Definitely some of it is just more repetitions. But it does sound like the Soviets had a different approach (for their top students anyway) than the memorization we learn here. Here’s the HackerNews stream I got that from.
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 equations/methods is paramount
teachers are astute at spotting students who memorize blindly, and will intervene to correct that
while rigorous about notation, the mathematical representation always comes after understanding, not before
the progression of teaching (order how material is introduced) is very well thought out
the old soviet textbooks are generally less verbose than North American ones (less fancy), but high quality in their expression, typesetting, and ESPECIALLY (!!!) the quality of the exercises
the Soviet Math textbook exercises are something to behold: they have funny/memorable setting (like jokes), they are short and easy to express, the numbers are chosen in such a way that the result will be a nice whole number, or pi, etc. Basically as a kid you can read one of those problems, lay down, close your eyes, and work on it in your head.
That being said, I did like some of the aspects from the so called “Western Math” (in my case Canadian university):
teachers are more approachable, more friendly
textbooks can be gorgeous (nice colorful plots, etc)
I was like this. I refused to do it the way they taught by carrying numbers - at least for a while. I would always try to find shortcuts. Probably good for me in the long run to try different methods.
I also had a class in 7th grade where they taught you fun stuff like the digits of a number that is divisible by 3 will always add up to three. How to do square roots by hand. A bunch of other stuff I can’t remember. I liked the class a lot.
China is moving to heavily regulate after school tutoring because of fears of the arms race it’s become leading to increased inequality of education. I saw an article on this on Twitter a while ago. Maybe I’ll dig it up. We may be headed down the same road.
Re calculation, I emphasized it to my students partly for speed. You can do some calculation in your head in less time than it takes to pick up a calculator, and a few seconds saved here and there adds up on a timed physics or math exam. And those exams determine grades, which are all most people care about. Devlin doesn’t like that. I don’t either but I want my students to do well in the game as it is.
Yeah even for non-applied situations - like arguing covid and someone is nibbling around the edges on some point that obviously won’t move the needle more than a % or two either way.
I mean like Dan pointed out without a ballpark estimate of what right should look like your risk of catastrophic error goes up several thousand percent.
I may have a reputation amongst my former colleagues (I’ve been called rainmain). I would write down a number for my neighbor to see in a room full of chemE’s while they unholstered their calculators. After 30-60 seconds they come up with 98.7. I’d have written down 98.5. It’s just quick mental math, but there are times it’s not really a conscious process.
Even more, when data doesn’t make sense the numbers literally wave at me “hey Dan” until I can figure out what’s wrong with them. Of course I can’t keep my mouth shut, pointing out errors is not always popular. But that’s the thing with applied science. If it doesn’t work it will bite you in the ass. So being right is king.
the problem is that when we perpetuate the anecdotal evidence, we are comparing special treatment that promising students got in ussr/russia, to average students in usa. i’ve also experienced good instructions just outside moscow, which was pretty good, but not as good as top high school in moscow who specialized in math/physics, and i experienced an average suburban high school in usa, which isn’t the same as an urban high school or magnet or private. the only obvious difference is that russian curriculum does more hours on algebra/geometry starting in like 4th or 5th grade. in usa, that sort of advancement comes maybe grade 8 or 9.
No idea what common core is so I googled it and here’s the first example I found.
How would you do the mental math for 82 - 49?
I do, 2 - 9 is 3, subtract 1 from 8, then 7 - 4 = 33, like I learned to do it on paper 40 years ago.
Probably 82 - 40 = 42 - 9 = 33 is quicker, but it’s not how I learned and isn’t necessary for subtraction. I mean this is so simple you can pretty much just see that 82 - 49 is going to be 33 without any calculating.
Common core is
This just seems weird to me but maybe it’s easier to add by 10 than to subtract by 10?
For multiplication I’d break it down instead of trying to do the paper calculation in my head:
82 * 49 = 82 * 50 (= 4100) - 82 = 4018, or
8200 / 2 (= 4100) - 82 = 4018
this is the myth in action. what i remember of first and second grade in good old ussr is memorizing addition and multiplication tables upto 100. then noone bothers to think of the right ways of doing 82-49.
Here’s an article on China and after-school tutoring.
after-school tutoring will be prohibited during weekends, public holidays and school vacations
More than 75% of students aged from around 6 to 18 in China attended after-school tutoring classes in 2016,
China’s for-profit education sector has been under scrutiny as part of Beijing’s push to ease pressure on school children and reduce a cost burden on parents that has contributed to a drop in birth rates.
Keith Devlin talks and writes a lot about math education on his blog and on twitter (when he’s not cursing all things Trump), among other places. Here’s a short article where he talks about de-emphasizing calculation.
I think one of Common Core’s greatest strengths, which is also why it drew so much criticism, was how it taught students to do the same thing in different ways. Some of those ways may seem counterintuitive or slow to some people (thus the criticism), but it may really help others. We’re already seeing a few different ways of 82-49 here, and none of them have really been wrong. And for those who have just one preferred way, it’s still good to show how there are different ways of thinking about problems, and to see how when moving away from arithmetic and into other areas of math, like geometry, the pictorial ways of solving problems earlier can really pay off.
In college I had a young Russian math professor. I would ask him any math question in his office hours. The answers started with “yes, as we learned in high school…”.
The best question I asked him was about the definition of piecewise smooth being redundant. How could a function be continuous on an interval but not differentiable anywhere on the interval?
but of course, a function can. As he learned in high school…
Construct a function as the sum of a series of repeating triangle functions /////\ where the height is cut in half and the frequency doubles each time. This is a continuous function which is not differentiable anywhere.
