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It is written by a mathematician who has taught in Russia, the US and Brazil. They have a lot to say about how math is taught in the US. The paper also has a lot of sample problems.
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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…
I don't like the second question. Probably the kid is supposed to see the 'trick' :he drank a full cup of coffee since he didn't refill coffee and drank all. He added 1/2, 1/3 and 1/6 of a cup of milk and drank it all, so (3+2+1)/6=1. He drank the same amount of coffee and milk. I think it is ok as a brain teaser, but there will probably be one kid in the class to see it and all the other kids feel dumb or whatever.…
These word problems are intended quite precisely as introduction to algebra. They show you the kinds of questions that algebra can solve in a "structural" way, which makes it way easier to grok algebra later on since motivation for the subject has been provided in such depth.
A good review article on the subject: Persson, Ulf and Toom, André: Word Problems in Russian Mathematical Education, available at http://toomandre.com/my-articles/swedish/ULFENG.PDF
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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…
I don't like the second question. Probably the kid is supposed to see the 'trick' :he drank a full cup of coffee since he didn't refill coffee and drank all. He added 1/2, 1/3 and 1/6 of a cup of milk and drank it all, so (3+2+1)/6=1. He drank the same amount of coffee and milk. I think it is ok as a brain teaser, but there will probably be one kid in the class to see it and all the other kids feel dumb or whatever.…
If you see the trick, you save some time on the calculation. If you don't you have to add some more numbers. It's not that difficult.
My college had a decent-sized contingent of Bulgarian & Romanian international students. The difference in their math abilities upon entry was striking. While most of my American-born classmates struggled in discrete math, linear algebra, and vector calc, my Bulgarian friend was like "I learned this when I was 9." They were frequently tapped as TAs by the professors, because they understood the material on a level th…
I am Bulgarian. I moved to the UK when I was 12. I had to join primary school halfway through Year 6 (the last year of primary school). The level of mathematics shocked me. They were still learning factorisation, something I had learned years ago. It was a breeze. Of course, in secondary school (ages 12-18) the content eventually caught up with me. Part of me wishes I could have somehow kept studying the Bulgarian wa…
My college had a decent-sized contingent of Bulgarian & Romanian international students. The difference in their math abilities upon entry was striking. While most of my American-born classmates struggled in discrete math, linear algebra, and vector calc, my Bulgarian friend was like "I learned this when I was 9." They were frequently tapped as TAs by the professors, because they understood the material on a level th…
I am Bulgarian. I moved to the UK when I was 12. I had to join primary school halfway through Year 6 (the last year of primary school). The level of mathematics shocked me. They were still learning factorisation, something I had learned years ago. It was a breeze. Of course, in secondary school (ages 12-18) the content eventually caught up with me. Part of me wishes I could have somehow kept studying the Bulgarian wa…
All the schools I know of here in the London area start around 0830 to 0900. Some operate a club for busy parents to drop off their kids early but classes don't start until the rest of the kids show up.
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I am Bulgarian. I moved to the UK when I was 12. I had to join primary school halfway through Year 6 (the last year of primary school). The level of mathematics shocked me. They were still learning factorisation, something I had learned years ago. It was a breeze. Of course, in secondary school (ages 12-18) the content eventually caught up with me. Part of me wishes I could have somehow kept studying the Bulgarian wa…
UK maths teaching is fairly terrible. Not only do they start later, it's almost never taught meaningfully, instead relying on memorising rote formulae. I grew up hating maths, it wasn't until YouTube came along and the sheer amount of _good_ maths content on there that I started to 'get' the bits I just never understood as a teenager. Most of my friends will still say things like 'I just don't get algebra / I don't d…
Some education systems put an emphasis on critical thinking, some on absorbing tons of information. Polish education is notable for memorization. One area where it doesn't seem to hurt is medicine. It appears Polish doctors and nurses are very much appreciated when they migrate. Perhaps critical thinking is not a useful skill in medical practice? Once upon a time I was reading an article about Polish migrants in Norw…
I was having a discussion about this recently, recalling the vast majority of my experiences with medical doctors who obviously just follow a cook book approach to how they practice medicine. Worse than that is how many doctors cannot correctly explain test results. Seems like although they completed a lot of schooling they did not take enough math.
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?
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.
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Romanian here, the "I learned this when I was 9" might have been a slight exaggeration so that your friend could make a point, but as an another anecdata I can say that I distinctly remember one of my first calculus classes while I was in 9th grade (I think I was 15 years old at the time) and our maths teacher trying to explain to us how real numbers are defined and, more importantly, what that definition really mean…
Do the students bring any motivation to the classroom? Like, is there a culture of "study hard and pay attention in maths and sciences, because that's how we escape poverty" or something like that? Here in New Zealand, middle class parents put a high premium on being happy and fulfilled, and most (that I've seen across several schools) don't really prime their kids for academic success by saying "this is important, w…
Those attending “olympiads” were brainwashed into thinking that somehow they were superior and at some point we had to look down upon those whom, god forbid, chose something else but maths. Some indeed went on to have high paying office jobs in western countries, many of whom are now turning back. Apparently being trained to win olympiads doesn't yield an entrepreneurial spirit nor does it lead to riches, and after a life wasted they now just want to live a bit.
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I don't like the second question. Probably the kid is supposed to see the 'trick' :he drank a full cup of coffee since he didn't refill coffee and drank all. He added 1/2, 1/3 and 1/6 of a cup of milk and drank it all, so (3+2+1)/6=1. He drank the same amount of coffee and milk. I think it is ok as a brain teaser, but there will probably be one kid in the class to see it and all the other kids feel dumb or whatever.…
>I think it is ok as a brain teaser, but there will probably be one kid in the class to see it and all the other kids feel dumb or whatever. If you see the trick, you save some time on the calculation. If you don't you have to add some more numbers. It's not that difficult.
This trick discussion reminds me of the great anectode about von Neumann:https://news.ycombinator.com/item?id=5950755