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posted by mrpg on Friday March 16 2018, @12:35AM   Printer-friendly
from the ∫-√(1+[f(x)']²)dx dept.

Suppose, a litre of cola costs US$3.15. If you buy one third of a litre of cola, how much would you pay?

The above may seem like a rather basic question. Something that you would perhaps expect the vast majority of adults to be able to answer? Particularly if they are allowed to use a calculator.

Unfortunately, the reality is that a large number of adults across the world struggle with even such basic financial tasks (the correct answer is US$1.05, by the way).

[...] In many other countries, the situation is even worse. Four in every ten adults in places like England, Canada, Spain and the US can't make this straightforward calculation – even when they had a calculator to hand. Similarly, less than half of adults in places like Chile, Turkey and South Korea can get the right answer.

-- submitted from IRC

High number of adults unable to do basic mathematical tasks


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  • (Score: 0) by Anonymous Coward on Friday March 16 2018, @12:53AM (13 children)

    by Anonymous Coward on Friday March 16 2018, @12:53AM (#653221)

    If you don't use certain skills often enough, they atrophy. I forgot the Pledge of Allegiance and long division (by hand), for example. And different people forget different skills at a different pace. Yes, some of these are obvious, but what is "obvious" is a matter of perspective.

  • (Score: 0) by Anonymous Coward on Friday March 16 2018, @01:24AM (11 children)

    by Anonymous Coward on Friday March 16 2018, @01:24AM (#653253)

    I work at a college and this isn't just people who have been relying upon calculators since they graduated that have abysmal arithmetic, I see plenty of students that just graduated high school who basically can't even do basic algebra even though it was required to graduate.

    A large part of the problem is students that aren't willing to do the work, but there's also the issue of schools failing the students. When I was in elementary school, I was required to memorize the times table to 10x10, it would have been better to extend it to 12x12, but a whole generation of students wasn't expected to do even that much as they grew up with inexpensive and powerful calculators.

    What's more, multiplication and division are a particular problem because of the way they're often taught and represented. You've got the times table that's commonly laid out in a way that's analogous to a cross product, but you'll have teachers also teaching it as repeated addition, which is more or less analogous to a dot product and then students don't get told about that until calculus 3. And they'll first find out about scalars and vectors sometime in high school when they take physics, if they do, or otherwise it's likely late in calculus if they take it.

    The result is that the meaning of multiplication is somewhat random. Sometimes it results in bumping a result up to another dimension and sometimes it just scales the size and students have no way of knowing which it is without skills that aren't taught in math classes.

    There's plenty of other problems, but by trying to spare the students a bit of confusion, they cause all sorts of confusion that lasts for years afterward and probably never gets addressed.

    • (Score: 1) by Ethanol-fueled on Friday March 16 2018, @01:48AM (1 child)

      by Ethanol-fueled (2792) on Friday March 16 2018, @01:48AM (#653265) Homepage

      Algebraic. Fucking. Manipulation. That's all undergrad math is, to include math majors. Get a few gems like this one, [radartutorial.eu] and practice solving (isolating) for as many variables in those equations as you can.

      I don't share your gripes about multiplication tables, but definitely do where students are taught things when it would make sense to explain a higher meaning to them (your linear algebra example). We were taught complex numbers in 7th grade, but they were improperly called "imaginary numbers," and again it was just algebra with specific rules, no applications. It would have made more sense if we were given an intro to quaternions(I/Q modulation is a thing in the real-world) or just given a cartesian-style plane and taught that a complex number is "two numbers in one," much like how vectors are. And basic vector operations are also something which should be taught at a lower level.

      The biggest problem with lower-level math is that it's not often taught by showing the student what the interpretation of the symbology is. For example not all classes which first teach determinants teach that you can interpret it as an area of a parallelogram -- it's just numbers to crunch. Not all trig classes teach basic vector operations, and they should, and knowledge of linear algebra or even basic matrices are required to understand the meaning of those.

      Perhaps America is just unenlightened nowadays. I hear European schools are teaching students early calculus and thermodynamics so they can avoid the explosions of all those grenades and bullets refugees are tossing through their windows.

      • (Score: 3, Touché) by PiMuNu on Friday March 16 2018, @11:32AM

        by PiMuNu (3823) on Friday March 16 2018, @11:32AM (#653517)

        > Perhaps America is just unenlightened nowadays ... all those grenades and bullets refugees are tossing through their windows.

        I'm pretty sure European high schools are safer than US ones.

    • (Score: 2, Insightful) by Anonymous Coward on Friday March 16 2018, @02:04AM

      by Anonymous Coward on Friday March 16 2018, @02:04AM (#653272)

      I work at a college and this isn't just people who have been relying upon calculators since they graduated that have abysmal arithmetic, I see plenty of students that just graduated high school who basically can't even do basic algebra even though it was required to graduate.

      That's because they focus entirely on rote memorization and teaching to the test. So no, it was not "required" to graduate; they simply had to pass enough of the tests and homework assignments. No understanding of anything is required. The same is true of the vast majority of colleges and universities. It is simply easier and cheaper to test for rote memorization, so that is what happens.

    • (Score: 0) by Anonymous Coward on Friday March 16 2018, @06:57AM (4 children)

      by Anonymous Coward on Friday March 16 2018, @06:57AM (#653422)

      When I was in elementary school, I was required to memorize the times table to 10x10,

      Go back to Japan, you Kumon shill! What is 11X 15, in Coca Cola? Yah, you Oriental educated types always fail when it come to creative thinking. Um, what was I talking about?

      • (Score: 1, Informative) by Anonymous Coward on Friday March 16 2018, @09:33AM (1 child)

        by Anonymous Coward on Friday March 16 2018, @09:33AM (#653468)

        11X 15

        1+5 = 6, so 165.

        Multiplying a two digit number by 11 is as easy as adding the two digits together and sticking the result in the middle. Until the sum ends up being two digits, then you need to think a bit more.

        • (Score: 1, Informative) by Anonymous Coward on Friday March 16 2018, @08:15PM

          by Anonymous Coward on Friday March 16 2018, @08:15PM (#653772)

          11 * x = 10x + 1x has always been easier for me

      • (Score: 0) by Anonymous Coward on Friday March 16 2018, @01:42PM

        by Anonymous Coward on Friday March 16 2018, @01:42PM (#653587)

        What is 11X 15

        That depends on the value of X. ;-)

      • (Score: 0) by Anonymous Coward on Saturday March 17 2018, @05:54AM

        by Anonymous Coward on Saturday March 17 2018, @05:54AM (#653973)

        first off, I'm American and white.

        Second off, the basis for improvisation and creative problem solving is memorized facts. It's neither practical nor necessary to rederive them every time you need them.

        People claiming otherwise are usually middling at best because they aren't bright enough to know what to memorize and what to understand in depth.

    • (Score: 0) by Anonymous Coward on Friday March 16 2018, @10:33AM (1 child)

      by Anonymous Coward on Friday March 16 2018, @10:33AM (#653494)

      When I was in elementary school, I was required to memorize the times table to 10x10, it would have been better to extend it to 12x12

      Ah, memorizing...

      My brother was taught to memorize, I was taught to multiply. He is getting better, but he still asks me when things start getting complicated, because asking me is just as fast as pulling out his phone and opening the calculator app.

      I still don't have everything memorized up to 10x10, but I can calculate the remaining ones in my head, just like an can calculate 72x72 in my head.

      • (Score: 0) by Anonymous Coward on Saturday March 17 2018, @05:47AM

        by Anonymous Coward on Saturday March 17 2018, @05:47AM (#653969)

        People who haven't memorized their math facts make incompetent mathematicians. We expect certain things to be memorized because constantly looking things up makes progress incredibly slow. It also results in unnecessary cognitive load.

        The 12×12 multiplication table includes enough values that you can quickly do in your head and extend to be able to handle most college math.

        I can do far more than 12×12, but without those memorized values the process is grossly inefficient.

    • (Score: 2) by Immerman on Friday March 16 2018, @03:34PM

      by Immerman (3985) on Friday March 16 2018, @03:34PM (#653627)

      It was at least 12x12 for me, possibly more, and I never really got them all down, had to recalculate many from nearby ones I could remember, and I rarely used most of them, even having earned a math degree. The thing is, arithmetic and math have fairly minimal overlap, and wherever non-trivial arithmetic is needed, calculators can do the job faster and more accurately. The days of "you won't always have a calculator with you" are pretty much gone. It's one of the things that really pisses me off with "new math" - they're busy teaching shortcuts for arithmetic, shortcuts which generally obscure the underlying principles, when everyone is already carrying around the ultimate shortcut. Especially horrible since the only reason anyone needs shortcuts are to perform repetitive tasks, and the only repetitive math tasks students are ever likely to perform without a calculator in their entire lives, is the classwork that is supposed to help them learn something useful.

      I'm curious as to your reference to the cross-product and dot-product similarities, I see neither similarity, except perhaps in general layout, which is simply a symptom of the limited ways of presenting information on a 2D surface, and not reflective of any underlying similarities. I'm generally opposed to drawing attention to those kinds of similarities, as they're far more likely to confuse than enlighten. I mean a "times table" is a *table* for crying out loud - it's right there in the name - it's for looking up information, and has absolutely zero relationship to matrices or cross-products beyond the fact that information is laid out in a grid fashion.

      Meanwhile repeated addition is what multiplication IS - that's the very *definition* of the operation. Just as exponentiation is repeated multiplication. It's shorthand for a more tedious operation, accompanied by the derived rules for how they interact with other operations, and how they can be calculated without resorting to tedium. And those rules don't always map well to vectors, complex numbers, quaternions, matrices, etc - but those are much later constructs that had to discard some of the traditional rules that didn't make sense, and/or add additional operations to exploit new possibilities. You talk about the results of multiplication being "random", but that's hardly the case: you *can't* multiply vectors by each other - the entire concept is undefined. You can perform cross- or dot-products, but neither is "multiplication" in a traditional sense. You also can't "push up" to another dimension - the cross-product is undefined for two-dimensional vectors, it can only be performed between vectors in 3+ dimensional space. It's not uncommon to exploit the calculation when working with 2D vectors, but that's a useful "cheat", recognizing that you can exploit degenerate-forms of higher-dimensional calculations for convenience - it's NOT a mathematical operation.

  • (Score: 2) by Pino P on Friday March 16 2018, @05:23PM

    by Pino P (4721) on Friday March 16 2018, @05:23PM (#653690) Journal

    And then there are people who deliberately forget the Pledge of Allegiance because it's statolatry [wikipedia.org]. If pressed, they recite a playground rhyme [playgroundjungle.com] derived from an accident during a TV ad production in January 1984 [wikipedia.org]:

    I pledge allegiance to the flag
    Michael Jackson makes me gag
    Pepsi-Cola burned him up
    Now he's selling 7 UP