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Math Education Science

Children May Instinctively Know How To Do Division Even Before Hitting the Books, Study Finds (medicalxpress.com) 48

Posted by msmash from the closer-look dept.
An anonymous reader shares a report: We often think of multiplication and division as calculations that need to be taught in school. But a large body of research suggests that, even before children begin formal education, they possess intuitive arithmetic abilities. A new study published in Frontiers in Human Neuroscience argues that this ability to do approximate calculations even extends to that most dreaded basic math problem -- true division -- with implications for how students are taught mathematical concepts in the future. The foundation for the study is the approximate number system (ANS), a well-established theory that says people (and even nonhuman primates) from an early age have an intuitive ability to compare and estimate large sets of objects without relying upon language or symbols. For instance, under this non-symbolic system, a child can recognize that a group of 20 dots is bigger than a group of four dots, even when the four dots take up more space on a page. The ability to make finer approximations -- say, 20 dots versus 17 dots -- improves into adulthood.
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Children May Instinctively Know How To Do Division Even Before Hitting the Books, Study Finds More

Children May Instinctively Know How To Do Division Even Before Hitting the Books, Study Finds

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  • Ask any kid to divide 15 cookies evenly... (Score:4, Insightful)

    by gurps_npc ( 621217 ) on Friday February 25, 2022 @05:28PM (#62304357) Homepage

    they will do it perfectly. If there are 4 kids, they will each get 4 cookies plus another one that is bigger than a half.

    • Re: (Score:1)

      by Anonymous Coward

      I think 3 kids will get 4 1/2 cookies as you say, and one will be crying with a pile of broken cookie halves that don't add up to 4 1/2 cookies. (because there weren't 18 cookies)

    • Correct, its called sharing food.
    • No, no divide! No share cookie!! All for me!!!!

      OM NOM NOM NOM....

      • It's been a while since an actual cookie has been seen around Cookie Monster lately. He's been in the kitchen with his grandfather lately.

    • Oh, that powerful BIG COOKIE we used to eat in preschool has been de-powered over the years. Remember, this was a product of Mrs. Fields and The Original Cookie store. You just can't find anything to go with Five Alive like that anymore.

    • Unless one of them is a little smarter (or more devious) [giantitp.com] than the others.

    • 4 kids, 4 cookies each = 16 cookies, when you wrote 15.

      More realistically, it'd be 3 cookies each, which leaves 2 cookies, which they can chop each in half to make it all fair.

      The version I heard was you have 2 kids, siblings. Parental unit offers them both a divisible foodstuff that they both like, such as cake. One must cut the treat in half. The other gets to pick which half they get.

      The evenness of the division will be atomic.

    • Re: (Score:2)

      by ljw1004 ( 764174 )

      Ask any kid to divide 15 cookies evenly... they will do it perfectly. If there are 4 kids, they will each get 4 cookies plus another one that is bigger than a half.

      Has a joke gone over my head? That's not how you divide 15 by 4!

      My kids (age 6, 6, 8) would be unable to divide 15 cookies into three equal shares without tears and tantrums...

    • No can do!

      You need cyber cookie notice and get approval before you share any cookie with anyone ...

    • Because only politicians promise 18+ cookies when they in fact only have 15..

      -Mods can't even do math.

    • Re: (Score:2)

      by Potor ( 658520 )
      who the fuck rated this insightful?

  • Why do we have idiots insisting 1/4 is bigger than 1/3?

    • Why do we have idiots insisting 1/4 is bigger than 1/3?

      Nothing says adults can divide.

    • Because they're not accurately converting it to "divide the cake into 3 or 4 even slices. You get one slice. With which do you get more cake, 3 pieces, or 4?"

      They're using the denominator as the numerator.

    • Worse example (Score:5, Interesting)

      by Roger W Moore ( 538166 ) on Friday February 25, 2022 @06:30PM (#62304621) Journal
      You think that's bad? One of my son's primary school _teachers_ once tried to persuade me that 6/9 was smaller than 2/3 after I pointed out her grading error on a maths test we were supposed to go over with our kids. Her reasoning was that "2/3 was only missing one piece of the pie" while "6/9 was missing three pieces".

      • Did that teacher go to college or collage?
        What do you call the teacher that finished last in their college (or possibly collage) class?
        Teacher.
        (I usually use that line to explain to people why their particular doctor failed so miserably.)

      • Re: (Score:2)

        by uncqual ( 836337 )

        Let me guess, a Public School? (Using the word "public" in the sense it's used in the United States).

        • Yes, only it was in Canada and the deputy principal was appalled when we showed him the nice written explanation she had provided...although she remained "teaching" at the school for several years after.

      • Re: (Score:2)

        by olau ( 314197 )

        Fractions are actually a horrible, non-intuitive invention. I don't get why the primary school system spends so much time on it. With decimals, she wouldn't have made that mistake.

        I'm not saying there's anything wrong with the concepts or anything - the notation is just really confusing. Trying to make people wrap their head around a confusing notation is a waste of time.

        I think spending more time with decimals, and teaching people about numerical errors is a much better use of time.

        • Because fractions, or rationals, are a part of math. Equivalently, you could say calculus is just confusing notation for what is simply a summation. That would be wrong too.

        • Fractions are actually a horrible, non-intuitive invention. I don't get why the primary school system spends so much time on it. With decimals, she wouldn't have made that mistake.

          The last part is definitely true: on a previous question on the same quiz, she graded my son wrong when he said that 2/5 was closer to a half than to zero. I pointed out that since 2/5 is 0.4 it is definitely closer to 0.5 than 0 and she did accept that in this case I "might" (her words) be right.

          However, I disagree that fractions are non-intuitive. They are an extremely simple convention and one that's essential to understand to do a lot of higher-level maths like algebra and calculus. They are also si

        • So because it is confusing to you we should just drop the whole thing?

          Many things taught in school are not so much just to teach you that topic as much as it is to teach critical thinking and problem solving. It also reinforces division skills etc. etc.
    • Good point. Nine out of 12 adults can't understand a simple fraction.

    • Re: (Score:2)

      by gweihir ( 88907 )

      Why do we have idiots insisting 1/4 is bigger than 1/3?

      Because there are a lot of people that can see which number is larger, but context is beyond them. The human race has a lot of idiots in it. It only becomes a problem when the idiots are what I like to call "idiots of the 2nd order", namely people that do not understand their limits and vastly overestimate their skills and insights. (The scientific literature calls them "subjects of the Dunning-Kruger effect".) Anybody that has trouble with numbers and knows it will just pull out a calculator and no harm do

  • This is old news. Plato figured this out a long time ago. And I still think it's the only true ground for mathematics. Cf. Meno 84c. ff..
  • that most humans who lacked the ability to instinctively process the difference between 2 dingos and 25 dingos wound up getting eaten (by dingos) a long, long time ago.

  • Duh (Score:2)

    by nagora ( 177841 )

    This is some fucking obvious shit. What do these people think evolution has been doing for the last billion years?

    • Re: (Score:2)

      by Entrope ( 68843 )

      Your fourth word says it all. Youth will instinctively multiply, not necessarily divide. THAT is what evolution has been doing for all that time.

    • Re: (Score:1)

      by Tablizer ( 95088 )

      > What do these people think evolution has been doing for the last billion years?

      Mostly multiplying.

    • Re: (Score:2)

      by gweihir ( 88907 )

      Actually, no. This is not about the ability itself. This is about how an individual human develops. Some of the skills kids have go missing in adults, for example, and it would be nice to know why and how it could be prevented.

  • I suspect dividing is now instinctual.
    How many divides can you name?

  • Kinda like the new math they teach in school. They break down a math problem in 8-10 steps, when I was in school, it only took 4 steps !
  • Look, I wasn't unique - all the kids in my third grade class already knew how to write in cursive. Most of us memorized the times table printed on the inside of that yellow folder which I'm pretty sure was everywhere. We couldn't wait for the teacher to let us use cursive (which they didn't do until fifth grade, IIRC). Division - well , we weren't in a hurry for that, but most of us saw it coming and some of us already understood long division by the time the teacher showed it to us.

    Ah, to be pre-adoles

  • the language used to describe the act is more difficult than the act itself.

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