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By about 1/4th of the way through I wanted to just know what 'russian math' looked like. By Halfway it was pretty clear they weren't going to tell me. I skimm

By about 1/4th of the way through I wanted to just know what 'russian math' looked like. By Halfway it was pretty clear they weren't going to tell me. I skimmed the last half, nothing stood out. What does "Russian Math" look like?

deleted 5y ago
[deleted]
frant-hartm 5y ago
> school's curriculum is based on Russian teaching traditions that emphasize reasoning and deeper understanding early on, not just memorization and practice drills. "The child should be brought to abstract level as soon as possible," she says, "meaning early introduction of algebra and geometry, not only arithmetic," and helping children figure out principles for themselves rather than spoon-feeding them.
- dehrmann 5y ago
  I buy into having a deeper understanding, and in both work and school, it's pretty clear who has a deeper understanding and who's going through the motions. That said, how is it that there's such range in pedagogy? So many people have studied teaching that you'd think we'd have a better idea of what works. Or maybe it's that goals are different.
  - fallingknife 5y ago
    The goals are different. The goal of the Russian school is to teach math. The goal of public schools is to dumb down the curriculum until everyone is equal.
    - tsukikage 5y ago
      That's an interesting take, since the Russian school's teaching methods originate in Soviet public schools. If that's the difference, why were the goals so different there, and how do we make US public school goals more like the Soviet ones?
      - iammisc 5y ago
        The soviets were nationalists who believed the utility of the citizenry was in their contribution to their country. You reinstill love of country, which really means love of society and others, which is another word for philanthropy, and you will quickly get this. In America, instead of education and work being for the greater purpose of your nation and people, education is for the individual. As usual, most people find more motivation when helping others than themselves, but the focus on ourselves in American education means it's easy to slack.
  - ajuc 5y ago
    I think a big part of this is society's expectations. For example while there was bullying in my primary school - there was no bullying because you were good at math. The opposite was true - if you were bad at math it meant you're "dumb" and kids will laugh at you. It wasn't all perfect - it was uncool to try hard (means you're dumb and have to work for it and that's boring) but it was very fashionable to instantly know every answer. So teachers had it much easier because kids had intrinsic motivation to learn math. Another part of it was probably that the unemployment was at 20% at that point and everybody realized you have to be well educated to have a chance of good job.
  - Sponge5 5y ago
    Not goals - incentives. I'm from Czechia and for me math education changed dramatically for the last year of high-school. All of a sudden it was crunch time to get the best result at the standardized tests that are part of government's examination. Up until that point the math classes were very much Soviet-style understanding-first, daily hour-long homeworks that are described in the article. Final year was about technique memorization. Once you're gaming a system, education quality tanks.
    - dehrmann 5y ago
      The dilemma with tests is that we need them to measure competency, but once you introduce them, the specific form the test takes becomes a target, itself.
- hellbannedguy 5y ago
  I wish American teachers could teach the reasoning behind math. I don't think most math teachers know themselfs though---even at some colleges. I don't think I have even seen a math book that goes into depth on why a equation, or problem, is solved a certain way. I would like to see most memorization in math, and most subjects nixed for good. I have found, including myself, my early difficulties in math were due to just memorizing how to do a problem. It wasen't until I started over (I went to a CC early. I hated high school socially, and it affected my studies. Going to a CC was the best move I made.) I took basic math, and algebra, trig., at the community college. It made inorganic chemistry, and physics, so easy.
  - BeFlatXIII 5y ago
    I went from terrible at timed tests of regurgitating basic arithmetic facts to one of the better math students in my school once the curriculum moved on to requiring some understanding of what was going on.
deleted 5y ago
[deleted]
credit_guy 5y ago
Sample problem for K-1 [1]: "Jane fills a bag with three types of chips. There are 3-point, 4-point and 7- point chips. Jane picks 3 chips worth 15 points. Which chips did she pick?" Sample problem for grades 5-6 [2]: "Pinocchio drank half a cup of black coffee. He then filled the cup back up with milk and drank one third of the mixture. Again he filled the cup to the top with milk, drank one sixth of the mixture and filled it back to the top with milk one final time before he drank the whole cup. Did he drink more coffee or milk?" [1]https://f.hubspotusercontent30.net/hubfs/981338/Blog/Elementary_School_Problems.pdf https://f.hubspotusercontent30.net/hubfs/981338/Blog/Element... [2]https://f.hubspotusercontent30.net/hubfs/981338/Blog/Middle_School_Problems.pdf https://f.hubspotusercontent30.net/hubfs/981338/Blog/Middle_...
- xmprt 5y ago
  Those are pretty challenging problems and they also require a bit of working out. How many of these problems are students expected to solve in, say, and hour long test?
  - eps 5y ago
    These represent classes of problems and the test checks which classes students have covered in their studies and which they slacked on. These two are straight-forward problems, both will be allocated some basic nominal time. You either know how to solve them or you don't. Sometimes there'd be problems that are more puzzling, because they'd combine several problem classes and will take time to unfold (this is typical in math olympics). These will be allocated more time as they require thinking and searching for a solution.
    - dkn775 5y ago
      From the examples I guess it is the ability to intuitively manipulate fractions? Like “oh that’s kind of like .8 of this other thing so it’s close to X” ?
    - xmprt 5y ago
      I see what you mean by classes of problems. Some of the problems from the above links I know how to do (although working out might take some time and a pen and paper) and then there are some problems where I don't know where to start. I was just never taught how to think about numbers that way even though the link says those problems are for middle school children.
dragosmocrii 5y ago
I studied in a top school in Moldova which follows a curriculum whose foundation was defined during the Soviet union times, so could be pretty close to the Russian curriculum. Just as an idea, in grade 10-11 I was studying limits, complex numbers, derivatives, grade 12 was dedicated to integrals and solving problems with them. Math got progressively harder starting with grade 5. I remember I was filling about 2-3 notebooks of 48 pages (little squares pattern) per semester with homework and in-class class problem solving. We always had homework to do, and often it would take me hours to come up with a solution to the more difficult problems that would give me a 10 (grade A+). My nephew who finished grade 4 has no homework (Canada), but I remember my grade 4 I had so much homework for each subject (math, French, Romanian, geography, arts, etc). Heck, in grades 1-4 we even had summer homework, which were books containing exercises for various subjects, and I remember that vividly because I hated to do homework in the summer. I'm quite sure that good Russian school are also quite intense..
- lentil_soup 5y ago
  How old is grade 10-11? I always get confused with these as each country numbers grades differently
  - dilyevsky 5y ago
    Can’t speak for Moldova but had what seems to be same level (specialized math school) in Russia and 10-11 was 15-17 yo (you could start at different age back then)
  - dragosmocrii 5y ago
    grade 12 is usually 18yo, grade 11 is 17yo, etc
ajuc 5y ago
I don't know if it's that, but for me math "clicked" when in 2nd class of primary school in Poland we had a whole year of solving intuitive math problems. Basically linear equations of 1 or 2 variables, but that was without knowing what any algebra or even what a variable is - we started with only basic addition and multiplication. Teacher asked us (one by one) to describe how we would arrive at the answer to problems and why that way. Sometimes it would be a contest - who guesses the answer first and that person gets to explain the process and bask in the glory of being the smartest kid ;). And then we were shown how to write that solving process as equations and practiced changing from problems to equations and vice versa. At the end of the year most kids understood algebra.
vkazanov 5y ago
Not sure about these after-class schools, but I can compare my ex-ussr school and uni education with math or CS undergrad textbooks I read a lot in English these day. Not sure about early education though. 1. Russian math books are straight to the point, superconcrete. Hard to read in a linear fashion but very useful when student is serious about going through it ("Problems in mathematical analysis" by Demidovich is a perfect example, Mark Vygodskiy's "Elementary Mathematics Reference"). 2. In most textbooks I remember nobody tries to build a dumbed down explanation of things. This might lead to the book being harder to understand without teacher's help. I remember how some American undergrad-level introductory math analysis books were trying to skip proofs, avoid certain details, giving too many intuitive explanations (). 3. Mid and late school math is pretty advanced, especially when compared to US typical level. These days I live in UK. Kids go to school early here: 4-5 years. My daugther is 6 and is comfortable with trivial math. I've read a few secondary school textbooks and they feel quite ok. So maybe this is a US problem. EDIT: a few example books added
seer 5y ago
I have a feeling it was more about the quality of the teachers than anything else. I moved from “Deep” Russia itself to the periphery of the USSR (Bulgaria) when I was in first grade, and my parents had the foresight to make me repeat that grade so as to help me with learning a new language. The quality difference was astounding. In 1992 Russia by first grade I was learning english with flash cards technique, drawing human shapes, animation, perspective, and some pretty good maths. The knowledge I gained there allowed me to learn almost nothing but the language up until about 3rd grade. And it was a school in the middle of nowhere. I think the USSR trained some very good teachers and just sent them around everywhere, places they would not have gone themselves on their own volition kinda thing. Oh and I remember teachers where highly respected, a thing I saw slowly degrade while the country was going through the 90s reforms.
- spoonjim 5y ago
  Respect for teachers is a huge part of it. People want status as much as they want money. If culturally America venerated teachers the way it venerates soldiers we’d have fewer wars and smarter people.
  - FredPret 5y ago
    Or smarter wars?
    - kwere 5y ago
      make the military teach!
thundergolfer 5y ago
Check out 'Word Problems in Russia and America' by Andrei Toom. Toom contrasts the poor state of the American math curriculum with his experiences with the Russian style, particularly its centering of 'word problems'.
ymolodtsov 5y ago
I think the key difference is that it quickly moves from what's considered problems for kids (Ally had 3 apples, Booby had 2, etc) to abstract tasks and fundamental theorems in algebra, geometry and other areas. The way math was taught in USSR and is still largely taught in Russia is by going as quickly as possible to calculus. I definitely studied limits and derivatives in school (around grade 8 or 9 out of 11 as I recall) and we briefly touched integrals in the last grade. There are some areas they don't really include, although in my opinion they should have, like mathematical statistics, which could be even more useful, but still. That is a common approach recreated in some other subjects. For instances, teaching Russian includes not just basic syntax and phonetics but also just basic linguistic exercises like dissecting complex words and learning classifications, which you don't really need to talk it but they provide a deeper understanding.

deleted 5y ago

[deleted]

frant-hartm 5y ago

> school's curriculum is based on Russian teaching traditions that emphasize reasoning and deeper understanding early on, not just memorization and practice drills. "The child should be brought to abstract level as soon as possible," she says, "meaning early introduction of algebra and geometry, not only arithmetic," and helping children figure out principles for themselves rather than spoon-feeding them.

dehrmann 5y ago
I buy into having a deeper understanding, and in both work and school, it's pretty clear who has a deeper understanding and who's going through the motions. That said, how is it that there's such range in pedagogy? So many people have studied teaching that you'd think we'd have a better idea of what works. Or maybe it's that goals are different.
- fallingknife 5y ago
  The goals are different. The goal of the Russian school is to teach math. The goal of public schools is to dumb down the curriculum until everyone is equal.
  - tsukikage 5y ago
    That's an interesting take, since the Russian school's teaching methods originate in Soviet public schools. If that's the difference, why were the goals so different there, and how do we make US public school goals more like the Soviet ones?
    - iammisc 5y ago
      The soviets were nationalists who believed the utility of the citizenry was in their contribution to their country. You reinstill love of country, which really means love of society and others, which is another word for philanthropy, and you will quickly get this. In America, instead of education and work being for the greater purpose of your nation and people, education is for the individual. As usual, most people find more motivation when helping others than themselves, but the focus on ourselves in American education means it's easy to slack.
- ajuc 5y ago
  I think a big part of this is society's expectations. For example while there was bullying in my primary school - there was no bullying because you were good at math. The opposite was true - if you were bad at math it meant you're "dumb" and kids will laugh at you. It wasn't all perfect - it was uncool to try hard (means you're dumb and have to work for it and that's boring) but it was very fashionable to instantly know every answer. So teachers had it much easier because kids had intrinsic motivation to learn math. Another part of it was probably that the unemployment was at 20% at that point and everybody realized you have to be well educated to have a chance of good job.
- Sponge5 5y ago
  Not goals - incentives. I'm from Czechia and for me math education changed dramatically for the last year of high-school. All of a sudden it was crunch time to get the best result at the standardized tests that are part of government's examination. Up until that point the math classes were very much Soviet-style understanding-first, daily hour-long homeworks that are described in the article. Final year was about technique memorization. Once you're gaming a system, education quality tanks.
  - dehrmann 5y ago
    The dilemma with tests is that we need them to measure competency, but once you introduce them, the specific form the test takes becomes a target, itself.
hellbannedguy 5y ago
I wish American teachers could teach the reasoning behind math. I don't think most math teachers know themselfs though---even at some colleges. I don't think I have even seen a math book that goes into depth on why a equation, or problem, is solved a certain way. I would like to see most memorization in math, and most subjects nixed for good. I have found, including myself, my early difficulties in math were due to just memorizing how to do a problem. It wasen't until I started over (I went to a CC early. I hated high school socially, and it affected my studies. Going to a CC was the best move I made.) I took basic math, and algebra, trig., at the community college. It made inorganic chemistry, and physics, so easy.
- BeFlatXIII 5y ago
  I went from terrible at timed tests of regurgitating basic arithmetic facts to one of the better math students in my school once the curriculum moved on to requiring some understanding of what was going on.

deleted 5y ago

[deleted]

credit_guy 5y ago

Sample problem for K-1 [1]: "Jane fills a bag with three types of chips. There are 3-point, 4-point and 7- point chips. Jane picks 3 chips worth 15 points. Which chips did she pick?" Sample problem for grades 5-6 [2]: "Pinocchio drank half a cup of black coffee. He then filled the cup back up with milk and drank one third of the mixture. Again he filled the cup to the top with milk, drank one sixth of the mixture and filled it back to the top with milk one final time before he drank the whole cup. Did he drink more coffee or milk?" [1]https://f.hubspotusercontent30.net/hubfs/981338/Blog/Elementary_School_Problems.pdf https://f.hubspotusercontent30.net/hubfs/981338/Blog/Element... [2]https://f.hubspotusercontent30.net/hubfs/981338/Blog/Middle_School_Problems.pdf https://f.hubspotusercontent30.net/hubfs/981338/Blog/Middle_...

xmprt 5y ago
Those are pretty challenging problems and they also require a bit of working out. How many of these problems are students expected to solve in, say, and hour long test?
- eps 5y ago
  These represent classes of problems and the test checks which classes students have covered in their studies and which they slacked on. These two are straight-forward problems, both will be allocated some basic nominal time. You either know how to solve them or you don't. Sometimes there'd be problems that are more puzzling, because they'd combine several problem classes and will take time to unfold (this is typical in math olympics). These will be allocated more time as they require thinking and searching for a solution.
  - dkn775 5y ago
    From the examples I guess it is the ability to intuitively manipulate fractions? Like “oh that’s kind of like .8 of this other thing so it’s close to X” ?
  - xmprt 5y ago
    I see what you mean by classes of problems. Some of the problems from the above links I know how to do (although working out might take some time and a pen and paper) and then there are some problems where I don't know where to start. I was just never taught how to think about numbers that way even though the link says those problems are for middle school children.

dragosmocrii 5y ago

I studied in a top school in Moldova which follows a curriculum whose foundation was defined during the Soviet union times, so could be pretty close to the Russian curriculum. Just as an idea, in grade 10-11 I was studying limits, complex numbers, derivatives, grade 12 was dedicated to integrals and solving problems with them. Math got progressively harder starting with grade 5. I remember I was filling about 2-3 notebooks of 48 pages (little squares pattern) per semester with homework and in-class class problem solving. We always had homework to do, and often it would take me hours to come up with a solution to the more difficult problems that would give me a 10 (grade A+). My nephew who finished grade 4 has no homework (Canada), but I remember my grade 4 I had so much homework for each subject (math, French, Romanian, geography, arts, etc). Heck, in grades 1-4 we even had summer homework, which were books containing exercises for various subjects, and I remember that vividly because I hated to do homework in the summer. I'm quite sure that good Russian school are also quite intense..

lentil_soup 5y ago
How old is grade 10-11? I always get confused with these as each country numbers grades differently
- dilyevsky 5y ago
  Can’t speak for Moldova but had what seems to be same level (specialized math school) in Russia and 10-11 was 15-17 yo (you could start at different age back then)
- dragosmocrii 5y ago
  grade 12 is usually 18yo, grade 11 is 17yo, etc

ajuc 5y ago

I don't know if it's that, but for me math "clicked" when in 2nd class of primary school in Poland we had a whole year of solving intuitive math problems. Basically linear equations of 1 or 2 variables, but that was without knowing what any algebra or even what a variable is - we started with only basic addition and multiplication. Teacher asked us (one by one) to describe how we would arrive at the answer to problems and why that way. Sometimes it would be a contest - who guesses the answer first and that person gets to explain the process and bask in the glory of being the smartest kid ;). And then we were shown how to write that solving process as equations and practiced changing from problems to equations and vice versa. At the end of the year most kids understood algebra.

vkazanov 5y ago

Not sure about these after-class schools, but I can compare my ex-ussr school and uni education with math or CS undergrad textbooks I read a lot in English these day. Not sure about early education though. 1. Russian math books are straight to the point, superconcrete. Hard to read in a linear fashion but very useful when student is serious about going through it ("Problems in mathematical analysis" by Demidovich is a perfect example, Mark Vygodskiy's "Elementary Mathematics Reference"). 2. In most textbooks I remember nobody tries to build a dumbed down explanation of things. This might lead to the book being harder to understand without teacher's help. I remember how some American undergrad-level introductory math analysis books were trying to skip proofs, avoid certain details, giving too many intuitive explanations (). 3. Mid and late school math is pretty advanced, especially when compared to US typical level. These days I live in UK. Kids go to school early here: 4-5 years. My daugther is 6 and is comfortable with trivial math. I've read a few secondary school textbooks and they feel quite ok. So maybe this is a US problem. EDIT: a few example books added

seer 5y ago

I have a feeling it was more about the quality of the teachers than anything else. I moved from “Deep” Russia itself to the periphery of the USSR (Bulgaria) when I was in first grade, and my parents had the foresight to make me repeat that grade so as to help me with learning a new language. The quality difference was astounding. In 1992 Russia by first grade I was learning english with flash cards technique, drawing human shapes, animation, perspective, and some pretty good maths. The knowledge I gained there allowed me to learn almost nothing but the language up until about 3rd grade. And it was a school in the middle of nowhere. I think the USSR trained some very good teachers and just sent them around everywhere, places they would not have gone themselves on their own volition kinda thing. Oh and I remember teachers where highly respected, a thing I saw slowly degrade while the country was going through the 90s reforms.

spoonjim 5y ago
Respect for teachers is a huge part of it. People want status as much as they want money. If culturally America venerated teachers the way it venerates soldiers we’d have fewer wars and smarter people.
- FredPret 5y ago
  Or smarter wars?
  - kwere 5y ago
    make the military teach!

thundergolfer 5y ago

Check out 'Word Problems in Russia and America' by Andrei Toom. Toom contrasts the poor state of the American math curriculum with his experiences with the Russian style, particularly its centering of 'word problems'.

ymolodtsov 5y ago

I think the key difference is that it quickly moves from what's considered problems for kids (Ally had 3 apples, Booby had 2, etc) to abstract tasks and fundamental theorems in algebra, geometry and other areas. The way math was taught in USSR and is still largely taught in Russia is by going as quickly as possible to calculus. I definitely studied limits and derivatives in school (around grade 8 or 9 out of 11 as I recall) and we briefly touched integrals in the last grade. There are some areas they don't really include, although in my opinion they should have, like mathematical statistics, which could be even more useful, but still. That is a common approach recreated in some other subjects. For instances, teaching Russian includes not just basic syntax and phonetics but also just basic linguistic exercises like dissecting complex words and learning classifications, which you don't really need to talk it but they provide a deeper understanding.