5 ms·

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 sk

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?

sershe 6y ago
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.
- pmiller2 6y ago
  Well, 2 is prime, and so is 57, so it makes sense those would be math focused schools. ;) [0] —- [0]: https://hsm.stackexchange.com/questions/6358/story-of-grothendiecks-prime-number https://hsm.stackexchange.com/questions/6358/story-of-grothe...
  - arduanika 6y ago
    > And indeed 57 looks a bit prime for some psychological reason It tricked me, until I read the link.
    - alanh 6y ago
      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.
      - Arnt 6y ago
        My maths teacher made me prove that, my first proof by induction. Try it. You know you want to procrastinate with a nice proof by induction now.
        dmurray 6y ago
        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.
        dan-robertson 6y ago
        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.
        6y ago
- madaxe_again 6y ago
  > 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.
- aivisol 6y ago
  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.
lsh123 6y ago
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 ;)
- alboy 6y ago
  > 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. [1] https://en.wikipedia.org/wiki/Nikolay_Konstantinov https://en.wikipedia.org/wiki/Nikolay_Konstantinov
golergka 6y ago
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.
- roveo 6y ago
  Ha-ha, the #57 mafia is freakin everywhere, now I even meet you guys in HN comments :)
  - golergka 6y ago
    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.
  - Fnoord 6y ago
    What does this number, and the other one, refer to?
de_watcher 6y ago
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.
- neuronic 6y ago
  Yep, school is moving at the pace of the slowest common denominator.
- emteycz 6y ago
  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.
  - gerland 6y ago
    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.

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?

sershe 6y ago

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.

pmiller2 6y ago
Well, 2 is prime, and so is 57, so it makes sense those would be math focused schools. ;) [0] —- [0]: https://hsm.stackexchange.com/questions/6358/story-of-grothendiecks-prime-number https://hsm.stackexchange.com/questions/6358/story-of-grothe...
- arduanika 6y ago
  > And indeed 57 looks a bit prime for some psychological reason It tricked me, until I read the link.
  - alanh 6y ago
    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.
    - Arnt 6y ago
      My maths teacher made me prove that, my first proof by induction. Try it. You know you want to procrastinate with a nice proof by induction now.
      - dmurray 6y ago
        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.
        dan-robertson 6y ago
        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.
        6y ago
madaxe_again 6y ago
> 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.
aivisol 6y ago
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.

lsh123 6y ago

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 ;)

alboy 6y ago
> 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. [1] https://en.wikipedia.org/wiki/Nikolay_Konstantinov https://en.wikipedia.org/wiki/Nikolay_Konstantinov

golergka 6y ago

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.

roveo 6y ago
Ha-ha, the #57 mafia is freakin everywhere, now I even meet you guys in HN comments :)
- golergka 6y ago
  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.
- Fnoord 6y ago
  What does this number, and the other one, refer to?

de_watcher 6y ago

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.

neuronic 6y ago
Yep, school is moving at the pace of the slowest common denominator.
emteycz 6y ago
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.
- gerland 6y ago
  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.