This was a surprisingly interesting and well-written article. I hope people read it and not just the comments here :-)
I'm unsure if it implies that "lame school exercises" are unnecessary or just not sufficient (I've recently read articles about how teaching "insight" without exercises is detrimental, though perhaps doing problems implies getting that repetition-work).
Does anyone have good experiences with keeping kids math-interested as they get into their teens? My kid used to enjoy math in school, and love talking about math problems ("can you help me set up that triangle pyramid thing with the sums again"), but now is seemingly disillusioned and finds the school exercises boring. Combine that with, well, teen-age, and I fear it's going to be hard to get back the spark. Not that it has to come back, but I'd hate for the interest to turn into dislike due to lack of opportunities.
My biggest issue with math education is that after we learned the theory we never went back and developed an actual plan for solving the problems. For example, we learned a dozen different ways to approach integration, but after all this we never really put together a workable strategy for approaching a problem and deciding what tools to use.
It's like trying to teach someone to swim by just throwing them in the water over and over and expecting them to eventually figure it out.
As a result, the primary emotion students learn to associate with math problems is fear. Instead of the sense of confidence that comes with having a plan, each problem feels like "will things work out or will I get lost and waste hours without actually ever finding a solution".
I would say the opposite, we're teaching them how to swim (the exercises the article talks about) without a swimming pool (real problems).
The best strategy is one suited to you because you came up with it yourself, in my opinion. Other than the big kludges (u-substitution, etc.), teaching specific/mechanistic integration processes directly would have been an uncomfortable way for me to learn.
A more structured approach would definitely help! And I think that's the reason why ao many are affraid of math
you face the exact same problems with coding, arguably more so as the trial and error and debugging process is worse than any proof i’ve ever had to do. if you can’t figure out how to apply basic integration techniques without a teacher formally sitting you down and saying exactly what situations to use each formula in, you haven’t learned shit
Axiom Maths is trying to import the concept of maths circles to the UK, providing support and materials for schools to host their own circles.
It is run by a team with deep expertise in mathematics education, including the founding head of King's Maths School, a state school that is one of the top performing sixth forms in the country.
Practically speaking (running a little maths circle in the UK for my children, and some of their friends from nursery and primary school), I have found the Nrich website to be the single best source of resources: https://nrich.maths.org/about-nrich
There is also https://parallel.org.uk/ by Simon Singh, but this is aimed at ages ~10+.
The book by Rozhkovskaya has some really nice activities in it. https://www.amazon.co.uk/gp/product/1470416956
The book by Zvonkin described in the article is a very good motivator, particularly for the honest descriptions of lessons gone badly wrong, and staying up late cutting out pieces of cardboard! But it's quite difficult to use as a teaching resource.
A nice source of middle- and high-school aged problems: https://www.usamts.org/
One of the joys of high school was discussing these with a friend (after submission---but one could forego the contest and just do the circle thing with them for fun).
When my kid was three I encountered this lovely book and thought I'd read it to attempt to replicate something like it (despite all the warnings that it's a journal and not a guide); unfortunately I never got around to finishing the book (nothing against the book, just got distracted) and now the kid's already past seven :) But what little I read was delightful; thanks for posting this summary!
I have a similar experience. The book skips the first 20 weeks. Many of the activities require materials and I could have benefited from a more prescriptive curriculum. Some other math circle curricula are not as inspiring but are much easier to follow.
The book skips the first 20 weeks for the boys but covers those activities for the girls (around the end of the book). So I'd suggest reading the girl circle and then coming back to the boys circle... I've absolutely loved that book and I've been trying to incorporate some of the ideas in games with my son.
That said, do keep in mind that despite being from 3 to 7, his son is actually 3 years old and 10 months when he started (and I think the same for the daughter, I forgot). Personally, I've noticed that my just turned 3 years old son is not developmentally ready for a lot of the activities yet (but he's been surprisingly good at other activities), so I do think that you need to adapt depending on the children you try this on.
Yep, I thought the idea seemed cool, but I couldn't figure out how to execute it.
A couple of other books that I think are useful and easier to execute than Zvonkin's books are the books by Christopher Danielson. Which One Doesn't Belong? is great to play with a child and Talking Math with Your Kids has some good ideas (way too short though)
It ends like this, largely cancelling out the rest of the article:
>In the second iteration of the circle, all of his notes are completely useless, and all of his initial attempts to teach anything fail, because these are different kids with different aptitudes and different interests. Zvonkin, raised in a communist society and a believer in the absolute malleability of human nature, is fairly bowled over by this, especially by how young all these differences are manifesting. Reading between the lines, it sounds like he got quite lucky with his first set of children, and that the second group were much more challenging to teach.8 The most eloquent testimony to this is that after about a year he gives up, and the journal ends abruptly.
I would say in a nutshell, teaching results:YMMV
omg, 'midwit teacher deducts marks for failing to write answers in a designated format'
this is exactly the math teacher my kids have. So frustrating.
In this country many teachers have been taught that it's important for kids to be able to use a range of approaches to solve a problem.
They then force them to use each of the prescribed set of methods even when they are totally inappropriate for the task. Any deviation from the method they are told to use for that question is wrong. No creation of your own adapted methods is acceptable.
In other words, the teachers were taught that kids should use different methods, but seemingly weren't taught why.
I have this book, it's a fun read but difficult to replicate on your own. Tried on my children but it's hard work and I'm not a mathematician like the author and the society is different.
> All joking aside, we fledgling mathematicians understood that the single most important thing was not raw intelligence or knowledge (Americans tend to lag behind in the latter compared to all international students). What mattered was passion. The way to become successful in mathematics, like almost every endeavor, is to care about it, to love it, to obsess over it.
This is the most important point from the article. My theory is that if you are not obsessed with something, you won’t be good enough with it, wether it’s a math, coding, business or something else… Thats how most of us got started in tech from the early ages.
It depends on what you mean by “good enough”. Most developers today aren’t particularly passionate about it, and certainly not obsessed, but the demand for them is high enough so they still are “good enough” to have relatively cushy jobs.
That's a good point, but it can also be that the employer is satisfied with the "good enough" results.
While it is true that the current high demand on a job market allows many to have "good enough" skills for employment, I would argue that passion, curiosity, and obsession are the driving forces that lead to better outcomes both for individuals and the industry as a whole. These qualities inspire deeper engagement and lead to more quality work. For routine tasks, basic competence might suffice. However, for solving complex problems, it won't...
Passion/curiosity/obsession often leads to voluntary, extensive practice and learning. This typically results in faster skill acquisition and a deeper understanding of the subject matter. While becoming competent without any of these is possible, the path is often slower and limited.
Also, both the tech industry and the job market are evolving rapidly. Passionate/curious/obsessed developers are more likely to keep up with new technologies and methodologies, potentially leading to better long-term career prospects and adaptability. The pace of change in our industry demands a continuous hunger for knowledge and a relentless pursuit of excellence.
In the end, if you don't want to be a mediocre developer with a mediocre career, such stuff matters.
As a teenager who dislikes the current schooling system, what I am most curious about is actually why something like the "mathematical circles" do not exist in the west.
To some extent, a similar social group is formed by robotics teams in my experience. A dedicated teacher/coach and a bunch of people who like electronics can really get amazing things done. Why is this the case?
I am under the impression that such things do/can exist, but ad hoc. For example, if you were to take extracurricular lessons at a RSM or similar private tutoring business, you could/would probably find a number of similarly inclined teens who might be interested in creating a circle.
Similarly, my experience attending a science & math magnet school in the 90s was that -- basically mirroring my later experience in college -- a subset of the kids taking advanced math classes in high school naturally tended toward hanging out & studying/practicing/researching together.
More formally, there are tons[1] of local, state, regional and national math competitions that target elementary, middle and high school students, and -- just like robotics -- it's up to volunteers (teachers, students, parents) at the school level to decide whether to invest time & resources to create a local team/club.
When I was in school, we had MathCounts teams at younger ages, and Math Olympiad (and Science Bowl & Science Olympiad -- my team made it to the national event in Science Bowl, actually) in high school. I'm under the impression that this is pretty common, at least in urban/suburban areas.
[1] https://artofproblemsolving.com/wiki/index.php/List_of_Unite...
Maybe you already know or could try to find other peers who like math, and see if you can get something started? I think there's a good chance that if you approached a supportive teacher with "my four friends and I want to start a math club, can you help us?", it would get the ball rolling. Perhaps you could put something up on the bulletin board or equivalent you kids have these days, data kiosks or hovergrams or whatever.
Why not join the robotics team? Plenty of problems like inverse kinematics and probably newer mathematical approaches.
I think this must be a very stupid question, but I’ll ask it anyway. I always thought the Soviet Union was smaller than the US population wise, and really did punch above their weight. But Soviet Union census of 1970 lists 241,720,134 people, while the US census of 1970 lists 203,392,031 people.
https://en.m.wikipedia.org/wiki/1970_Soviet_census
https://en.m.wikipedia.org/wiki/1970_United_States_census
Is this statistic somehow not representative?
If so, what’s up with that?
If not, is the belief that the Soviet Union was smaller than the US population widespread and wrong? If it is widespread and wrong, where’s it come from? (Although, I must admit the possibility that it isn’t widespread, and was just unusually wrong. In which case the answer is just that I’m unusually bad at geopolitics, which would not be surprising at all).
The OP is wrong. The USSR had a larger population than the US by around 20% from 1950 to 1990: https://www.cia.gov/readingroom/docs/DOC_0000380594.pdf
Chances are he's only counting the population of Russia proper, which would be a bit like only counting the US East Coast population.
My guess is rather that he's conflating the US with US + Western Europe.
And then you can make the appropriately similar conflation of USSR with Warsaw pact countries.
Probably just conflating Soviet Union with Russia, which does have a smaller population. The Soviet Union encompassed so many more countries.
To be fair, the US and Western Europe were a somewhat combined bloc wrt. trade and being allies. So in that respect the combined USSRs population is smaller? But purely US v USSR, the latter has always had more people
The SU and Eastern Europe countries were also such a 'combined block' though (both for trade via COMECON and militarily via the TFCMA (aka 'Warsaw Pact'). Although AFAIK Western Europe had a much higher population than the Eastern European socialist countries.
But in general, the education and health care systems were usually the 'flag ships' with easy and free access for the 'working class' (which also means extreme discimination against anybody else though).
I don't think anybody except you thought it was smaller. Why are you suggesting theres a widespread misconception instead of the more likely alternative - you made a mistake?
The article strongly implies this.
> These days, the same scenes are dominated by Chinese and Indian kids. But China and India have large populations — the Russians were punching way about their weight, demographically speaking.
Also
> Well, with the Soviets it all went in the opposite direction: they had a smaller population, a worse starting industrial base, a lower GDP, and a vastly less efficient economic system. How, then, did they maintain military and technological parity1 with the United States for so long?
Even Napoleon's weapons were vastly superior to the Russian ones at the time... oh, wait :)
I did cover that option. Although, the thing that brought it to mind is the fact that the author made the same mistake.
USSR was feminist in some regards. Women had women-only spaces to learn math and science. There is a lot more equality of performance in STEM in former soviet populations.
Also a huge drinking problem that is not entirely but mostly concentrated in men.
As mentioned in the article, that might be completely explained by their comparative poverty.
> This theory is related to the curious fact that, on average, the more feminist your society, the fewer women there are in math and science — which makes total sense if you assume that on average women are good at math but uninterested in it.
This isn't a complete explanation: we can see this by looking at other STEM fields. The early years of computer programming were dominated by women, yet nowadays, women are proportionally uninterested. You don't get such a dramatic demographic shift because of innate tendencies, but this was contemporaneous with a shift from programming being considered low-status to high-status work. Is this perhaps social, rather than directly economic?
To take an example from elsewhere in the thread (https://news.ycombinator.com/item?id=41718072): I can see the “you must use this method” prescription hitting girls harder than boys, since girls tend to drift towards copying / collaborative play, and boys tend to drift towards competitive play. This prescription might make mathematics seem less like play, to girls – which would be ironic, since real mathematics is an incredibly collaborative endeavour.
(Which raises the question: do girls inherently prefer copying play, and boys inherently prefer competition play? Who knows? I suspect not, but I think it'll be a long time before we find out.)
> The early years of computer programming were dominated by women, yet nowadays, women are proportionally uninterested.
We eliminated the job women were dominating (programmer) by combining it with the one men were dominating (analyst).
At the same time law and medicine were seeing huge increases in the proportion of women practitioners, so the status thing doesn’t make a ton of sense as an explanation. Besides, it was not high status in the 80s when this was going on (or the 90s… arguably it’s still not, just high pay)
The author raises an interesting question as to how the Soviets produced so much scientific talent, but his discussion of math circles strikes me as more of a tangent than a convincing answer. Were these math circles really so widespread, and were they a big part of producing mathematical and scientific question? He doesn't address this. However, the book he is reviewing is available online [1] and I see from skimming it that Zvonkin says only one of his students ultimately chose math as a profession. My hunch is that the structure of the formal education system in the USSR played a larger role.
And that one was his own son, if memory serves. Genetics and family culture may play a big role.
Another girl, not his daughter, from the girl's circle also became a mathematician (whereas the daughter is a professor of film studies). So, yes, genetic, family culture (most of the parents of the kids from the math circles were teachers or academics), interests...
The real answer is that we (I speak as a Russian) didn’t have such advanced computers in the USSR. What was routinely solved numerically in the US, had to be painstakingly traced analytically, and new methods had to be developed for such approaches, and mathematical education had to be boosted so enough people could work in the field (mostly developing new weapons, sadly).
It's all part and parcel of a deeply mathematical culture.
"Math as a profession" is a limited subset of "professions that rely heavily on math", despite what some mathematicians might say.
[flagged]
If you study much of 20th century mathematics and physics, you'll certainly find Soviet mathematicians showing up everywhere. Control theory, probability, nonlinear differential equations, etc. Just from the names of theorems alone, it's pretty hard to miss.
The Soviets produced a lot of outstanding mathematicians.
It's remarkable in absolute terms and it's even more remarkable considering that Soviet education was generally anti-science for much of its existence (e.g. see [0]).
IIRC Stalin eventually left a group of mathematicians and physicists alone because it was clear that if they were suppressed the Soviet Union couldn't win wars or plan the economy.
My initial hypothesis would be that creating this kind of playground in the otherwise dismal intellectual atmosphere, combined with the ability to select the best people from all over the empire, and the urgency and funding that came with the wars and cold war, played a major role in their ability to do important work.
[0] https://en.wikipedia.org/wiki/Repression_of_science_in_the_S...
They invented space ships, for one thing.
Russian was a scientific power in the 19th Century before Soviet Union, and continued during the Soviet era. The west had limited access to it, due to the Cold War.
https://en.m.wikipedia.org/wiki/Science_and_technology_in_Ru...
Soviet Union wasn't called a superpower for nothing. USSR had many world class achievements in scientific and applied areas, and some organizational achievements in social and manufacturing areas. There are examples and counterexamples, but the result is what we have, and while at some areas ex-Soviets were seen as backwards people in early 1990-s, in some others they really brought some positive advancements to the West - or First World - when the borders became open.
This is one example, and there could be many - both where USSR had an edge and where it was behind. I believe here we want to have the overall picture - and that picture was that there actually were some novelties which were interesting on the West, even though in overall quality of life and some associated parameters USSR was notably losing. Or, saying it from another end, USSR wasn't advanced enough to avoid dissolution after - not necessarily caused by - the Cold war, even though it had some achievements unavailable on the West.
Lol what
Quantify in my opinion requires qualify because, how many is "a lot?" But broad strokes, the USSR was an intellectual powerhouse. Add as many "in spite of"'s as you like, but in my opinion the "a lot" target is achieved. You mention science and I'll get to that, but I want to first target what I feel is a general misconception of the Soviet Union as like, a bleak concrete-ridden, muddy backwater of labor camps (it kinda was of course) with nothing to contribute to the world.
Post revolutionary periods always produce fantastic art, literature, and social experiments. See post-revolutionary American religious scene for an example. In the Soviet Union, there's a clumping of great literature around 1917. Summary: https://en.wikipedia.org/wiki/Russian_literature#Early_post-...
> The Imaginists were post-Revolution poetic movement, similar to English-language Imagists, that created poetry based on sequences of arresting and uncommon images. The major figures include Sergei Yesenin, Anatoly Marienhof, and Rurik Ivnev.[65] Another important movement was the Oberiu (1927–1930s), which included the most famous Russian absurdist Daniil Kharms (1905–1942), Konstantin Vaginov (1899–1934), Alexander Vvedensky (1904–1941) and Nikolay Zabolotsky (1903–1958).[66][67] Other famous authors experimenting with language included the novelists Boris Pilnyak (1894–1938), Yuri Olesha (1899–1960), Andrei Platonov (1899–1951) and Artyom Vesyoly (1899–1938), the short-story writers Isaak Babel (1894–1940) and Mikhail Zoshchenko (1894–1958).
Sorry for the big copy paste, but, there's just so many of them, and to literature nerds, what they did was "groundbreaking." I know it sounds silly but let us literature nerds have our thing.
Then there's a bunch of fun leftist / communist poetry, from Vladimir Mayakovsky and Nikolai Tikhonov (the "Could nails from such people be fashioned" guy).
And on and on. Art had some interesting characters as well, "in spite of" the Socialist Realism thing. Isaak Brodsky, for example.
Re: science, as someone else linked, efforts were hampered slightly by the repression of science that was perceived as in opposition to dialectical materialism, but in general the Soviet Union seemed very determined to create a lot of engineers.
You have Fields medal winners: Grigory Margulis (interestingly he suffered from the Soviet antisemitism mentioned in this article), Vladimir Drinfeld, and Sergei Novikov. And you have nobel prize winners such as Nikolay Semenov, Nikolay Basov + Alexander Prokhorov, Pavel Cherenkov (the Cherenkov radiation guy) + Ilya Frank + Igor Tamm, Leonid Kantorovich (basically invented linear programming), Pyotr Kapitsa, and Lev Landau.
Then there's the obvious such as the fact that the Soviets were first to put a satellite in orbit, first to put a human in orbit (arguably far more useful than putting a human on the moon, though putting a human on the moon is probably more inspiring).
What is interesting is how during the time these may not be "contributions to science" due to the USA and the Soviet Union often not sharing advancements in science with eachother because of the Cold War. Imagine if the two nations had been cooperating with eachother. Then again maybe there wouldn't have been a "Space Race."
Regarding Soviet prowess, I always considered the fact that going to higher education considerably shortened and made easier your military draft term to be a main factor.
Everyone who could went to university, because why wouldn't you? This incentive pressure and selection bias we're probably insane.
That and even better: it opened the doors towards a lot of the better jobs, both in terms of working conditions and offering some amount of breathing room.
Education was a more significant social elevator in the East than in the West, first and foremost because the ground level was much lower.
The main cultural difference is that Americans don’t value maths and physics as much as they value law and business. Harvard Law school is still the thing you aim for when you’re a smart kid. MIT is what you aim when you’re good AND you’re really into it.
In France, the top thing to do is go to Polytechnique, which is an engineer school created by Napoleon. So culturally French people push their kids towards learning maths.
It is so interesting that those are always so country-specific here in Finland it is Medicine and industrial management.
the provenance is unclear, but somehow Napoleon wound up with both a construction problem and a theorem to his name
(if your kid has neither aptitude nor taste for maths, what do you do? push them towards ENA?)
> if your kid has neither aptitude nor taste for maths, what do you do? push them towards ENA?
Usually business school, HEC is the second highest viewed thing. ENA is something you may do later, either after political science studies, or after polytechnique, or business school.
Those hyperlinks to other relevant content seem especially devious from this author. I have dozen new tabs of reading open now.
From the book being reviewed:
> All joking aside, we fledgling mathematicians understood that the single most important thing was not raw intelligence or knowledge (Americans tend to lag behind in the latter compared to all international students). What mattered was passion. The way to become successful in mathematics, like almost every endeavor, is to care about it, to love it, to obsess over it. And in this, Eastern Europeans had a clear superiority, a cultural advantage. They had been trained, from an early age, to love mathematics more intensely.
IMHO this is what drove American superiority in software engineering for several decades. The people who self selected into software engineering really loved the field.
I suspect we'll see a continuous slow decrease in all aspects of quality of software as those who have a genuine love and passion for the field are replaced by those in it just for the money.
Good example of passion from early bell Labs: https://www.youtube.com/watch?v=tc4ROCJYbm0
Other examples I can think of (from my Gen Z experience, growing up in SoCal):
- Elementary school: Making custom action replay codes, hacking game saves with programs, CheatEngine/memory/hex editor and following YouTube tutorials, Javascript "document.contentEditable=true" hack and changing stuff on websites, pressing F12 and changing random javascript code until something interesting happens or breaks.
- Middle school: making sites on Weebly/freewebs, embedding chats and flash games on them, sharing them during computer class
- High school: Making PHP sites/vbulliten/Newgrounds/flash games, later iOS apps
I wasn't the only one doing these things. There were always like 3 other kids like me in any classroom that would do the same things.
Most of us ended up becoming passionate SWEs, besides one that became an accountant.
> I suspect we'll see a continuous slow decrease in all aspects of quality of software as those who have a genuine love and passion for the field are replaced by those in it just for the money.
And that's exactly how progress looks like!
When you need to know 6502 assembly to make a game, only geniuses can make games. When you can click one together in Roblox, game development opens up to many more people.
So the average game developer won't be as smart. But that's not because the new tools make us stupid.
The same applies to any kind of software. (Or photography, or music, or movies, etc.)
The average quality might go down when the floodgates open, but with modern tools the geniuses can produce even better stuff than before.
Hasn’t that happened already? As someone who started coding a long time ago and who did it for fun, I’ve seen the industry move from enthusiasts to mainstream and finally to massive comp optimisers who spend more time on angling for a promotion than building.
I’ve fallen in and out of enjoyment of engineering many times. But I still come back because I love making something that adds value.
There will always be space for the builders who give a shit.
As someone who has needed to hire quite a few developers, I will say that the biggest communality of the greatest software engineers are those who are in it for fun. So I ask about side projects, I ask about what they did as kids, I ask about what they're excited about... Someone who is just there for the money can be great in a bigger company but has no place in a startup.
You say it like trying to get paid well is a bad thing?
No human on earth doesn’t want to get paid well. Some are purely mercenary. Those I would prefer not to work with or hire.
(There are a lot of caveats. Someone might have always worked for jerks and has checked out, etc.)
I like to be passionate about what I am doing, but there's plenty of great projects / companies to work for. So might as well look after the money, too.
(Generally, the companies that can afford to pay you well, are also those that can afford to treat you well.)
> IMHO this is what drove American superiority in software engineering for several decades. The people who self selected into software engineering really loved the field.
People in the Soviet Union had much less access to computers than in the US. And the first years after the fall of the USSR were quite lean for the vast majority of the population. Only by the late 90-s people in the xUSSR started getting enough money to buy computers en-masse.
> Only by the late 90-s people in the xUSSR started getting enough money to buy computers en-masse.
Well that, and computer continued getting ever cheaper.
> I suspect we'll see a continuous slow decrease in all aspects of quality of software as those who have a genuine love and passion for the field are replaced by those in it just for the money.
This seems narrow minded. In the early days of software development, the barrier for entry was incredibly high. The possibility of people making high quality, unique software is greater than it ever has been.
It's also narrow minded to insist that only passion for engineering itself can produce high quality results. It's like claiming famously wealthy musicians can't and don't make remarkable, impactful music.
> It's also narrow minded to insist that only passion for engineering itself can produce high quality results. It's like claiming famously wealthy musicians can't and don't make remarkable, impactful music.
I think you're making a logical fallacy, or at least you seem to be implying that the set of "famously wealthy" people is disjoint with the set of people who are passionate.
Sure, famously wealthy musicians can make great music. So can poor ones. But I haven't seen a lot of lazy, uninspired musicians make great music.
> But I haven't seen a lot of lazy, uninspired musicians make great music.
that almost sounds like a joke setup. ;-)
I never said anything about laziness, so I’m not sure why you’re adding that qualifier. I take it you believe that without pure love or enjoyment in something, a person could only be lazy.
Inspiration doesn’t require passion for the art to come first, or even at all. Look at Gene Simmons. He co-founded one of the most successful, influential rock bands ever, driven by the goal of becoming rich and running a successful business, not by an unadulterated love for music.
I was looking for an antonym for "passionate". You're right that "lazy" doesn't quite capture it.
> Look at Gene Simmons. He co-founded one of the most successful, influential rock bands ever, driven by the goal of becoming rich and running a successful business, not by an unadulterated love for music.
This is a good example because while Kiss certainly has popularity, few of their songs are really loved for their musicality. Kiss' music is more about being a good time than good music per se.
Sort of like how Garfield is an effective comic product but not actually really funny in the way that other comics are.
In both of these cases, the creator is passionate about something and working hard at delivering it. They're passionate about providing a certain product experience, and less so about "art" (for however you want to define that).
But imagine a version of Gene Simmons that didn't have the passion to master playing the bass and also didn't have the passion to grind every day at making Kiss a world-known rock band. That person isn't someone you'll ever hear of.
> the barrier for entry was incredibly high
Hmm, for some values of "incredibly".
John Carmack, a juvenile delinquent, dropped out of university and went on career programming, soon upending the game industry.
Linus Torvalds released Linux while being a university student, five years before obtaining a master's degree.
Vitalik Buterin dropped out of university and created Etherium, funded by a grant from Thiel foundation. Whatever you may say about cryptocurrencies, Etherium is a nontrivial piece of software, showing remarkable longevity in the fast-moving field.
None of them had a ton of formal qualifications. None of them had to obtain a license. They could just sit at a computer, write great software, and release it to the world, changing the world quite much.
What they all have is a passion for (and resulting deep knowledge of) computers, mathematics, logic, plus independent thinking, and, well, not asking for permission.
This is what a low barrier to entry plus universal availability of powerful tools (computers, compliers, etc), and books leads to.
(High barriers bring very different results: look now many small aircraft still fly with engines designed in 1950s, burning leaded avgas. A worthy challenger still fails to step over the sky-high barrier.)
For Carmack and Torvalds, I’d argue the barrier to entry was still very high at that time. Both had the opportunity to attend university, which in itself gave them access to people and resources they otherwise wouldn’t have had. Additionally, they had access to personal computers when almost the entire world did not, along with the time and resources to focus on their interests. They were extremely fortunate to have that kind of privilege.
As for Buterin, I have no idea who they are, so I can’t speak to them.
> IMHO this is what drove American superiority in software engineering for several decades. The people who self selected into software engineering really loved the field.
IMO it was funding that made the difference. People outside of USA did not have any less passion towards the field.
I think the comment you replied to is not so much comparing USA vs rest of the world, but USA then and now.
Any amount of funding gets immediately sucked into the abyss. The entire mathematical research community in Soviet Union probably cost less than a series C startup.
The only sense in which this is true is if choosing that field is a death sentence relative to other society outcomes due to lack of resources.
Survivorship bias. Eastern Europeans are actually very bad with math, no better than your regular American. But immigrants you see were very really motivated to leave the post-Soviet hell, so they had to show excellent results.
Math is taught horrifyingly badly in Eastern Europe. It presented as something extremely overcomplicated and most teachers, having a laughably low salary they barely survive on, don't care teaching it in a way kids would understand.
> Survivorship bias. Eastern Europeans are actually very bad with math, no better than your regular American.
Most people everywhere are bad at math. However, Eastern Europeans and Asians have a larger percentage of people who end up good at math compared to the US. And it's not even close, if you look at math competitions. Immigrants and children of immigrants are over-represented among the US team members.
I've long pondered a similar question - why are there so many Indian and Pakistani women in SWE in comparison to western women? Are Indian/Pakistani women better than western women in engineering? Is the education there better? How are these countries successful in mitigating this gender gap?
My theory is that this is actually caused by sexism and gender discrimination. There are smart, intelligent women everywhere, but due to sexism many career options have been traditionally closed for women in these societies, while SWE (as a completely new field) isn't. Their high numbers can be explained by the lack of opportunities in other areas. If you're an intelligent woman in Pakistan, IT is one of the few ways to prosper, meanwhile a woman in the West has way more opportunities.
I think it used to be the same principle with science in EE. Like, you're a highly intelligent person, you strive for success and recognition. In US, the classic path is entrepreneurship, but that was pretty much closed / very difficult in the Soviet block. You could get into politics, but you have to bend the knee to the party line. Science is one of the few avenues where you can thrive intellectually, get recognition and keep yourself relatively unaffected by politics.
I agree this has an effect as well - software engineering is one of the few fields which provide good living in those countries.
However, coming from (relatively poor, but relatively gender-egalitarian) Eastern Europe, female engineers aren't anywhere close to the amount in e.g. India and Pakistan, so I don't think it can explain the disparity completely.
Immigrants and children of immigrants are over-represented among the US team members.
Still survivorship bias. Immigrants from China and India are not selected randomly from the population, they're selected by their means and determination to emigrate. Furthermore, if you include the fact that the US caps the number of visas granted on a per-country-of-origin basis and the fact that China and India have the 2 largest populations in the world, the people who successfully obtain visas from these countries are the survivors of the most stringent selection process.
You can also look at Fields Medal winners. The majority of award ceremonies have at least one Slavic person: https://en.wikipedia.org/wiki/Fields_Medal
> Eastern Europeans and Asians have a larger percentage of people who end up good at math compared to the US.
These are two different claims:
Eastern Europeans and Asians who are in the US have a larger percentage of people who end up good at math.*
Eastern Europeans and Asians who are in their respective countries have a larger percentage of people who end up good at math.*
If you are making the first claim, you're just restating the parent comment's survivorship bias claim. If you're making the second, then you are making a strong claim, but it would be interesting to see data behind it. (I don't have any insight one way or the other.)
> Immigrants and children of immigrants are over-represented
That's exactly the bias. Immigrants are self-selected for higher risk tolerance, higher endurance, often wider or deeper knowledge, and readiness to think hard and work hard to achieve a better place in life.
Unsurprisingly, these same qualities help achieve results in studying and professional career.
Coming from a culture that respects abstracted knowledge (Chinese, Jewish, Russian, Indian, etc) helps additionally, but is by far not sufficient by itself.
There are lots of Chinese and Indians, are you sure that there is a larger percentage who are good at math? When you take 1.4 billion x2 compared to 380 million Americans, the percentages don’t have to be high. Immigrants from those two countries at least, also tend to be in highly educated and more well off segments of those societies. You could find a lot of Chinese refugees from Vietnam in the early 80s not actually good at math, and instead having typical problems refugee communities have. You’ll also find this in African immigrant populations today if you compare refugees from east Africa to Africans who went the work visa route. Race isn’t really an indicator of anything compared to education background and the resources your family has access to (and inter generational knowledge on using those resources).
> They had been trained, from an early age, to love mathematics more intensely.
Nonsense, sounds like post-hoc rationalization. Maybe talk to some actual Slavic people. Sure the Russians had "math clubs" and "chess clubs" but it wasn't as if the US didn't have RadioShack and garage/ham culture. Talk to some of the older generations that still remember the Berlin Wall and you might also understand why so many women from the ex USSR states are in STEM while it's the opposite in the West. TL;dr: STEM was a quick way to prosperity, the eastern bloc countries were poor, and engineers are useful even in a communist regime. They studied math because there wasn't much else they couldn't have done.
Hah. In the USSR an average engineer earned less money than an average worker.
I'm not joking.
But STEM was seen as far more prestigious than manual labor. This was very much a cultural thing, pushed by the government (engineers are useful!).
Another thing, there was a huge societal pressure to excel at school. It was common for parents to check their children's marks every day.
There's a very famous picture about it: https://en.wikipedia.org/wiki/Low_Marks_Again - a kid knows that his parents are going to check his marks and berate him.
And this attitude was everywhere. For example, getting low marks and then overcoming them was a theme for a lot of iconic Soviet cartoons and stories ("The country of undone homework", "Vovka in a Faraway Kingdom", etc.). I have not seen anything similar in the US.
in case anyone else were interested:
https://www.youtube.com/watch?v=2NlnJsCEzSM "The country of undone homework"
https://www.youtube.com/watch?v=YpygndkMSWA "Vovka in a Faraway Kingdom"
(I was already shocked that one of the leading roles in the romcom Три плюс два was a physicist, but then again Young Sheldon might provide evidence that pop culture in the Old Country is more STEM-accepting now than it had been in my day?)
EDIT: I love how the exclamation point cries out "Halt!" and the question mark demands "Where [do you think you're going]?" (and the doodle of Kyzya)
EDIT2: Vovka needs much more russian-specific cultural background than Homework. I recognise the golden fish (Только ты — рыба моей мечты), but not any of the other tales. I'll probably eventually run across filmstrips explaining each/each family of tales, but if anyone would care to give pointers to specific ones, I wouldn't mind any spoilers!
Is the "sam" of the samovar the same as the "sam" of "sdelai sam"?
> getting low marks and then overcoming them
Do I understand https://www.youtube.com/watch?v=qvrS6z4tUtI correctly to mean that it wasn't possible to join a scouting troop without good marks?
Where they might have the opportunity to make music videos with famous singers? https://www.youtube.com/watch?v=NepI7BTYpnY
Thanks for the correction!
Lagniappe: https://www.youtube.com/watch?v=WOnxu62nz9g
EDIT: wait a moment, now I'm confused: if her (Lena's?) marks weren't an issue for induction, why does it matter that her friend got jealous and ruined her test?
(or did I get this story right, but it wasn't necessarily a general all-Union thing, just that in this specific case a 2 would have been problematic for her troop/school/family?)
> Hah. In the USSR an average engineer earned less money than an average worker.
But in the USSR, your ability to buy something was generally not limited by the amount of money you had. It was limited by whether you'd be allowed to buy the thing for other reasons.
> But STEM was seen as far more prestigious than manual labor.
Sounds like an engineer's money may have been worth much more than a laborer's?
> Sounds like an engineer's money may have been worth much more than a laborer's?
Not in general. It heavily depended on individual circumstances.
For example, machinists could earn a bit more money by using factory tools (lathes, drills, etc.) to make replacement parts for cars. And a lot of workers were stealing some of the product their factory was making. There was a common attitude of "everything around is common, so everything's around is mine".
On the other hand, engineers had more career perspectives. They were more likely to be promoted to managerial positions.
That depends on what you are buying. Some things worked like health insurance in US, some others weren't. Housing you don't buy at all, a car you need to know a secret way to jump the queue or be in a right position. Fancy stuff -- you need to have friends who can sail and bring it to you.
But there was plenty of stuff you just buy, from air plane tickets to beer and meat.
This is not true at all. Communists made a big emphasis on stem over law and classics, and most communist leaders had stem background.
In communist state prestige is money.
Universities in eastern bloc were really elite places. Only low single digits percent of people were able to enroll. Also majority of degrees were in STEM, education or medicine as they were deemed useful for the state. To get degree outside of STEM, political background of your family was checked and things like having family member (even say uncle) who emigrated outside of country or having grandparents who owned businesses or farm decades ago will get you discarded. So the smart kids usually have very limited path forward, so STEM it was (if you were lucky)
6 years ago and 10 years ago, with a few comments: https://hn.algolia.com/?q=Math+from+Three+to+Seven
This book and the culture it come from are so influential, that many people who did "enrichment" have already been exposed to many of the activities in the book. Most famous may be the Scratch JR / code.org introductory computer programming, but with pencil and paper.
Ah good find. Macroexpanded:
Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers [pdf] - https://news.ycombinator.com/item?id=17018583 - May 2018 (20 comments)
Math from Three to Seven: Chapters One and Three [pdf] - https://news.ycombinator.com/item?id=8811334 - Dec 2014 (21 comments)
The USSR was indeed the most reading country in the world. Soviet citizens spent approx. 11 hours a week reading books, newspapers and journals on average, which was twice more as the British, North Americans and French people did. It was the findings of the world study of 1966.
Not a good metric for producing scientific talent, and it doesn't distinguish reading fiction from actually educating yourself. For the purposes of producing scientific talent, reading fiction helps you as much as watching TV.
I bet a lot of scientific talent was inspired (on either side* of the Iron Curtain) by the genre of fiction this dude is reading: https://barykin-pin-up.ru/#/i/kniga-luchshaya-podruga
* Lem (Cyberiad, etc.) was all I could get of theirs, on mine.
I don’t know any definition of actually educating yourself that would exclude reading fiction. And why are you focused on the purpose of producing scientific talent?
The article is trying to explain why the Soviets were so good at keeping up with the US in science/math
Right... tell me you didn't read the article, am I right. That's why I didn't bother replying. I often feel the impulse to reply to "show everyone that this guy is talking nonsense" but if that's obvious other people will see it too, so I say nothing.
This is an incredibly pessimistic view. Do you have any sources to these claims?
Yes, people had a lot of time for hobbies. Reading, writing poems, electronics. Sometimes I watch old interviews of people on the streets and compare with the interviews they do on the streets now. It's night and day. Even people, like working class, drunk in a bar in the end of 80's collapse were more well spoken and intelligent then the people now. Either it's Putin, emigration or capitalism or whatever but there is a serious degradation in the populace.
According to Zoya, Birkins, boob jobs, and Jaguars are the current topics of conversation? (that said, museums did see an uptick of entries when they offered reduced rates for patrons wearing Louboutins)
I blame Катя Кузнецова (1986); she wanted the red sports car with the radio and the little dog, after all: https://www.youtube.com/watch?v=jvdlAgreRug&t=4574s
Lagniappe: https://www.youtube.com/watch?v=DgdP5U28jHc
I've noticed this aspect in general of revolutionary societies. What I'm personally quite selfishly interested in is whether this is unique to leftist revolutionary societies - were Germans or Italians in 1936 having spirited debates about fascism and how best to serve the Fatherland? I have no idea, from what I've read so far it sounds like no.
Meanwhile, for example in Spain in the same time period, there was a remarkably broad activation of the population in revolutionary activism and political engagement, which allegedly doubled productivity and dramatically increased agricultural yields, which to me indicates that the anarchists were basically everywhere (how else did they syndicalize such wide swaths of the economy?).
Similarly there's the whole French Revolution cafe / salon culture.
Fascism was explicitly and proudly anti-intellectual, eg https://en.wikipedia.org/wiki/Achille_Starace#:~:text=On%20o...
I think you’re missing a lot of historical context. If by “intellectual” you mean cosmopolitan university professors and government administrators then yes. This also closely associated with internalization, relativism, and Jewish culture.
If by “intellectual” you mean learning, reading, thinking, then no.
I have been trying to join/create a circle as an adult. I asked some of my online friends but no interest so far.
It's interesting to me, as if you read Benjamin Franklins biography, he mentions creating a literary circle being super important. I suspect many of our important thoughts leaders through history created small social circles where they hyperfocused on their domain with friends in a more social way
Peripheral, but not totally irrelevant: Psmith was an Edwardian dandy of PGWodehouse’s imagination
And I thought it was a pun on p-zombies...
My parents grew up in the Former Soviet Area so I will share this anecdote: Both of my parents studied Chemistry. Math is really important in our family. You are shamed if you don't understand something logical. My dad still had to do military service even if he studied. There was no strong incentive to study other than the fact that it was free and something to do for people who had no jobs, only 1 hour of TV per day, etc.
My hot take is that lack of entertainment and the fact that education was one of the only free things available to them was a large contributing factor.
He almost lost me when he said the USSR was punching about its weight with a lower population which is untrue. The USSR had a significantly higher population than the US during the Cold War.
Every study which examines different populations across the world and expects them to be identical will be confused.
If every cultural group was equally interested in math, that would be shocking.
[flagged]
Can we please stop calling "russian" on everyone from ussr and/or having a Slavic-sounding name.
[flagged]
"Please don't post shallow dismissals, especially of other people's work. A good critical comment teaches us something."
Would you like to share why or do you just want to insult the piece?
Curious (not) how Soviets just became ‘russian’. This is soft propaganda once again.
Cast your mind back 33 years . . .
The Union of Soviet Socialist Republics (USSR) was formally dissolved as a sovereign state and subject of international law on 26 December 1991 by Declaration № 142-Н of the Soviet of the Republics of the Supreme Soviet of the Soviet Union.
If Russians punch way above their weight demographically and are so good at math - how come then that the French have even more Fields medals per capita?
Maybe this article was written by a Russian troll farm, as it is essentially claiming Russian math supremacy.
Can't speak for my own kids (yet), but personally I was able to hold my interest in math through my teens for 2 reasons:
1. I had some good teachers who showed (glimpses) of the how and why, not just the "what", so it helped math feel like it made sense, rather than being just facts and calculating algorithms to memorize. One demo that left a particular impression on me was the teacher asking us to go around the unit circle in increments of 10 degrees and plot the ratio of the opposite side and hypotenuse of the inscribed right triangle. Watching the sine function -- until then some mysterious thing that just existed with no explanation or context -- materialize in front of me on graph paper was magical.
2. I was shown that math is useful. In another great high school demo, the teacher assigned every student a length, width, and height, to be cut from construction paper and taped together in a box. After we were done, we laid out all the boxes together and computed their volumes. Then the teacher worked through the calculus on the board to figure out the dimensions of the box with the highest possible volume, given that fixed amount of construction paper. That was a really big moment for me, because until then I "hated" math, being a silly waste of time messing around with numbers and shapes just for the sake of doing it.
I think the amount of approachable math content online is incredible. Some comments mention 3Blue1Brown on YouTube, which is good but can go on a bit and maybe be a bit advanced. I think Numberphile is great for having a lot of videos, each of which is pretty short, and which still show some small proof of some problem. There are also books of interesting mathematical tidbits or puzzles, eg the Martin Gardener or Ian Stewart books. I guess one other thing to say is that it probably helps for you to appear to be interested in the math things instead of you being interested in your kid doing what you want (ie looking at the math things)
There are a good amount of entertaining maths communicators on the internet. I'd like to recommend standupmaths/matt parker, as well as looking at the SoME playlists which contains some interesting content too
> Does anyone have good experiences with keeping kids math-interested as they get into their teens?
The first step would be to get them into a math circle. There are 100s of them https://mathcircles.org/map/. I run a math circle as well, and work with a bunch of teens/preteens. I've had a lot of success with them. AMA.
> Does anyone have good experiences with keeping kids math-interested as they get into their teens?
Not a parent, but what kept me engaged at that time was programming simple games or interesting visualizations and animations. I "discovered" quite a bit of useful trigonometry, linear algebra and statistics by just fooling around and following my curiosity. And the intuition I gained definitely helped later on with university math
For the "exercises are important and also build conceptual understanding", see "BASIC SKILLS VERSUS CONCEPTUAL UNDERSTANDING, A Bogus Dichotomy in Mathematics education" by H. Wu.
The big challenge in teaching is not to make the exercises seem lame.
I haven't read this whole article yet (PDF here https://math.berkeley.edu/~wu/wu1999.pdf), but this idea is my #1 problem with Tom Lehrer's "New Math" song. His big complaint at the beginning is that the emphasis is too much on understanding and not on efficiently/correctly calculating an answer. As funny as the song is, I don't think that complaint has aged well at all. Also the old algorithm was just as complicated as the new one, but at least the new one makes it easier to see what's going on, so the whole joke kind of falls apart.
As far as I understand the article, the author (and myself) absolutely wants people to practice longhand addition etc., and is pushing back on the idea that you can teach how to calculate XOR how to understand place value.
If some of the kids go on to study CS, they can then think about the similarities and difference between decimal, hex and binary addition, how half and full and ripple-carry adders work, and how you add bigints. At that point you need both a conceptual and a procedural understanding of digit-wise addition.
If you want to do say 67 + 24, perhaps even in your head, there are more efficient ways to add than the standard algorithm, and I think that's what new math was trying to get at. But at some point you might want to add 25137 + 1486 and then your neat tricks no longer work and you need something that scales.
For me it was this curriculum, which should be better-known: https://www.elementsofmathematics.com/
One place it is offered in-person is the St. Louis area where I grew up: https://megsss.org/about-us/
The article seems to imply though that the nurture/nature quotient is very low. As a one off example, I've always been interested in exact (applied) sciences, my kid much less.
> I hope people read it and not just the comments here :-)
This got my upvote!
have you tried TFA's tack of, instead of throwing him on the mercy of the school exercises, presenting a problem or two?
> "Problems worthy of attack prove their worth by fighting back" —PH
In a small way, yes, and throughout "three to seven", actually up until she was nine, we had a lot of fun with what I think I can call problems (especially while home-schooling during the pandemic, where we had time to keep going back to these from different angles). But I'm not able drum up much interest these days, so I was wondering if people here had any insights on what if anything has worked with tweens, as opposed to how the younger ones learn.
For me it was Math Magic Tricks and Math Puzzles. [0] [1]
[0] https://matthewfurman.com/math-magic-tricks/
[1] https://solveordie.com/math-riddles/for-teens/
I learned basic trig around ~10 because I wanted to make spacewar/asteroids-like games, which led naturally into matrix math, later on.
Parsing also interested me around ~12 (text games this time), but while I made some mechanical attempts, the theory never clicked until much later.
Sometime around that time I learned about recursion by reverse-engineering the display code for a tile based first-person maze crawler one of my father's colleagues had written. (yes, fib should've been simpler, but drawing those perspective walls was way more concrete)
[perspective was luckily something I'd been introduced to in second grade, so it was old hat at this point, and the scaling math was straightforward; the only jump I needed to make was grokking that having drawn the walls visible from this square, one could use the same routine, with fresh parameters, to draw the walls from all the still-visible neighbouring squares, etc. Unfortunately z-buffers make this entire approach obsolete; but maybe he'd take it as a challenge? this is trivial with z-buffering, but how might it even be possible without?]
Might Processing sketches (or whatever the new shiny might be) interest your kid?
Personally, that's how most of my math learning came. As a teen, I started to program and wanted to understand mathematics tools to solve specific problems, so I learned trig, Bezier curves, cryptography, number theory, etc like this.
Then later between my love of point and click adventure games and puzzles plus the fact that I had good foundations in maths, pure mathematics problems became increasingly fun.
I still have to make to that point, but answer from what I remember from my time there:
Abstract math, or "math per se" was utterly uninteresting for me. My drive was to solve actual problems I had or wanted to solve. For example, making something out of wood with complex shapes, or drawing with the computer. I would say you have to find an area of interest with which the kids get passionate, and needs math to solve the problems.
Try dropping him in one of these math discord groups (for eg: Summer of Math Exposition)? Teens care a lot about social approval and seeing so many people having fun with math might help.
when i was 12,13 i really enjoyed the algebraic manipulation parts of calculus without having to think too hard about setting up problems. just practicing integration, differentiation and limits was a good start
i didn’t even know i enjoyed math until i was fortunate enough to take multivariable calculus my senior year of HS, you don’t really get to do any cool shit in typical public schools so it’s hard to keep the interest
School is where you kid spends the majority of the time. If they find it boring, and the school is unable/unwilling to provide enrichment, then it is an uphill battle to resist that. The ideal solution is to make the work they do at school engaging, then they'll seek out enrichment at home themselves.
There might be math-oriented stuff online (3Blue1Brown is one off the top of my head) that keeps them wanting to understand more. That might anchor their school work a bit, or give them something extra to try. Books can help too.
The ideal solution is to make the work they do at school engaging, then they'll seek out enrichment at home themselves.
One thing I haven’t seen brought up in this discussion yet: technology. Seriously, what hope does a teacher have for getting students to engage when they’re competing against all the might of Silicon Valley? The industry is spending billions every year to discover and implement the best techniques for stealing teenagers’ attention and focus away from everything else in their lives.
There’s a growing chorus of people who want to get phones out of classrooms. That’s a strong first step but students’ struggles don’t end when they go home for the night. I volunteer as a tutor with high school students at an after-school homework club. We aren’t allowed to take their phones away! You can imagine how much of a Herculean struggle it is for these kids to put away their phone and actually get some work done.
A new law in Belgium will forbid smartphone usage at primary school (age 6..12) at least. There's hope.
Being a product of the US school system, the most important lesson it taught me is that teachers as well as students are caught up in a system that's bigger than they are, so in order to educate oneself, one need merely (a) organise one's own time effectively, but (b) avoid doing so indiscreetly, such that it could force other pawns to call one's lack of genuine participation to the attention of the Man.
90% of success in primary and secondary schooling is just showing up; as long as you keep your grades up, they won't demand mental attendance, only the physical.
I agree, but would like to add that the US public school system also has a bad habit of teaching to the test, namely standardized testing like the ACT or SAT. As it turns out, my time would have been better spent learning how to budget long term or navigating the US healthcare system as opposed to learning maths rarely seen in the wild or that the mitochondria is the powerhouse of the cell. The information imparted to me during the entire four years of high school has largely been forgotten, "replaced" by more practical knowledge that I wish I'd had even a tiny bit of upon entering adulthood.