This is a very good thread, but when I read the title, I thought it would be random tricks to quickly do computations in your head, like how to square three-digit numbers (which I can do in less than 30 seconds BRAGBRAGBRAG :D)
But yeah, I never really thought of the Chinese number naming system that way. I always thought it was simpler than the English one, which introduced fancy new words like "Twenty" and "Eleven" for things that were just "2 tens" and "ten plus one," but I didn't realize that it was subconsciously making me think and know more about math.
Really, though, quite a few people in this thread are equating correlation to causation. By that, I mean that the socioeconomic status (at least here in America) has very little to do with ability in math. I was talking with some of my Asian friends a couple years back (all 1st gen Chinese and Koreans) and we realized that most of our parents immigrated to the US with anywhere between $40 to $100 dollars in their pocket, and they lived off of that money plus whatever intelligence they had in their brains, and that was it. Currently, I'd put us all in the upper-middle class, maybe? Single family household in a nice neighborhood with a decent school system, with about half of us attending private schools, and the rest attending public magnet schools. Chronologically, their current income definitely didn't make our parents good at math. Our parents' math skills let them earn their current income! In fact, Art Benjamin (Harvey Mudd professor that does a lot of cool math stuff) said that the single most reliable factor of determining someone's yearly income was the number of mathematics classes they took in college.
Also, realize that the materials for learning math are relatively inexpensive. To learn English well, you need to first learn the language, but eventually you'll need to read famous literature by authors of the past few centuries, in order to expand your vocabulary or familiarize yourself with past writing conventions. These could be borrowed for free from a library, I suppose, but if people in some poor and unfortunate neighborhoods may not live close enough to a library to access it regularly and practically. To learn math, what do you really need? A pencil, paper, calculator (if you're getting lazy), and math problems (many of which are easily memorized, and can be given to you for free by a family member or friend). With relatively low costs, I doubt socioeconomic status greatly impacts one's ability to learn math.
And people have said that Asian parents make kids work harder. However, this alone does not make Asian kids particularly good at math. With this fact, one must also consider that the main area of knowledge that Asian immigrant parents can teach to their first generation Asian-American children is math. Asian parents can make their kids work hard to learn English, but if the child needs help at home, what can they do? By about fourth grade, I was helping my parents with English, simply because the ability of the human brain to learn a new language before seven is incredibly strong, and my parents had English as their second language, with no exposure to native English speakers until about twenty years ago. Math, however, is the same internationally. Everyone does the same addition, subtraction, differentiation, linear regression, Fourier transform, and so on, up to a very very high level (at which point it's more of an individual thing than a country thing). So while Asian parents can't help their kids with English past maybe 10 or 11 years old, their mathematics knowledge can be a college or graduate school equivalent, a more than sufficient amount to guide a child through their high school education.
On July 09 2010 05:35 Golden Ghost wrote: Sorry but this argument is just wishful thinking of the OP. You have so much different ways of using the numbers. For example where and English speaker would pronounce 24 as twenty-four in the Netherlands it would be vierentwintig (four and twenty). And when you take 81 it becomes eighty-one in English, eenentachtig (one and eighty) in Dutch and quatre-vingt-un (four twenty one) in French. If you would look to all different systems you would most likely find out your theory wouldn't hold up.
My paper would only hold up if you have the group of people from different races studying at the same level of mathmatics. Thus it can only be tested on a country with different kinds of race/nationality (USA, Canada, Australia and New Zealand) studying at the same level. People seem to be comparing the level of mathematics from their country/school with the level of mathematics from their country/school. They are not studying at the same level of mathematics nor the fact they can study at higher level proves in anyway they have natural mathematic skills. Someone put their hand up if they are from USA or Australia: a Dutch, French or Russian are dominanting math in their class and not Asians.
Also I'm Korean, not what you would call "wishful" thinking.
I do understand what you are saying but my point is that when you try to compare the two numeral systems in English and Chinese you have to have at least 1 control group. There are more languages in the world (and outside Asia) that use the same way to pronounce numbers as the Chinese. When you get them into the equation you will see that your points won't hold up as neatly as you'd like.
I know you only want to compare people taking the same classes thus inducing a third languages in the equation will make it difficult but the third language is necessary.
I'm at work at the moment so I can't give you the specific languages but when I'll come home I'll edit them in.
(oh and wishful thinking can be explained in two ways: 1) I'm xxx and this is why we are so good at xxx. So no need to criticize my family for the strict education. 2) I'm xxx and this is why people of xxx are so much better at xxx. So it has nothing to do with my work ethic they are all better. both are wishful thinking if there is no hard proof to back it up.)
aw. i thought this was going to be about secrets like indian math secrets
11 x 12 = 132 (add the two digits 1+2 and put that number in between 12) 11 x 13 = 143 (add the two digits 1+3 and put that number in between 13) 11 x 20 = 220 11 x 27 = 297 11 x 29 = 319 (2+9=11, so you carry the 1 over)
On July 09 2010 23:14 29 fps wrote: aw. i thought this was going to be about secrets like indian math secrets
11 x 12 = 132 (add the two digits 1+2 and put that number in between 12) 11 x 13 = 143 (add the two digits 1+3 and put that number in between 13) 11 x 20 = 220 11 x 27 = 297 11 x 29 = 319 (2+9=11, so you carry the 1 over)
There is also the finger trick you can do when multiplying 6-10
If you take your hands then label from bottom to top your fingers on each hand going from 6-10 6=pinky 7=ringer etc.
now take you're two hand and align up 8 and 7 on differnet hands ie your middle to touch your ring finger
now at that connecting point count those 2 fingers along with all the fingers below them there should be 5
that's how many 10's you have so 50
now with the remaning fingers above that multiply them togheter (your left vs your right hand)
you should have 2 on the left * 3 on the right making that 6
I am a math guy myself, and I have to mention a few things here
1- Their system is really good for early learners. Asian children learn math earlier than others for that reason.
2- Although its good for getting a strong and early base in mathematics, it DOES NOT give you the tools you need to do well in upper level math. It simply has no relevance to what you would actually be doing at high levels. What it DOES do is give firm fundamentals in math, which are extremely important.
3- In my opinion the higher SAT scores have nothing to do with the counting, and more to do with asian culture. From my experiences in the past in school my asian peers were CONSTANTLY nerding out and studying, where as the white students were more focused on trying to get by without doing much at all. I don't think asians are "just better at math", its more like "Asians, for the most part, work really really hard in school and are more prone to be interested in mathematics.."
On July 10 2010 06:43 Surrealz wrote: 3- In my opinion the higher SAT scores have nothing to do with the counting, and more to do with asian culture. From my experiences in the past in school my asian peers were CONSTANTLY nerding out and studying, where as the white students were more focused on trying to get by without doing much at all. I don't think asians are "just better at math", its more like "Asians, for the most part, work really really hard in school and are more prone to be interested in mathematics.."
this.
In the US especially (and probably also western Europe?), there is this kind of stigmatism towards math... lol I always remember this time on the plane coming back from math camp (wooo) when I was still under 15 and had to pay to sit at the back of the plane (stupid rule, really...) There were a bunch of younger (white) kids there. I mentioned I had just gotten back from math camp, and all of them were immediately repulsed. I asked them why they didn't like math. Each one simply said "it's boring."
What? Boring?? Math is the language of the universe! XD
I asked them what was boring about math. They didn't have anything to say. Maybe one of them said it was "hard" or something.
Asian kids, on the other hand, are encouraged (if not forced... lol) to go into math/science and be good at it. Asian kids are taking SAT math classes, AP calculus,... and doing math competitions. At math competitions in the US, probably half the kids are Asian. (Actually the older they are, the fewer Asian kids are there... lol.) At higher and higher levels, up to the top 30 freshmen on the USA Math Olympiad, about half the kids are Asian. But interestingly, at a level higher than that [like the top high school math kids], there are more white kids than otherwise... but there are certainly a lot of Asians who are really really good. And you don't get to that level by just "talent" -- you have to put in a LOT of time, and it tends to be Asians, who are encouraged to do math/science/stuff from a young age, who are willing to and not afraid to put in that kind of time. (or forced to )
Anyone can do calculus, its just a matter of having strong algebra skills. Kids in the US are NOT trying in their early algebra classes and are struggling in calculus. In my high school calculus class there were people who didn't know how to solve a complex fraction for example, and thus suffered. Bad algebra and lack of interest in performance based classes that are 90% tests are really killing the average student here in the US.
If you aren't good at something and aren't being pushed to do well at it, you are NOT going to like it. Asian people are not superior at math, its really just superior STUDENTS are good at math. Asians are almost always going to be pushed, its part of their culture.
On July 09 2010 04:41 mucker wrote: How do you explain the black children performing so poorly? They are learning the same numbers as the white kids when they grow up.
I would venture to say it's the fucked up school system where they generally live. You should watch The Wire season 4, it's all about the schools in inner cities. Eye opening shit.
On July 09 2010 11:45 igotmyown wrote: So the US is better than the rest of the world at multiplication because it uses ounces/pounds/inches/feet/miles instead of meters and grams.
If all American kids learns pounds conversion during infancy, YES! This is infancy people. They don't even know what numbers look like. =__=
And another thing, did you just generalize chinese to all asians? Koreans don't learn chinese characters, they learn western number symbols, especially in infancy and in the US. If koreans (or maybe korean americans) aren't worse than their chinese/japanese counterparts in mathematical ability, I think this hypothesis is pretty bunk.
On July 10 2010 06:43 Surrealz wrote: 3- In my opinion the higher SAT scores have nothing to do with the counting, and more to do with asian culture. From my experiences in the past in school my asian peers were CONSTANTLY nerding out and studying, where as the white students were more focused on trying to get by without doing much at all. I don't think asians are "just better at math", its more like "Asians, for the most part, work really really hard in school and are more prone to be interested in mathematics.."
this.
In the US especially (and probably also western Europe?), there is this kind of stigmatism towards math... lol I always remember this time on the plane coming back from math camp (wooo) when I was still under 15 and had to pay to sit at the back of the plane (stupid rule, really...) There were a bunch of younger (white) kids there. I mentioned I had just gotten back from math camp, and all of them were immediately repulsed. I asked them why they didn't like math. Each one simply said "it's boring."
What? Boring?? Math is the language of the universe! XD
I asked them what was boring about math. They didn't have anything to say. Maybe one of them said it was "hard" or something.
Asian kids, on the other hand, are encouraged (if not forced... lol) to go into math/science and be good at it. Asian kids are taking SAT math classes, AP calculus,... and doing math competitions. At math competitions in the US, probably half the kids are Asian. (Actually the older they are, the fewer Asian kids are there... lol.) At higher and higher levels, up to the top 30 freshmen on the USA Math Olympiad, about half the kids are Asian. But interestingly, at a level higher than that [like the top high school math kids], there are more white kids than otherwise... but there are certainly a lot of Asians who are really really good. And you don't get to that level by just "talent" -- you have to put in a LOT of time, and it tends to be Asians, who are encouraged to do math/science/stuff from a young age, who are willing to and not afraid to put in that kind of time. (or forced to )
I think you are forgetting that Asians make up less than 10% of the US population
mmm whites are less than 50% now. plus most of the 10% of Asians are first-generation --> pushed very hard and probably pretty smart (many have parents who came over for school... then again there are lots of restaurant owners too.) And I guess this goes back to--probably less than 20% of white Americans even (claim to?) like math...
On July 09 2010 23:14 29 fps wrote: aw. i thought this was going to be about secrets like indian math secrets
11 x 12 = 132 (add the two digits 1+2 and put that number in between 12) 11 x 13 = 143 (add the two digits 1+3 and put that number in between 13) 11 x 20 = 220 11 x 27 = 297 11 x 29 = 319 (2+9=11, so you carry the 1 over)
There is also the finger trick you can do when multiplying 6-10
If you take your hands then label from bottom to top your fingers on each hand going from 6-10 6=pinky 7=ringer etc.
now take you're two hand and align up 8 and 7 on differnet hands ie your middle to touch your ring finger
now at that connecting point count those 2 fingers along with all the fingers below them there should be 5
that's how many 10's you have so 50
now with the remaning fingers above that multiply them togheter (your left vs your right hand)
you should have 2 on the left * 3 on the right making that 6
then you just add up the two numbers
50+6=56
7*8=56
GO sliderules!
There's also this trick, to let you square any two digit number in a matter of 2-3 seconds. First, memorize your squares up to 25. That shouldn't be too hard, if you practice. I think most people have at least up to around 15-16 memorized.
After that, for numbers from 25-75, do this trick: 1.) Look at the distance from the number you're squaring to 50. For example, 56 is 6 above fifty. 42 is 8 below fifty. 71 is 21 above 50. Easy enough. 2.) Now, find a corresponding number that is that same distance away from 25. If we're squaring 56, which is 6 above 50, then we count 6 above 25, which is 31. For 42, our number is 17, and for 71, our number is 46. For these new numbers that we have, the units digit will be in the hundreds digit of our final answer. 3.) Square the distance. For 56, we square 6 and get 36. For 42, we square 8 and get 64. For 71, we square 21 and get 441. 4.) Add the numbers you get from steps 2 and 3 together.
So we get, 56 x 56 = 3100 + 36 = 3136 42 x 42 = 1700 + 64 = 1764 71 x 71 = 4600 + 441 = 5041
With practice, you can square two digit numbers between 25 and 75 instantly. It's not too hard to prove why this trick works, if you just spend some time with it.
For numbers 75-100, do this trick: 1.) Find the numbers distance from 100. For example, 91 is 9 away from 100. 2.) Subtract this distance from the number. 91 is 9 away, so we do 91 - 9 = 82. 3.) Multiply your answer from step 2 by 100. 4.) Square the distance, and add it to your answer from step 3.
So 91 x 91 = 8200 + 81 = 8281
This computation, too, can be fairly quick. The most difficult numbers are ones close to 75, and the ones close to and above 25. Even these, though, can take less than 5 seconds.
if i had known that this topic would've been that interesting for you guys, i would've posted that shit when i first learned it years ago. i wonder what else i know that you guys don't
Ah I didn't know this trick yet, thanks for sharing.
When I square I use the round up/down to easy numbers trick. For example 37^2 = 34*40 + 3^2. This way you only have to multiply with single digits. Also calculate from left to right so you can call out numbers almost instantly. This trick also works with squaring 3, 4, or 5 digit numbers. For example 523^2 = 546*500 + 23^2 (again, only multiplying with single digits). The hard part of 4 or 5 digit numbers is not the calculations itself, but remembering the numbers.
if i had known that this topic would've been that interesting for you guys, i would've posted that shit when i first learned it years ago. i wonder what else i know that you guys don't
Well, everybody knows stuff a lot of other people don't. So feel free to make a topic in which you explain things you think is not known to the general public. I always like to learn new stuff
EPT
)
