521–530 of 558 posts
As a Portuguese citizen, I was not exposed to Russian mathematics during my entire academic career until I entered university. Whilst slightly better than the UK, our educational system was also not brilliant when it came to maths, and we only started to do calculus close to Year 12 (the last year before university). Anyways, my one and only brush with Russian mathematics was as follows - I flunked Integral and Diffe…
Portugal has still made a lot of progress. My father, who grew up in the Açores in the 50/60s, says that back then school stopped at 4th grade.
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Portugal has still made a lot of progress. My father, who grew up in the Açores in the 50/60s, says that back then school stopped at 4th grade.
Oh yes, without a doubt. Even if you compare the level of teaching in my life time, from the 80s when I was in primary school to now it has improved dramatically. Portugal was really a developing country all the way up to the 70s and mid 80s, we have roads and infrastructure now :-) completely different place.
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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.…
Without the trick you get: Coffee concentration before first,second,third,fourth drinking = 1,x,y,z x = 1/2 y = x*2/3 + 0*1/3 = 1/3 z = y*5/6 + 0*1/6 = 5/18 Coffee drunk = 1/2 + 1/3 x + 1/6 y + z = 1/2 + 1/6 + 1/18 + 5/18 = 3/6 + 1/6 + 2/6 = 1 Milk drunk = 0 + 1/3(1-x) + 1/6(1-y) + (1-z) = 1/6 + 2/18 + 13/18 = 1/6 + 5/6 = 1 Which is a bit fiddly but hardly impossible. I think there is pedagogical value in doing the a…
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T.b.h. as somebody from ost-block country, I did hate the cast-system based on the performance. In my school we had a class that selected for the worst students, and surprise, it created a class where so many people failed. I was in class that had an even mix, some really smart kids, some not so much, and some comparable to the worst of the D-class. Like third of the of my classmates went for the sports-focused high-…
How did the A class become ordinary while B&C had a mixture of top and average? Was it that the ordinarily smart students were motivated by the sorting exams than the top smartest students?
Even more anecdotal thing, in my class there were more people doing extra-curicural contests, like Math-Olympiad and the like. We were even encouraged by teahers, along the lines of "No, try it even if you don't have top grades, that is the sort of thing where you need to understand what you are doing, not just ave all the right answers on the test." :D
Last hypothesis of mine is, that because we had a mix of sudents, the smarter(?) of us spend some time explaining to others (mix of goodnes of heart, being bullied and even having like a pay-for-homework manufacture?) ... and as they say, you learn best, when you explain?
But I could be completely wrong, rose-tinted glasses and long forgotten traumas and all that :D
Lots of comments asking what is "Soviet/Russian Math" actually like, and how is it different. I was lucky to get an education in three systems (Soviet Math, Romanian Math School (influenced by both French and Soviet Math school), and finally in a world top 40 university in North America. I would summarize the Soviet/Russian Math/Physics approach like this: - understanding of the mechanism/intuition behind the equatio…
Do you happen to remember any specific textbook? I'd be interested to see an example, assuming that they're still available in some format.
Lots of comments asking what is "Soviet/Russian Math" actually like, and how is it different. I was lucky to get an education in three systems (Soviet Math, Romanian Math School (influenced by both French and Soviet Math school), and finally in a world top 40 university in North America. I would summarize the Soviet/Russian Math/Physics approach like this: - understanding of the mechanism/intuition behind the equatio…
As I was reading the summary, I was thinking "well, of course -- that makes sense. Any teaching curriculum has got to be like that so what is so special about Russian math curriculum?". Then I read in other comments about US math curriculum and I was shocked to learn that not only they were NOT doing this, but they didn't have a better alternative. This is mind boggling. It seems almost idiotic. My schooling was done…
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That’s very insightful - when I switched to US high school, the approach to math was baffling - everyone had programmable graphing calculators, whereas I wasn’t allowed any calculator at all, and took a lot longer to solve the most basic problems. Most questions were answered by the teacher as “it’s a formula, you follow it and memorize it” (which sounded ridiculous to me for the exact reasons above - I was taught to…
I never understood why graphing calculators were required for basic calculus or math courses. Always wondered if it was part of a marketing deal with the company that manufactured them. The course is said to require a particular make and model of graphing calculator.
Meanwhile, most kids around me could not do something as simple as 49/7 without a calculator.
It's a loop. If you have a calculator, you use it more, so you never get better at maths, so you use a calculator more.
It's a weird article. I think this idea of 'Russian math' is very nebulous, and is probably used as marketing tool nowadays by some schools abroad. I have graduated from one of the top physics/maths high schools in Russia, and yes we had great math education there, but that was an outlier. Outside a handful of schools the math education is pretty dismal. And even in the good math schools there are different ways of t…
> What definitely exists in Russia (or at least some big cities) is a system of free after-school classe I've been studying in a "respected" Soviet / early post-Soviet school. These classes were super elitist and had a huge disconnect in their level from what you were taught in regular classes. I was a straight A student and was shut off very quickly. The problems were enormous in their difficulty and teachers had ze…
Olympiadnikas and nomenclature in particular bring back a lot of memories.
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Without the trick you get: Coffee concentration before first,second,third,fourth drinking = 1,x,y,z x = 1/2 y = x*2/3 + 0*1/3 = 1/3 z = y*5/6 + 0*1/6 = 5/18 Coffee drunk = 1/2 + 1/3 x + 1/6 y + z = 1/2 + 1/6 + 1/18 + 5/18 = 3/6 + 1/6 + 2/6 = 1 Milk drunk = 0 + 1/3(1-x) + 1/6(1-y) + (1-z) = 1/6 + 2/18 + 13/18 = 1/6 + 5/6 = 1 Which is a bit fiddly but hardly impossible. I think there is pedagogical value in doing the a…
It is not impossible but I dont think generally grade 5-6 students have a chance to solve this (of course it depends how much training they received)
Another solution is with geometry:
Start with a 1x1x1 cube of coffee. Remove top half and replace with milk. Now remove left third of resulting combined shape (leaving a 2/3 x 1/2 x 1 cuboid of coffee). Now remove front sixth (leaving a 2/3 x 1/2 x 5/6 cuboid). Now drink it all. Now add up the volumes of the shape and write down the answer.