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One-ten-two plus Five-ten-six:

Discussion in 'General Discussion' started by Primer, Jul 30, 2011.

?

There are 20% more girls in the class than boys. If there are 45 boys, how many girls are there?

  1. 54

    196 vote(s)
    98.0%
  2. 67.5

    4 vote(s)
    2.0%
  1. Primer

    Primer
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    From my drunk thread post:

    Quote - CarbonCopy: I have no idea if this belongs here, but this is a great article and the comments are so awesome.

    http://thelastpsychiatrist.com/2011/07/why_we_are_terrible_at_math_an.html#comments

    Can you get the answer? Do you agree that Americans are awful at reading and math? If anyone can pick out who I am in the comments I will give you $20*. /quote

    This is a fairly interesting topic but I want to start out that as an English speaking human being, I've already handicapped myself. English is actually a fairly difficult language to learn math with - it's clumsy. I'm not saying it's isn't a strong language but an incredibly difficult one to start out with.

    It all starts out with basics. Read these numbers out loud 4, 8, 5, 3, 9, 7, 6. Without looking at them, spend the next twenty seconds memorizing these numbers and write them down. If you're English, you have a 50/50 chance of remembering the entire string. If you're Chinese, you're almost certain to get it right. We human beings have memory loops that only last for about two seconds; within that two seconds, you can easily memorize whatever you want. Chinese language allows them to memorize these numbers because they can fit those seven numbers within the two second memory loop.

    Now, I'm pulling some text off of Malcolm Gladwells Outliers and out of Stanislas Dehaene's book The Number Sense.

    Dehaene Writes: Chinese number words are remarkably brief. Most of them can be uttered in less than one-quarter of a second (for instance, 4 is "si" and 7 is "qi"). Their English equivalents are - "four", "seven" - are longer: pronouncing them takes about one-third of a second. The memory gap between English and Chinese apparently is entirely due to this difference in length. In languages as diverse as Welsh, Arabic, Chinese, English and Hebrew, there is a reproducible correlation between the time required to pronounce numbers in a given language and the memory span of it's speakers. In this domain, the prize for efficacy goes to te Cantonese dialect of Chinese, whose brevity grants residents of Hong Kong a rocketing memory span of about ten digits.

    For example, we say fourteen, sixteen, seventeen and nineteen; but one could logically expect us to say oneteen, twoteen or fiveteen but we do not. Past twenty, we start changing convention to decade-number; ie: twenty two. Each number in our language has a different form, our numbering system is highly irregular. The Chinese has a very logical numbering system. Eleven is ten-one (obviously not the actual language but we will represent the Chinese numbering system this way), twelve is ten-two and Twenty-four is two-tens-four, ect. By learning how to count quicker, using a logical numbering pattern they're learning the numbering system faster than we can.

    There is also another bonus; if you ask an English seven-year old to add 37 + 22, they have to convert the words into numbers first. 2 plus 7 is 9; 30 and 20 is 50; which makes 59. Ask an Asian child to add three-tens-seven and two-tens-two, and then the necessary equation is right there, embedded in the sentence: five-tens-nine. There is a reason why kids become disenchanted with math at an early age; conceptually, it's a very difficult system to learn in English because of how clumsy our mathematical system truly is. Asian kids can learn to hold more numbers in their heads because it's quite simple and logical, which leads them to less frustration and will likely lead them to enjoying math more - they have a built in advantage to their system.

    Focus: Discuss.

    Alt-focus: Did you, like Omegaham, teach yourself a different, more simple numbering system? Figured out the English language by making your own at three? What did you figure out before the system beat it out of you?

    Edit: I don't know why but it won't let me post with quotes. I keep getting errors.
     
  2. scootah

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    I'm curious how stupid the reading population is. The answer for total class size is either 99 or 112.5 depending on how you interpret the question (54 girls, or 67.5 girls). One answer is achieved through basic reading comprehension and simple algebra. The other is achieved through stupidity. Show of hands - who's an idiot?
     
  3. Nettdata

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    I didn't even think about it or do math at all and just chose the whole number answer.

    Unless it's a class at medical school full of cadavers, it's the only viable option. Odds seemed pretty good.


    I'll PM you my mailing address for where you can send the cheque.
     
  4. scootah

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    The alterrnate option is that the guy who wrote the question didn't think it through, or there were an odd number of ginger kids in the class.
     
  5. Disgustipated

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    I know I'm not a unique and precious snowflake but what's all this shit about converting figures into words and remembering/processing them that way? I remember numbers by their visual representation, just the same as I would anything else.

    If I think of a cat, I visualise a cat - not the word "cat" (okay, maybe I do both now that I put the idea in my head).

    If I think of the number 9, I visualise "9" not "nine".


    P.S. Dibs on the 0.5 ginger if Scootah hasn't got to her already...
     
  6. sartirious

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    My ex has a dual degree in Math and Accounting, and our former roommate is going for her PhD in math at George Mason this fall. Her boyfriend already has his PhD in applied math from the University of Iowa. My current roommate has a masters in Math (and was my former instructor for Diff Eq), and his girlfriend is a highschool math instructor. Before I went into economics I spent a considerable amount of time in the Electrical and Computer Engineering department - so I'm quite familiar with all the stereotypes about the AZN's being unfairly quick at the numbers'n'shit.

    But how come no one ever mentions the Czech's? There were at least as many of those in the post-graduate math and engineering programs, and they were all ridiculously smart when it came to coursework. Dumb as bricks when it came to common sense, but what do you expect from the former Soviet Bloc?
     
  7. Trakiel

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    Call me Caitlyn. Got any cake?

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    I tried for about 10 minutes to figure out what line of idiotic reasoning to use to arrive at 67.5, and was stumped. I couldn't figure it out. So I looked at the original thread and found the answer:

    Wow.
     
  8. xrayvision

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    Maybe one of the girls in the second answer choice only has one breast.
     
  9. Nom Chompsky

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    The question is vaguely worded, and isn't really indicative of any sort of stupidity. In English, the phrase "X% more" often refers to the relationship between A & B -- i.e., B = A + .2A, and not the relationship between B and (A + B). Either answer is entirely reasonable, and it's due to the semantics of the language.
     
  10. Chellie

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    I admit to using one of the short cuts the author of the post ranted about. I just multiplied by 2 and moved the decimal left. This is bad? I always figure out percentages that way.

    It never even occurred to me to think of the problem in the context of the other possible answer, I guess my brain just automatically reduced it to the easiest solvable equation.
     
  11. Lasersailor

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    Percentages are easy to determine in your head using the number 10. I.E. For this one, you want to find out 20% of 45. Take 45, divide by 10, gives you 4.5. Since you want 20%, multiply that answer by 2 to give you 9 more girls.

    It's how I work out tips for the standard 15%. Take 45, divide by 10 to get 4.5. Divide that in half to get 2.25 for 5%. Add the 10% and the 5% to get $6.75.
     
  12. Frank

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    Since it's 20% you can just divide by 5 and save yourself a step, especially in this case since 45 is divisible by 5.

    Despite having a degree in math I'm not very good at arithmetic, if I'm not dealing with nice fuzzy round numbers that can be easily solved with tricks like the Lasersailor mentioned I'm useless. People always try to give me the bill at restaurants to figure it out, they'd be much better off using the calculator on their phone.

    With the right numbers I can use some basic properties though, 53 * 48? Just multiply 53 by 50 and then take out 106. So in my head it looks like:

    (48*53) = (48*53) + (2*53) - (2*53)
    =[(2+48) * 53] - (2*53)
    =(50*53) - 106
    =2650 - 106
    =2544

    Similarly (and probably more easily) you can do (50*48 ) + (48*3).
     
  13. Diablo

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    Here's a good one for multiplying the number 9 by anything and figuring it out quickly. Place your hands in front of you, fingers spread out. Using the number you want to multiply 9 by, working from left to right, lower that finger in succession. The fingers remaining up will give you your answer. Works for every number up to 10.

    Example: 9x6=?
    You put down your right hand thumb (6th finger from L to R) and are left with 5 fingers on your left hand, and 4 fingers on your right hand, ie 54.

    Blows your mind doesn't it!?
     
  14. Frank

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    If you need a trick to multiply any two single digit numbers do everyone a favor and kill yourself.
     
  15. Diablo

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    Oh I know, it's just something to think about as a simple work around for actually having to multiply two numbers together in your head. It's just another way of glossing over the concept of math without actually getting it.

    Edit, and sorry, I remember learning this in elementary school as a "teaching method" and just remembered it through the years.
     
  16. Popped Cherries

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    People try and determine total class size and base their answers or their assumptions on that.
    If you really read the question, it doesn't talk about total class size at all. It simply asks the relationship between the girls and the boys. Making the assumption that the class has to have percentages equaling 100 in the defined categories is the problem. The total class could consist of 10% boys 10% girls and 80% ducks.

    I was always taught that in word problems you can only find answers based on the information you are given. Adding your own take on the problem or adding additional wording will end up with you getting answers like 67.5 in the articles question.
     
  17. bewildered

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    My sister's husband is a math teacher. Whenever he's trying to teach young kids (he normally is a highschool teacher) how to do their multiplication tables, he gives them this rule. It's something to fall back on if you aren't sure about what you memorized.
     
  18. zzr

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    The question is not vaguely worded at all, and only one answer is reasonable. If you interpreted the problem as anything other than B=A+.2A, then you don't understand math. To illustrate, what happens when we say that there are 80% more girls than boys, when boys are 45? You can get either 81 girls (correct) or 405 girls using the "alternate method." What happens when we say there are 100% more girls than boys, or 120% more girls than boys. One method yields answers of 90 girls and 99 girls. The other method you are welcome to attempt on your own. You have either learned and understand math, or you have not/do not. There are no alternate answers.

    It's the same concept as the plane on the conveyor belt that someone mentioned in the comments in Primer's link. If you discern within a few seconds that the plane takes off, you have the potential to be an engineer or work in some other technical field. If there is any doubt in your mind about what the plane will do, go into a different field. There is no argument, no discussion, no alternate method of thinking.

    Can we make this poll public so we can know who the moron who picked 67.5 is?
     
  19. RCGT

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    This is my basic strategy for multiplication, division, etc. People look at me like I just grew another arm when I do this. I seriously went through all of high school stumped about why; I thought this shit was common knowledge, especially considering I never formally learned multiplication.* I actually think using shortcuts that you've derived for yourself is a great aftereffect of genuinely understanding the math. Using Frank's example, that shortcut illustrates that you've understood that multiplication is innately about grouping, and shows an intuitive understanding of certain mathematical properties (commutative, associative, etc).

    Efforts to make the US educational system more like Asian systems - by which we actually mean the stereotype of Asian systems - are pretty stupid for this reason. Rote memorization won't help you figure out the shortcuts, and figuring out the shortcuts for yourself is a huge part of understanding the material. (The "lack of creativity/out-of-the-box thinking" canard is, of course, a whole 'nother discussion.)

    *I moved in third grade - they hadn't yet gotten to times tables in my old school, and they had already gone past that part in my new school. Thank God.


    Speaking of language, while I do think that Chinese could facilitate math skills, I don't think that's the primary reason for the "Asians are better at math" thing. Some of it is just plain selection bias. The Asian immigrants who came over here on H-1Bs and the like are probably going to be inherently smart and well-educated - "Of course Asian immigrants are smart; we left all the stupid ones in Asia." So when their kids go into school, they're also brought up with that set of expectations and advantages. I know that when I was growing up, A's were taken for granted and didn't merit a whole lot of special praise. I imagine part is genetic (smart parents) and part is cultural (values/expectations).

    There's a process to doing word problems, though, that is actually really helpful even through upper-level calculus. All you have to do is write down all the information you're given using numbers and symbols. Then you can make "math" out of it without getting confused by the wording.
    Code:
    Boys = 45
    Girls = 1.2 * Boys
    Girls = 1.2*45 = 54
    Substitute terms and even an idiot could do it. (Of course, this requires understanding that "20% more than X" = 1.2*x, which may be asking too much of the average idiot.)
     
  20. effinshenanigans

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    I don't know if I feel good that I immediately knew it was 54, or bad that I don't even have a clue, based on the information provided, what alternative method could be used to get a different answer.

    In the context of this exercise, I guess I've broken even.