on."
Note that this was true at a time (some of my math teachers learned group theory in middle school) but that nowadays math education is much less abstract until the end of highschool.
At this point there is a specialized track (preparatory classes) to get into the most prestigious engeneering and buisness schools that will have you cram mathematics / physics / computeur science / english / a mix of litterature of philosophy in two or three years.
The student then get into the various school according to their grades on a serie of national exams.
This track is very competitive (and as such often decried) but I believe that it is a very efficient way to get the top talents to the top institutions with a maximum of learning on the way (also note that this education is free and that the very best school will even pay you).
Note that a student can also choose to get to college and ignore this track.
> A British mathematician was giving a talk in Grothendieck's seminar in Paris. He started "Let X be a variety...". This caused some talking among the students sitting in the back, who were asking each other "What's a variety?". J.-P. Serre, sitting in the front row, turns around a bit annoyed and says "Integral scheme of finite type over a field".
To the question "what is 2 + 3" a French primary school pupil replied: "3 + 2, since addition is commutative". He did not know what the sum was equal to and could not even understand what he was asked about!
To be honest, what he's criticizing is also what is lacking in post-primary school math education. The mechanical reduction (3 + 2 -> 5) leads to a road block when you start thinking into solving equations.. because there's no single path of reduction. You need to see the formulas as material you can transform in your mind.
I don't believe anyone here thinks France is an Academic backwater. France has had some of the most brilliant scientist/mathematicians since the 1600's.
Ha! Yes I do. In fact you can tell my amateur-ness from this, that this misstatement didn't immediately jump out as wrong (though I do know there is no Nobel for math, when I stop and think about it).
I should have said the Fields Medal, as indicated in the article.
> I feel like it's worth pointing out here, for Americans who don't know better (no blame implied), that the French have one of the best mathematical pipelines in the world. They have almost as many Nobels (13 vs. 11) despite having 1/5 the population.
I’d much rather measure an educational system by how much it teaches the average person, than by how many Nobel prize winners it produces.
I studied Engineering for a period in France at the time (undergraduate) I was very impressed at the level of rigour and abilities of my French peers. However this does not seem to link well with actual abilities as a practising Engineer. For instance French engineers are not particularily coveted.
The strongest plausible interpretation of what the previous comment said is that it refers to the Fields medal, which has been described as the mathematician's Nobel Prize [0]. Assume good faith.
> It was very operational, you calculate, you manipulate concrete data
it's interesting that some academic approaches focus on the theoretical framework and conceptual depth, with the underlying assumption that the student would "get" it once the fundamentals are understood.
The other approach, mostly in the asian schools, teach rote and speed in mechanical/mental manipulation. For example, a student would do 1000 quadratic equations, mostly by rote using substitution into the formula. That constitutes "teaching" of the quadratic equation.
But in the end, who learned more? Not sure. But i do believe that being able to manipulate numbers very quickly leads to a quality of its own, and can make understanding harder concepts easier.
In fact, the Soviet approach also emphasized solving problems. There are books entirely devoted to problem sets, and there are other books devoted entirely to theory. My grandfather was a Professor of Mathematics at Moscow State University before we emigrated, and as I was growing up, he would always stress that it does one no good to just know about swimming if you can't actually swim. The people who learn the most are the ones who have competency in both theory and application. To get that competency, you alternate between focused practice in one and the other, just like an athlete alternates training different muscle groups.
The rote learner learned nothing more than the ability to regurgitate a mechanical process while the academic learner learned understanding, in my view. You have to work through some examples to solidify it but that should be totally secondary to understanding the meaning and concepts. Like a physics teacher of mine put it, rote math learning is like teaching sea lions to honk horns for fish - students give the right memorized answer and get the grades without really learning anything.
In my experience, it's easy to think one has understanding without actually understanding. The process of applying that tentative understanding to a problem to test it is essential to figuring out what the flaws are in the tentative understanding so that real understanding can eventually be achieved. Once it gets to the point that a person can crank through problems without significant errors, then I think further problems don't do much good except as an occasional refresher.
Hence the importance of word problems, I think. They force a synthesis of abstract and concrete that really tests/enhances understanding on all levels.
Everyone can learn to solve equations quickly if they’re forced to do it 1000 times. They might forget it the day after the test, the might not know why they’re doing anything, but you can be damn certain you know what you’re doing if just for that brief window in time.
It’s also clear if you’re succeeding or failing. I’ve noticed that private school parents in the US seem to hate homework. The kids get three optional problems a week and no tests. All the time that they might’ve spent thinking on their own about problems is instead spent in class, which really limits how much new stuff can be taught. The kids think they know everything because there are no grades. The kids that actually perform at grade level have private tutors giving them homework, while the rest are just playing fortnite and unable to do fractions.
> They might forget it the day after the test, the might not know why they’re doing anything, but you can be damn certain you know what you’re doing if just for that brief window in time.
What was the point then? It's a complete waste of time in that scenario.
Applying reasoning to a similar but more familiar domain is a good sanity check for said reasoning. Let's then apply what you said to programming. Would you say that the "academic learner" who read a lot of CS and programming books but haven't written a single program on an actual computer learned understanding, while a "rote learner" who keeps going through hundreds of small programming exercises learned to "regurgitate a mechanical process"? Doesn't pass the sniff test to me.
The way I see it, doing the thing gives you ample opportunity to figure out theory on your own - repeating a menial task prompts the brain to invent shortcuts. Meanwhile I can't imagine someone learning only theory to not fail spectacularly at practical tasks - because theory doesn't capture everything; there are lots of practical, intangible things that crop up when you start doing the work. On top of that, it's easy to feel you understand something without actually understanding it.
The best way, IMO, is what philipov's father said - you have to alternate between theory and practice. It's how you can build understanding faster while continuously validating it.
I did say you need to do some exercises, just not an extreme amount or at the expense of theory. And these math exercises are different from programming - they amount to applying some process to different numbers over and over again while at least there would be some degree of problem solving if you wrote a bunch of genuinely different programs.
>But i do believe that being able to manipulate numbers very quickly leads to a quality of its own, and can make understanding harder concepts easier.
Can you elaborate on this? Are you supposed to introspect while you're applying the quadratic formua 1000 times? How does being able to quickly add/subtract/multiply/divide help you better understand abstract concepts?
In my experience, those rote mental muscles mean that the basics are never slowing you down when tackling a harder problem. It's comparable to having a perfectly organized toolbox vs a mess of tools in your shed - you can do the same things, but you're free to focus on the core of the current task instead of distractions in the trivial parts.
This is precisely it. I have a math-heavy job and play/write music, and the same phenomenon plays out in both situations: when reading sheet music or thinking in music theory is in your muscle memory, your entire conscious mind can focus on the actual, creative task at hand.
This should be obvious from any number of examples, from driving a car to typing as a programmer. Reducing the friction between your brain and your tools simply makes you more effective.
It's very interesting because in the examples you described (music and programming at least), I sometimes feel limited by the tools I know.
I studied music theory for about 5 years more than 10 years ago and remember some of it. I like to compose music and sometimes like you said I'm really losing a lot of time/energy because I don't master the basics.
Yet some other times, I don't even think about music theory and let my inspiration go - and it's often better quality.
I find this effect to be true in programming as well. I find myself restricted by the frameworks I know and sometimes my mind can't think outside of it.
Yes, we can easily experience this by writing code in an unfamiliar programming language, or playing tennis left-handed. The theory is all there, but the muscle memory is missing.
I really dislike dealing with large engineering systems in Python, but I fully agree when I just need to solve a self-contained problem and don't need to worry as much about it being maintainable or readable (or more accurately, don't need to worry about interacting with Python code that other people have written). I currently work a lot with both Python and C++, and I find myself occasionally trying to write C++ Pythonically and it's a huge headache (eg map/filter or list comprehensions are infinitely more readable than stuff like std::transform).
Note that I don't mind conceptual depth. But if you fail to bootstrap then you're stuck. Calculation kinda helped me connecting the notation with simpler things and bring back confidence and gradual progress
Thank's for the insight. I struggled with geography until I discovered history...again, after high school of course. I still struggle with algebra, so I look forward to checking your suggestions out. I think my problem as a kid was I was just hyper, all the time. I could cut wood outside for 10 hours but couldn't sit still for a moment.
> I struggled with geography until I discovered history
Tangentially, a lot of fantasy authors seem to love maps for their own sake, and provide maps of their world as illustrations. I never saw the point of these; the map never really matters to the story.
But history books provide almost the same number of maps -- usually one, before the discussion of whatever -- and it just isn't enough. Those maps really matter to understanding whatever was going on; in the real world, geography is a huge deal.
My favorite sequence of maps in a book was “Black Hawk Down”. The first chapter begins with a world map, showing Somalia, and it lays the geopolitical setting for the events. The second chapter has a map of Somalia, showing where Mogadishu is, and sets the scene there. It keeps zooming in, until the final chapter shows a map so tight it has individual people (who you have since met) and which side of the street they were on.
It's more about deepening the story I think and making it 'bigger' I guess or another type of story telling. You look at a fantasy map and there's typically places on the map not even mentioned in the actual story as you say, but that helps build the setting.
Look at the map for the lord of the rings for example. A good number of the places in that map are barely mentioned in the actual trilogy. Yet that map's become one of the most iconic in fantasy in general.
It's more about what the maps inspire in your imagination while you read. When some random fantasy city name gets mentioned, you can look at the map and get perspective about where it is in the world.
It's also helpful I think to keep the world consistent for authors. It gives them a frame of reference for scale and distance in their stories and likely helps keep track of all the random names and cultures and such that they make up for their stories.
Imagine if the lord of the rings' world was like when we were still conquering and exploring all around, and then some dude, tolkien's lost brother, or something, twin, perhaps, with co-systemic minds, mapped out the unmentioned parts, and then you could just span the two things together.
If it were somehow possible to let kids chop wood for 10hrs, as the need arose, or whatever, and then they could go / go back to school when they were ready.
Agreed. There is a severe lack of mindfulness and focus in modern education, and strenuous physical exercise like chopping wood can be a real mindfulness-workout.
You’re right. I’m a French student myself and our education system has always been very "Cartesian". This is also partly due to the fact that we have a special competitive exam system for entering higher education (top business and engineering schools) where you spend 2-3 years absorbing unfathomable quantities of math, economics and history/geography. The emphasis on mathematical abstraction and especially proof here is insane.
My experience was the opposite. School in America tried to make me just memorize a bunch of stuff and it didn't work at all, but using resources like Khan Academy to build understanding and working through proofs of everything was all I needed. Lots of shallow exercises did nothing for me compared to a few deep exercises/proofs and reading.
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.
> Set theory alone you can get to continuum hypothesis.
Ironically, her independence from ZF would make the classical Bourbaki group shiver. The same way the earlier, better known, work of Goedel did.
I don't know, if you are aware of Bourbakis spirit. There is something much more important in this context as the content-wise difference between sets and numbers. I never would argue against applying naive set definitions in a suiting way. But Bourbaki had an agenda, and this agenda is not for everyone (certainly not for me).
I'm the right age to have done New Math [1] in my first years at school, my memory of it is that it seemed fine but at age five I wasn't really thinking about comparing different educational styles.
In my experience with Russian style mathematical thinking, it often involves hardcore theory in pursuit of some hard-nosed applications (where every assumption and approximation in the theory is well-motivated). When the two come together, there’s an ineffable magic and wholesomeness that I’ve seldom seen elsewhere. Some of the Russian Olympiad problems are absolute beauty.
> It also correlates with the pragmatic engineering of US history (electricity comes to mind).
I got my math degree in California (at Cal) and the approach was a lot closer to what you describe French books as. Many of my courses were just a semester-long discussion of proof after proof, with breaks for exams that were more proofs.
> It was very operational, you calculate, you manipulate concrete data. In French books it's all theorems and concepts.
"¿Por qué no los dos?" as they say? One can also detail how to "calculate" and "manipulate concrete data" in a rigorously correct way, involving precise concepts and perhaps some theorems. (Though an overemphasis on theorems is not necessarily good, either. Sometimes it can even signal a lack of attention to the actual "rules of the game" one is ultimately supposed to be studying, while a focus on direct manipulation would perhaps tend to avoid this. A good balance of the two styles is perhaps best.)
Personal experience. In USSR till 16, then 11th and 12th grade in US. Yes, the books and the curriculum were way harder in the Soviet Union, but it's largely pointless.
In USSR, there were 2-3 kids in the entire class who actually vaguely understood the material and the other 28 were just copying their homework.
In a US high school, by contrast, you can choose to take whatever level of math you are able to grok (AP, College Prep, etc...)
Given the average results, I vastly prefer the US system. USSR system was a one size fits all that didn't work well for the average pupil.
Underrated point. In Poland grades often don’t matter at all (e.g. for university admission). Cheating is widespread in school (but not at final exams after high school). Meanwhile in US your high school grades matter for university admission etc.
And, yes, it is often possible for students to complete these harder classes without much to show for it.
We had a very famous MIT professor on a 6 month sabbatical at our lab in the early 90's. He remarked on the difference between US and our institution in Belgium being that here you can just assume undergrad students would be fluent in basic math subjects, whereas in the US (in this case MIT) you would have to explain even very basic math.
Now 3 decades later we are also at a US level as math has in general been completely de-emphasized at all levels of education.
As for textbooks, at the time EU ones were pretty clean, mostly definitions, axioms, proofs and conjectures, plots etc, layed out in simple black on white, whereas US textbooks were extremely wordy, full of colour and irrelevant photos blasting away at your senses.
Sadly this seems to be the style that commercially won, but I doubt very much it is beneficial to the student.
I don't think just plopping all the subject material in front of a student and expecting everyone to immediately "get it". Some people may have the intuition to read a group of definitions or a proof and suddenly understand the higher level concepts gluing everything together, but that certainly doesn't work for everyone.
Anecdotally, having a textbook that explains a concept via examples without jargon and informative pictures, then throwing all the definitions and proofs at me has been much more helpful to my understanding in multiple subject areas.
I'd also throw "extremely wordy passages" in there as well because having something repeated & reframed multiple times has help me understand something from multiple perspectives - and remind me of a previous definition at a crucial point in the text.
I have a feeling that TV/media really did play a huge role in the decline of intellectualism in the western world. The USA loves its TV, hollywood and celebrities. It's been reinforced throughout the culture and it makes a lot of people very very wealthy. The more time you spend watching tv the more money they make. Though here's the crux for them, educated people think more and do more so they don't make good customers. So fill the TV with anti intellectualism. Then toss it the political usefulness of a mindless medium and you have a dangerous conduit so to speak.
A friend grew up in a household where his mother forbade TV and video games. During this covid-19 lockdown, instead of mindlessly watching TV like everyone else appears to be doing, he built a deck and is rebuilding his garage among other projects. Every other friend I talk to is sitting around drunk, high or watching TV. Few do some projects but it's mostly TV show chatter in the chat apps.
Personally I don't hate TV and I have netflix. Though I only really watch it in spates and when it is on, I am on my laptop or doodling in my notebooks. It's more for background noise than content. Though of course there are some times when I'm tired and just want to sit and watch an episode of a show.
Politics played a bigger role. Simply put they had to aim for lowest common denominator when setting standards else claims of discrimination would pile on.
Many school systems went so far as to either modify grading systems to prevent embarrassment or celebration of achievement. Schools types which attempt to provide a more specialized learn curriculum are regularly demonized for one reason or another.
If you want the best education then the word fairness needs to be applied properly. Fairness is insuring all students are offered the opportunity to learn and receive an education while accepting there are many who can learn more and should be offered the opportunity to do so even if that includes elevating them among their peers.
Educational achievement should be held in higher esteem that sports yet for some odd reason we do not consider fairness is sports an issue where some kids cannot compete because of ability yet in learning we do.
Schooling has indeed been dumbed down but that as happened in the more recent decades. TV/media manipulation has been at work slowly getting our intellectual capacity for decades, since WW2. I even will go as far as to say it was a direct result of WW2. Cant have kids growing up to be commies. Best have little Susie and Joey sit and watch wholesome american tv reinforcing traditional american values of imperialism, idealism, consumerism and obedience to authority.
Even if media is to blame for helping fueling anti-intellectual sentiments in the US, it's more likely an unintended byproduct than a massive conspiracy by media companies to purposely dumb down their consumers to buy more of their product.
I had an exchange year during High School where I moved from Germany to Florida for a year and attended a public school.
I hate to say this but to me the classes were laughably easy. While I was a 10th grader in Germany I could have easily graduated there.
I do however favour the US system of individual classes where you could advance in e.g. Mathematics but if you had trouble with language you could take a less-intensive course.
This doesn't work in Germany. You either advance with all subjects at once or you don't. One of the most stupid things that I have witnessed. In our 11th/12th grade we would have a huge difference between grades. About 20% of people were getting straight A's while over a third struggled to even pass. Barely anyone in the mid-range. Terrible system which makes it really really hard for teachers to teach a class.
You have a form of in Germany that in most of the states with the "Leistungskurse" or the "Profilklassen".
I'd argue that its extremely important to _not_ be able to drop courses since it contributes to a well-rounded education, something the US sorely lacks.
Yeah but this system is taking a huge toll on the teachers. Our maths teacher had to basically give two different courses within one class, because the gap was so big.
The big difference is also that German high school students are split into three different schools with the top school (Gymnasium) being much harder than US high schools.
In US high schools, students are not split and obviously they can't advance as fast.
I mean, could it be as simple as "Learning math is more important to Russians than to Americans?" And before you dismiss this as simplistic, consider everything that's competing for attention with "learning math." What things are Americans either preoccupied with or beset with, that Russians esp. Soviet Russians, weren't? I'm thinking, the profit motive. Particularly as concerns textbook publishers. And parents who need to pay for healthcare and that oversized house. And textbook readers who wonder how the hell they'll ever use this to find a job.
I think technical education in the soviet union was a lot stronger than it was in the free world, at least in the 20th century. When I was 16, I was enrolled in the top high-school maths units in the early 1980s in Australia. Maths was about 1/3 of the academic contact hours and the curriculum was pretty standard across all the Australian states.
A family from the Ukraine somehow managed to immigrate to Australia and their 16 year old girl was enrolled on our maths classes. She was years ahead of the rest of the class.
She said she was a very mediocre maths student at home in the Ukraine, said quite a few times that in her opinion we had been taught basically nothing in the Australian system. I don't know how much maths the average soviet citizen learned, but I got the strong impression that soviet students who were actually interested in the subject got a much better mathematical education than they would have in Australia/US/UK.
My 3rd grade Ukrainian math education carried me through 10th grade ("Accelerated" classes in a 36/36 school district). An anecdote, but basically I fell behind my Ukrainian peers very early. I remember coming back and a friend who was younger than me was already doing calculus when we weren't.
Russia had brilliant mathematicians even before the October revolution, however, the Soviet Union gave another incentive to become an academic - it pretty much guaranteed a highly respected job, even if the salary was modest, but also allowed most of the academics to not get involved in politics. So in a country where you couldn't form a business, being an academic or a doctor was pretty much the best career choice.
You could say that. I'm from Poland, so compared to Soviet Union it was communist-lite. I had a brilliant math teacher in high school. He had the reputation that if he was your math teacher you were automatically accepted at the local university. He was a legend in my town, and managed to stay under the radar of the communist regime.
No, learning math was never more important to an average Russian than it was to an average American. An average Russian has never knew math any better than an average American.
I guess its just anecdotes at this point, not data. But all my peers and friends from different schools, were solving quadratic equations in 4th grade in USSR/Russia. This was early 90's. I then studied in Canadian and US high schools and it took me until 9th grade to start learning any new math again at school.
In Soviet Union, quadratic equations were introduced in 7th grade, not 4th [1], so if you did in fact study them in 4th grade your experience is not typical. And while American 7th grade program does not cover quadratic equations, it includes intro to probability and statistics, which is far more useful in real world, and which was not covered in Soviet math classes until much later (if at all).
> And while American 7th grade program does not cover quadratic equations, it includes intro to probability and statistics
Depends on your program, of course. I did quadratic equations in 7th grade, and the first class that actually did any non-trivial probability was in 10th grade.
But how can they teach probability and stats without any calculus or real analysis? Are they just teaching a few cookbook formulas and leaving it at that?
I'm 28. We emigrated to Australia(from Russia) when I was in approximately grade 3-4. I basically did no mathematical study for 4-5 years, the system was that far ahead. From family in Russia I hear that ridiculous amounts of homework(2hrs daily if you're on top of everything) is still a thing for young children although there's all sorts of strange pro-putin insertions in the curriculum but ultimately I don't know, it seems like Russia as a whole has very quickly lost the few positives the Soviet Union brought. I felt the quality of teaching was much better aswell. It seemed like many Australian teachers did not fully grasp many of the concepts themselves. From what I understand the American curriculum is even more relaxed so I'm not entirely sure where the above commenter gets their information from or if they're being entirely honest.
I'm not entirely sure where the above commenter gets their information from or if they're being entirely honest
You left Russia when you were 10, so you were basically a child. Then you "heard from family" something you've never actually experienced. On the other hand, I was there in Soviet Union/Russia going through all 10 grades in three different schools, and then getting my masters in engineering, while tutoring high school students in math to make some cash. Then I tutored undergrads as a TA here in US while getting my phd.
You have very little actual experience of Russian education, and zero experience of American education, and you're questioning my honesty?
Average town (0.5M), average family (engineers), average school (not the best, not the worst), though the high school I attended had math specialization, so by the end of it I knew more math than an average Russian (or an average American).
it seems like Russia as a whole has very quickly lost the few positives the Soviet Union brought
Now imagine North Korea collapses, becomes like South Korea 30 years later, and someone makes a statement like that about it. Puts it in a different light, doesn't it?
Soviet/Russia never considered human as something important.
Russian management way sharper in moves and less humane.
Soviets proved to people that thousands can be killed - rich, clever, creative, dissidents or you were just unlucky. They showed life doesn't worth anything. But Communist Party and ideology is important.
Who cares how hard is it for you to study, Communist Party decides who can publish, which books you can read. You didn't decide anything.
This system is still alive and works. It just slightly changed outside to pretend to be democracy.
We have lots of Soviet teachers in Israel, they always said "it's better to solve something in 15 ways than solve 15 things the same way" and that resonated.
To be fair though, that approach is omnipresent in the math faculty in the Hebrew University - so it was not unique to the Soviet paradigm but it was interesting to see it in High School.
There is also a genuine sense of "let's try to do this!" that's very common in computer science but is more common in "soviet" math than "regular Israeli" math.
The most important distinction IMO was that these teachers were not _afraid_ of Math and could discuss higher level non-high-school concepts typically. Having a teacher that loves the subject is important.
In my high school year in international school(in germany) I've seen many students from diverse backgrounds. I could see balanced number of students taught from their own origin: US, asian or international school itself.
One thing I remember until now is that students from US kept using the phrase 'plug-it-in' whenever they substitute values into quadratic formula. Overusing that term made me laugh about their attitude towards math because it felt as if they didn't really care what's inside that magic formula that pops the answer out.
It felt so 'american' because I felt the same attitude when they treat computer programs:
'I don't give a shit about what's going on. Some smart asian kid will make me a magic machine that I just need to plug in the numbers and prints the answer, while I focus on making varsity football team next year.'
You can downvote me for my racism though. All excuse I can make is that they also laughed when I told them how their attitude towards math sounded like.
"Plug-it-in" is simply jargon for what would more properly be called substitution and reduction. One would use the exact same sort of reasoning when doing "proper" math proofs, so I think your attitude might be a bit misguided - there's no "magic" involved.
So much racism for treating functions as black boxes. That's what you're supposed to do: treat functions as black boxes, not express casual racism on hacker news.
Alternative point of view: functions is just a performance boost. You still have to understand what and how they do to use them correctly. Treating them as "black box" leads to shitty outcomes.
Coincidentally, there seems to be quite a lot of overlap with cultural background and one or another PoV on functions.
I was a huge fan of Russian Math and Science books and I used them to study for an entrance exam to IIT (its more difficult to get into IIT than Harvard) and came out in top 100 in the country.
But, inspite of coming out at the top of the exam, I found Russian maths books very interesting and sometimes very difficult to master.
This coming from a country full of brilliant mathematicians. Russian math books are not only hardcore compared to US - they are hardcore compared to India also!!
If you consider yourself good in maths, try solving the problems from this book!
There is simply no comparison of Soviet Math Books with the rest of the world. US is so far behind that this comparison is not apt. The closest is Indian Math books or books from Cambridge like S. L. Loney.
It's a hard comparison since Harvard and the IITs have different admission processes. Admissions to the IITs happen via a single exam, which is held at the end of 12 years of school education and is conducted over a few hours consisting of upper level physics, chemistry and mathematics. Harvard meanwhile has a lot more in terms of admission criteria, with essays, SAT scores and other things taken into consideration.
The easiest way to justify OPs stance is to compare the admitted / applied ratio for both schools, owing to the sheer number of people taking the IITJEE and the relatively low number of seats available (around 10k), the success ratio is lower than Harvard.
I agree - that could be the closest to a sound argument, but it's a very superficial one. Someone who claims to be highly intelligent by virtue of their alma mater should know better than to advance such an argument to an educated audience.
OP was not saying anything about intelligence or claiming to be highly intelligent. It was a personal (and very interesting, IMO) anecdote on their experience with math text books.
He said that getting into IIT was more difficult than getting into Harvard, which is a pretty clear claim about the intelligence of an IIT student, and by extension, his intelligence.
The IIT graduates I've met are generally quite smart, but I've also noticed occasional arrogance which can lead them to think, say, and do irrational things, such as implying the superiority of IIT to Harvard, e.g. comparing apples to oranges.
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 practically-oriented as well as late-bloomers who didn't take to math early but would have become reasonable applied mathematicians (I belong to this category). I guess we will never know.
To draw a parallel, one of the criticisms of the French system -- where mathematics is treated as the most important arbiter of intelligence (for grandes ecoles admissions) -- is that other aptitudes are almost seen as secondary. It optimizes too much for a very narrow aptitude -- which is great for producing Fields Medalists, but underoptimizes for talent elsewhere.
In my experience, while the American education system on the other hand is kind of a piece of cake from K-12, it somehow manages to catch up at the college level (more or less). At the graduate level, the differences in ability between a U.S. graduate student and a Soviet-system/Eastern European educated one is largely diminished. And it does this without over-optimizing for any particular aptitude so deep expertise is developed over a broader field in the U.S.
This is an interesting idea. Something that I have been thinking in the context of qualifying the quality of a nation's education program is how these things should be considered given that division of labor is the standard mode of operation. Germany for instance has a highly tracked education system, and consequently it has some world class scientists as well as some very talented mechanics but I suspect neither group is very good at the other's specialty. A country can have poor average math scores but be globally competitive in mathematics as long as some collection of people are trained well. The US for instance is largely terrible at mathematics (on average), but we have also produced a large number of world class mathematicians and scientists because we eventually dedicate serious resources toward training a small subset of the population to do these things well.
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.
> 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.
Yes, indeed. Most people don't realize that the soviets were awful at product engineering. Their consumer-oriented products (TVs, radios, cars) were pretty terrible when compared to their western counterparts. My pet theory is that this was, in part, due to the over-emphasis in theoretical approaches instead of practical applications (that plus the lack of resources and the communist ethos against consumerism).
I'm reminded of the engineer's triangle here: "Good, fast, cheap. Pick two." The problem with a lot of Soviet design was that they always had to pick cheap since there were often shortages of resources. Their designs were fundamentally influenced by scarcity, and it makes it difficult to make anything good, especially if you need something quickly. That doesn't excuse the fact that many designs were knockoffs and terrible in their own right, but it does explain their underlying design choices.
There's an interesting book titled "Made in Russia: Unsung Icons of Soviet Design" that details many examples of this. The one example that always struck me was the Soviet soda machines. They could not waste previous metal on soda cans, so the soda machines came with a communal cup. You put coins in the machine for soda, and it filled the communal cup like a fountain drink. But once you were done drinking you had to return the cup to the machine and press a button to clean it out and make it ready for the next customer. This process seems ghastly and ridiculous but makes sense when resources are scarce. It was the design tradeoff the Soviets made so that soda machines would be available in the first place.
But they were pretty good at engineering things like jets, helicopters, missiles, etc. I think the consume products were bad because they lacked market feedback and had trouble with supply chains, while the military products were good, arguably better than US equivalents in some cases, because of the more top-down, spec-driven nature of that work.
Yes, they were. Their military products actually competed in a "free market": they had strong competition from the US, NATO countries, China, etc. Ironically, this free market competition is what made Soviet weapons as good as they were :) I wonder if they ever thought about it in this way.
My dad had present from our relatives in Canada - basketball shoes (eventually stolen) and a calculator. That calculator pulled a lot of favours over time, he was the only one in town to have one. Dad couldn't believe you could just order anything from catalogue in 70s. Anything the world, you can buy. Such a unreal concept. He also got Beatles LP from somewhere (eventually confiscated from teachers).
It's a good point the access to many basics weren't there. I've finished high school in 2006, got my first PC in 1998. Very quickly I've learned to solve math problems using graphing calculator apps. Cheated my German classes by translating from German to English using Babelfish then to Lithuanian.
The only other time I ever had to do derivatives and integrals was math class at university... while studying for management degree!
I'm a Swede who returned to their native Croatia in the late 90s and early 2000s and found that kids were learning maths on a much more advanced level than we were in Sweden.
I've throughout my life learned that this goes for most of eastern europe. I can't explain why. If it's a more demanding education or if they have some sort of genetic/environmental predisposition for maths.
But the phenomenon has been pretty consistent in my experience with people from Romania, Bulgaria, Russia, Ukraine and the balkans.
One memory that stuck with me was how the village children would come back from their last day at school, beginning of summer, and show off their report cards.
Dozens of happy kids walking along a dirt road with their report cards in hand, ready to show them off to any adult that might give them a few Kuna or candy for the effort.
In a US college in the 80s, the math professors definitely seemed to be in awe of the Russians when it came to this stuff. And though I was in the US, early on I was in an utter hardware wasteland, and I do think that not having much hardware access improved my ability to just sit and think about things with pencil and paper.
Similarly, working on products with no debugger and a single LED for a UI meant that I had to reason very carefully about how the code I wrote worked. If I made a mistake there would be no feedback other than the behavior of the product.
I was taught in university by soviet professors and had to study soviet textbooks and from what I can tell, Soviet textbooks are extremely steep and unfriendly. There is not a single odd word and it even feels like they had to save the paper. Text is often describing schemes that are 5-10 pages before. It takes significantly more concentration to understand the whole thing. It feels like authors used to compete in the precision of information rather than making it more available for someone who is going to read it.
On the other hand, books from USA tend to be more friendly and will first explain the basic intuition and only then dig deeper if necessary.
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.
"Coding up a simulation and having a computer torture it until it confessed the results you wanted certainly takes talent, but it is arguably a different kind of talent than thinking deeply about the problem itself."
The classic answer to this question is that "math was cheap."
The Soviet Union was comparatively poor to the United States, so you create advantages where you can for the least investment. Math and national security are closely linked, aerodynamics, radio communication/RADAR, encryptions, etc. investment in rigor payed them dividends.
My wife’s 12 yr old niece lives in India. Every time I see her, she’s studying all day.
I happened to look at her math books. They had hundreds or thousands of word problems in one year’s cheap textbook. And she had solved ALL of them TWICE over within 8 months. It was unbelievable.
I haven’t seen anything quite like this in America.
Well I went to IIT and our education system is more like Soviet Style education, heck we used the same books for competition prep.
I aced every class always stood first in my class till class 10th and after that my performance dropped till I realized that "I am not supposed to care about understanding a concept in its entirety and solve problem based on only things I've learned however limiting it was". It was first unsettling to me because in earlier classes I always went into depth and tried building my understanding of a subject from ground up but in class 11th, there was no time for all that. I did what everyone does, I basically figured out how to solve problems based on pattern recognition, this literally required no understanding or even how things for together but remembering few rules and forumla and their order, and there you go - I cleared IIT just like that, no coaching or help required.
This literally killed all my love for subjects and it became a "game" to solve problems and acquire points. So I stopped bothering with deeper understanding all together and began having life as in hanging out with friends and girlfriend and only coming back to study when I am in mood to game the system again.
I never enjoyed this kind of labor, slow placed exploration made bigger impact on my mind and I've forgotten most of the things I learned in competition mode.
Thing is those students who feel like they can't build concepts in air without solid roots, they are going to suffer in Soviet Style education.
I'm not sure this is specific to any particular school of mathematical education. There is bound to come a point at which you cannot understand everything and have to start winging it. If you can cope with that, that's good, you are prepared psychologically for research mathematics. And just having learned the patterns will hold you in good stead. But if (as I did) you find the whole thing an insult to your pride then you are only preparing yourself for failure.
India (and a few other places) face this issue to a larger extent, I feel. When the judgement of your education comes via one single competitive exam, you tend to maximize that reward. In the Indian education system (and to similar extent afaik in china, south Korea and Japan), having nationwide tests that are the only factor for university admissions in math and science forces everyone competing to solve for performance in the exam. And it is far easier to do this by learning how to solve problems than by learning the material then using that knowledge to solve problems.
This sort of thing likely led to what one of my Russian professors was pretty proud of: That Soviet microbiologists with some bacteria, a pH meter, and some basic chemicals like sodium citrate could bang out publications, with some well-designed and elegant experiments. We Americans, on the other hand, would spend thousands of dollars on fancy machines, reagents, etc. and were less productive.
Soviet body builders only used free weights and a pull-up bar. You don’t need anything but that to get big muscles. Similarly, you don’t need anything except a chalk board to teach math and most other subjects.
If you think only Soviet body builders were juicing, you are sorely mistaken. FYI I am the furthest thing from an ideological defender of the Soviet system as you will find. I am just stating some truths.
Why is that relevant to the discussion? The GP doesn't even mention anything about others. You are the one saying, literally, "Soviet body builders only used free weights and a pull-up bar. You don’t need anything but that to get big muscles." which is patently false (when we talk about "body builder level" big) and then you get defensive when you are called out on it?
I think it really depends on the time period. During the beginning of decline (past 70s until collapse) very few people really believed in Soviet ideologies and corruption was pretty much at the core of soviet lifestyle.
Though before that I could definitely see any sort of doping would be very un-Soviet.
But you do need a computer to teach programming (generally.) The US has generally been about efficiency, there isn't much need wasting time on paper with a problem when we can understand the concept and solve the problem with a computer. That's my opinion of course, as an American. So I'm biased. When I was taking advanced math classes, my first thought when presented a concept was "how can I solve this by writing a calculator program to do it for me." Maybe that isn't common, I don't know, but while it might not be what everyone does...I think that is the American thinking on learning things.
I actually am very glad that we did not have computers in my school at the end of the 80ies. This was in Lithuania, then a part of the USSR.
We had programming classes, so without the computers we were taught the basic concepts: variables, assignment, conditions, loops. Just concepts in a pseudolanguage. Later, when I had access to the computers learning the languages boiled down to "what's the syntax for this concept?"
And then writing my programs with a pen and paper because I had no computer at home for a few more years.
Now I sometimes shake my head when I see comments like "I do not know programming, which language (or worse—fraamework) should I learn?"
It is so tempting to say "duh, learn programming and worry about the languages later".
Mathematics and problem solving are not mutually exclusive - understanding one is usually a sign you understand the other. Programming is just a layer of abstraction over one of these things.
Using only free weights and a pull-up bar will work. But it doesn't mean it's the most effective way to body-build. You can write a program from scratch in C to perform an task, or you could use all of the tools of your disposal to far more e f f e c t i v e l y complete the task, potentially without code. You don't need anything except a chalk board but there may be more effective ways to obtain the result you are looking for.
I have been working with a trainer for many years, and almost everything we do is with free weights and a bench. Free weights are much more difficult because you need to keep them stable. Machines trick you into thinking you are using more weight, but you are leveraging the machine. The only machines I like are leg press and cable machines that still make you keep stability.
A true bench press with a bar is much better than a machine imitation of the same muscle groups.
It's generally better to work out with free-weights because of the stabilization aspect, yes. Saying that Free weights are better flat-out is wrong in my opinion. Every piece of equipment in the gym is a tool if used effectively and at the right time. Your "core" program will be done with free-weights yes, the other equipment is great for auxiliary uses that compliment your program. Machines are great for end of workout sets because you're likely already fairly fatigued and form may be compromised. You can get that little extra by using machines to ensure perfect form while also safely adding that extra stimulation for the muscle groups being trained.
Is following along and learning / practicing math directly from a textbook still the most effective way to learn math?
Now that we have devices in our pockets and on our desktops with more and more capabilities that have educational use cases such as interactivity and AR, how would a calculus lesson be made in 2020? Could we just go down the street, aim our devices at cars passing by, or cars speeding up from a stop sign, and see how speed, acceleration, and position relate to each other in real-time? Or aim it at a pool table, bounce a cue ball off another ball and see how vector summation can work in real life? Or input the weight of a cue ball, the type of surface (felt?) and then see how the applied force can be estimated based on how fast the cue ball moves when you hit it? Interactive bits like this as examples and practice mixed in with the text?
I think that's a great way to get an intuitive understanding of the concepts, as an introduction to the subject, but at some point you really do have to sit down with numbers and equations and learn the theory behind it all and apply it to examples that aren't constrained by the reality you can physically experience in a classroom.
You would certainly have to sit down with numbers and equations, but that still doesn’t automatically imply that a textbook is the best way. You can derive numbers and equations via an app for example.
My question is this: if you always had the textbook’s author, who is an expert instructor with decades of teaching experience instantly available, in person, whenever you want a lesson or to be reminded of an equation or want to learn more about a subject, at no harm to him and his well-being: under which situations would you opt for the textbook?
To me it feels like a textbook is one way to store and transfer and spread knowledge, but is it automatically the best way to ever do so? Or is the textbook simply one technology, and we are still searching for the best way to teach as many people as possible with the resources and technologies at our disposal?
It's not just textbooks. The whole approach was different. You would be regularly called upon in class to do a problem on the blackboard. You would be graded on the spot publicly. There was no participation trophy type stuff. Teacher could easily make fun of you for not knowing something etc.
When I moved to Canada in 98 from Belarus, I had minimal language knowledge. I was also half way through school year. After my testing was done I was put in to next grade.
Even though I was not the best student in my home country, prolly mediocre at best. With some subjects being better than others, still it was surprising to me.
By next school year I also felt that science classes were way behind what I was used to, and even though I could only read and barely understood instructions, I still was able to do very well in all of my stem classes despite lack of language knowledge. Honestly it was kind of annoying that I had to do things that I already have done in previous grades.
As I have started getting better with English and started paying less attention in class and less to my homework, eventually I fell somewhat behind.
Easy answer: Russia's education was for engineers, US for snowflakes.
Also it extents to CS. It's 10x easier to find competent Russian programmers than in the US. They are dominating the various math contests or chess for decades.
My friend went to one of the best high schools in my country (Poland), where students would, on their own accord, practice using old Soviet math textbooks.
I got my hands on one of them where the task stated was usually something short, like: "доказать тождество", followed by a set of rather insane(at least for a highschooler) equations.
That bit about a dearth of equipment is true in most eastern block countries by the way. Case in point: the other day I asked my younger cousin, who's currently doing his master's, if they still use those multimeters with nixie tube displays like I did ten years ago.
My son started in the Russian School of Math - a pretty popular after-school program in many US cities. What is fascinating is the core theory that algebra can be grasped by children as young as 6. And there seems to be some truth to this given my son's experience.
One random shout-out: I think if more of us learned math from folks like 3 Blue 1 Brown we would love it enough to explore it more. I don't know if I'm smart enough to have become a master mathematician but I find myself falling in love with math with every video he puts out.
It's not just math. Physics too. People from India who went through engineering entrance exams like JEE will have fond (or horrific) memories of "Problems in General Physics" by Irodov (https://archive.org/details/IrodovProblemsInGeneralPhysics/m...). Every problem in there was something to wrestle with.
The International Physics Olympiad and the IITJEE have a high correlation in terms of material required as well as people who do well, it is probably the Olympiad with the highest correlation between Olympiad performance and performance in the JEE.
I feel lots of people have made the point that over time the emphasis on maths has been reduced such that education would be more useful to more people. I.e structuring the maths syllabus such that it would select for the maths super stars does a poor job of giving the run of the mill student much value from their maths education.
I do grad level maths every day but I’ve never stopped being a reluctant mathematician. Sometimes the maths of the problem is insightful and interesting but most of the time what I’m doing is battling to express/validate an intuition in a formal language.
I think that emphasis on maths as a language for the exact representation of your thoughts is maybe what the modern curriculum is up to, as opposed to the emphasis of maths as the language of your thoughts. Just the same way that you might write code to express designs; I think it’d be weird to think in code although certainly some (maybe even the best) do think about software in something closer to code than box diagrams.
What all of this shows is that education and economy are really not very related. This book makes the case:
> The Case against Education: Why the Education System Is a Waste of Time and Money
What happens is that companies just hire people who have proven that they are not dumb enough to drop out of school and just did what they had to to move on with their lives.
In the end the Western countries are richer, not because the students are great, but because they have great opportunity and learn what they need to, so they can get that opportunity.
The Soviet Union really was great at showing this, lots of super smart people, good schools, lots of government investment in high tech, more effective intellectual property theft then China now, cheap natural resources, cheap oil and so on. Jet they couldn't really make a competitive economy.
Teach people the basics as efficiently as possible, show them where they can learn more if they want to, give them some resources to do so if they want to and let them find their way in a market economy.
Heck, that was common knowledge some fifteen years ago during my freshman year. I personally never bought those American coursebooks. For the price of one brick, I could pretty much buy all the required self-study material printed form. After my sophomore year, they did away with the university press anyway and told the professors to just make their materials available in electronic form.
Besides, when you're in uni, you're learning to study, not learning to be hand-held.
Economic reasons aside, I think Soviet educators also believe that rigorous and challenging training will realize the greatest potential of students. The top students are self-driven and usually get the best resources anyway. It is the majority middle that need most rigorous and challenging training to realize their full potential. Unfortunately, US educators in K-12 decided to move in the opposite direction. David Klein's writing told appalling and sad stories of how National Council of Teachers of Mathematics (NTCM) won over the course of last 100 years:
- A quarter century of US 'math wars' and political partisanship
- A Brief History of American K-12 Mathematics Education in the 20th Century
By the way, US's upper-level college course and post-graduate textbooks are hardcore too. If you don't believe me, go check out the Graduate Texts in Mathematics.
My dad took the advanced courses for physics, math, organic chem in first year University of Toronto in 1970. I've seen his textbooks and they were on the same level of this. Much more advanced than what I saw in the 90s/00s. More focus on reasoning from first principles, less focus on easily approachable material.
Basically I'm saying that baby boomers had more advanced textbooks in their university period compared to what their kids got in the 90s/00s. But also less people went to university back then, it was more rigorously academic back then.
> because of the traditional scarcity of equipment, Russian students and scientists had to think rather than experiment
This heavily resonated with me. Early in my career (late 90's - early 00's), I had to develop the skill of dry running (basically running a given block of code with given inputs in my head and predicting the outcomes) because of scarcity.
I was in a domain where I had to build 100,000+ lines of C++ into a single executable, manually deploy to a remote Solaris machine and wait for up to 5 minutes for system re-initialization before I could run a simple test.
Needless to say, we learned to predict what our code does as we wrote it. The idea of unit tests re-running automatically as you write new code in the IDE would have been dismissed as an unattainable heaven (or maybe even considered downright satanic).
I had a student from the Soviet Union in my class. He said they had no funding for all the nice things we had in chemistry class. But that the difference was that he had never seen so many people unwilling to learn anything, as he had noted of American students.
Easy answer: Russia's education was for engineers, US for snowflakes.
Also it extents to CS. It's 10x easier to find competent Russian programmers than in the US. They are dominating the various math contents or chess for decades.
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 <concept> and if you think about it if <assumption> then <theorem>“).
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.
All the answers (and discussion here) seems to take the title question as fact. My initial reaction was - and I should say at this point I'm neither from nor live in either country, and have no national pride or whatever to be wounded by who has the harder-core textbooks - are they actually? Or do they just cover different material, that the US curriculum happens to get to later?
It's a pity Quora doesn't have a question 'body', like StackExchange does for example, such that the asker could've given an example.
The real question should be is why are US textbooks so hard when most people never need HS math after finishing school, and lack so many other skills that are never taught.
It alway baffles me when I see "why don't they teach how to do taxes?". Well they do teach you how to read and hiw to do maths? How hard it is the to put 2 and 2 together?
Taxes and maths are two very different things. The math part of taxes usually is easy, what's complex are the countless rules around it, e.g. what can be counted as a deductible expense and what not - additionally, most rules don't even make logical sense as they were written for political reasons (i.e. to appease one or another voter/corporate interest group).
Thinking is an important skill, which is why scientific experiments, essay writing and philosophy are so important. Integrating equations, not important.
Because Soviet math textbooks target a different audience: those kids who really enjoy math and derive pleasure in a bit of complexity (think Sheldon Cooper from BBT). You can call them elitist. Nobody cares about the other kids.
US textbooks, on the other hand, are targeted towards more general audience--the average student. That doesn't make them bad, just different.
Most American grad level math textbooks are as hardcore as it gets; undergrad, not so much, especially compared to such introductory texts as, say, Beginner's Course in Topology: Geometric Chapters by Rokhlin et al. which, I’d say, is extreme in its hard-coreness. (A popular text by Munkres, by comparison, is a children’s book.)
I don't know about the Soviets, but American books always seem to take longer to say less than other countries texts. I think it's a volume thing: Americans see 400 pages and think it must be twice the product of a 200 page alternative...
My father always told me that American textbook authors got paid by the page. That's probably not true, but it certainly feels that way when reading them.
Curious, with 2 smaller grade school children in the Midwest, that I am now "home schooling" during the pandemic, I find the teachers spend minimal time on math and I have to supplement them...a lot.
With the revolutions, the system was simply expanded, not created from scratch anew. So you would have the methods used to teach the elites be the foundations of the new system.
I can't speak for China, but in India there has not been a historically large amount of attention paid to writing textbooks in mathematics and physics. During high school, the students who seek challenging problems often fall back to Russian text books, especially in physics. More recently there has been a push by some Indian authors, so you will find some challenging texts by Indian authors, but still nowhere close to say Krotov or Irodov for physics.
I moved to Romania three years ago, and was surprised to find the same kind of specialist/vocational high school paths have been in use a long time in this country. Once you hit teen years you might find yourself, if you worked hard enough, in one of the more prestigious specialized high school institutions for one of many subjects, such as architecture, medicine, physics or the arts.
It seemed to me a huge pressure to put on such young shoulders, to commit to a career path so early, but that's the aptitude-based system that dominated under communism. Since the schools are so prestigious, much of that system still remains.
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.
The answer points to ingenuity due to a lack of resources which is susceptible to obsolescence.
School in the USA does a lot more than just educate, for instance child protection services and employment. The USA also takes everyone, specifically the violent and malicious, due to compassion.
The USA suffered:
- multiple World Wars
- a fifty year Cold War that was just as bad
- multiple nuclear standoffs
- horrific terrorism
- black market drug smuggling, probably the gravest problem today
- repeated invasions
- a Civil War which involved foreign intervention
- attempts at colonial occupation
- originally being made as a death camp and penal colony
America did this too. There was the New Math trend in the 50-60s which feels like common core. Here's a comedy song about it from that era.https://youtu.be/UIKGV2cTgqA
New Math was very far from Common Core. New Math included generous coursework on abstract algebra and discrete mathematics, both of which are almost entirely ignored in Common Core. Common Core is carefully considered, but pretty traditional.
Common Core is still a good curriculum for the minimal level of math US society wants primary and secondary students to learn. But it's not nearly expansive and innovative as New Math was.
I think it comes down to communism. According to Marx's book "The Machine" the end game of communism is essentially an omnibenevolent AI. Marx thought eventually all forms of labor would be mechanised into a colossal machine that would run the world. Thus, the whole point of education is to train the geniuses in math, science, and technology in order to bring about this machine god. That's, in my opinion, why there is such a huge emphasis on those subjects in the Soviet system. All the other subjects are full of questions and speculation, and in general seem useless from that perspective once you believe you've reduced the aspirations of the humanities' longing for justice and truth to an engineering problem to solve.
That’s fascinating... and somewhat terrifying. Because it seems clear to me that it won’t require communism or totalitarianism to achieve that kind of endgame (or at least, to get really close to it).
Perhaps the communist/totalitarian/power-hungry nations of the world are sitting back and waiting for us in western nations to build such a system (think AWS, but 30 years from now). All they have to do is get complete control of it by one method or another, and then they’ve won.
One would think a proper national defense-in-depth mindset dictates carefully considering and planning for such a future.
"once adopted into the production process of capital, the means of labour passes through different metamorphoses, whose culmination is the machine, or rather, an automatic system of machinery (system of machinery: the automatic one is merely its most complete, most adequate form, and alone transforms machinery into a system), set in motion by an automaton, a moving power that moves itself; this automaton consisting of numerous mechanical and intellectual organs, so that the workers themselves are cast merely as its conscious linkages"
I don't think it makes much sense to say this is a state of affairs Marx would want to see in a communist society; to be honest, I have no idea where you get the idea that Marx envisioned a totalizing AI controlling society from. The Fragment on Machines is highly debated and analyzed in Marxology, but it doesn't imply what you think it implies. Marx's description of communist society is actually quite the opposite (from his TGI):
>He is a hunter, a fisherman, a herdsman, or a critical critic, and must remain so if he does not want to lose his means of livelihood; while in communist society, where nobody has one exclusive sphere of activity but each can become accomplished in any branch he wishes, society regulates the general production and thus makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, criticise after dinner, just as I have a mind, without ever becoming hunter, fisherman, herdsman or critic.
Post-Marxist authors and other Marxists have quite a lot to say on machinery and totalization of society to administered control (which they view as a negative thing) - see Marcuse for instance.
Wouldn't having an omnibenevolent AI providing for everyone's needs free everyone from having to be a laborer, so anyone can choose to be one thing one day and another thing another day? I see my passage and yours working together.
From what I understand, Marx didn't see communism as subverting capitalism, but as the end result of capitalism. He just wanted to hasten the process along towards an outcome which he saw as already predetermined by economic forces.
Dan you continue to be a Nazi ideologue in the service of sociopaths. I have tried for years to help you but it's hopeless isn't it. You won't stop sucking their ass in the promotion of fascism. You horrible piece of evil.
I wish you would get what you have created for yourself but there is no justice. The innocent will be oppressed by the elitist liars you support as a sycophant and justice will never prevail. It's horrible. You could switch sides but they are tossing bones at you and you will sell out the good for a tiny token. It's horrible.
My compliments on your patience in the face of some really vile personal attacks. So far as I could tell, you never lost your temper, and you gave far more grace than seemed deserved.
Personally, I gravitate towards grayed-out comments. I think that they tend to be likely to be on one or another extreme side of the intellectual bell curve. Basically, they end up grayed out because either they are too dumb or too smart for the average Hacker News user. So if I manage to run an effective mental filter to discard grayed-out comments that are on the low side of the intellectual gray curve, then gravitating towards grayed-out comments makes it more likely that I am exposed to content that is in the highest intellectual range of Hacker News comments as a whole.
Thanks for the tip about "showdead". I totally agree that there's a big danger, if one follows the strategy I described, of personal bias making one confuse "intelligent" with "what I want to be true" or with "what I enjoy because it is contrarian". However, I am aware of this danger and work to mitigate it in various ways. Also, I should mention that I don't think that grayed-out comments are 0.5 likely to be highly intelligent - I'd say it's more like about 0.1 or 0.2. Overall, I think that the benefit of prioritizing grayed-out comments, to me, has been worth it so far.
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 separates Soviet Union (and now Russian) system is the practice of selecting kids with interest in mathematics / physics into special classes or schools for gifted kids. This government program feeds the mathematics and physics departments in the universities and allows kids who go through this program to get a very early start in mathematics. This is very similar to government sponsored sports programs with talented kids getting help with summer camps, or even all year round training schools.