• barsoap@lemm.ee
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    27 days ago

    Learning the actual algebraic laws, instead of an order of operations to mechanically replicate. PEMDAS might get you through a standardised test but does not convey any understanding, it’s like knowing that you need to press a button to call the elevator but not understand what elevators are for.

    Though “lazy teachers” might actually be a bit too charitable a take given the literacy rates of US college graduates mastering in English. US maths teachers very well might not understand basic maths themselves, thinking it’s all about a set of mechanical operations.

    • Halosheep@lemm.ee
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      27 days ago

      This guy is the the guy posting the answer and then spending hours fighting the idiots who got it wrong on Facebook.

      Nerd.

    • AbidanYre@lemmy.world
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      27 days ago

      Is it also lazy to learn Roy G. Biv to know the color spectrum instead of learning all the physics and optical properties behind that?

      Or what about My Very Elderly Mother Just Served Us Nine Pickles to know the planets instead of learning orbital dynamics and astrophysics?

      Christ man, it’s a mnemonic device for elementary schoolers.

      • barsoap@lemm.ee
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        27 days ago

        Those two things are memorisation tasks. Maths is not about memorisation.

        You are not supposed to remember that the area of a triangle is a * h / 2, you’re supposed to understand why it’s the case. You’re supposed to be able to show that any triangle that can possibly exist is half the area of the rectangle it’s stuck in: Start with the trivial case (right-angled triangle), then move on to more complicated cases. If you’ve understood that once, there is no reason to remember anything because you can derive the formula at a moment’s notice.

        All maths can be understood and derived like that. The names of the colours, their ordering, the names of the planets and how they’re ordered, they’re arbitrary, they have no rhyme or reason, they need to be memorised if you want to recall them. Maths doesn’t, instead it dies when you apply memorisation.

        Ein Anfänger (der) Gitarre Hat Elan. There, that’s the Guitar strings in German. Why do I know that? Because my music theory knowledge sucks. I can’t apply it, music is all vibes to me but I still need a way to match the strings to what the tuner is displaying. You should never learn music theory from me, just as you shouldn’t learn maths from a teacher who can’t prove a * h / 2, or thinks it’s unimportant whether you can prove it.

        • Maths is not about memorisation

          It is for ROTE learners.

          You are not supposed to remember that the area of a triangle is a * h / 2

          Yes you are. A lot of students get the wrong answer when they forget the half.

          you’re supposed to understand why it’s the case

          Constructivist learners can do so, ROTE learners it doesn’t matter. As long as they all know how to do Maths it doesn’t matter if they understand it or not.

          You’re supposed to be able to show that any triangle that can possibly exist is half the area of the rectangle it’s stuck in

          No they’re not.

          If you’ve understood that once, there is no reason to remember anything because you can derive the formula at a moment’s notice.

          And if you haven’t understood it then there is a reason to remember it.

          you can derive the formula at a moment’s notice

          Students aren’t expected to be able to do that.

          All maths can be understood and derived like that

          It can be by Constructivist learners, not ROTE learners.

          The names of the colours, their ordering, the names of the planets and how they’re ordered, they’re arbitrary

          No they’re not. Colours are in spectrum order, the planets are in order from the sun.

          Maths doesn’t, instead it dies when you apply memorisation

          A very substantial chunk of the population does just fine with having memorised Maths.

            • AbidanYre@lemmy.world
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              12 hours ago

              But +, -, *, and / are all binary operators?

              As far as I know, the only reason multiplication and division come first is that we’ve all agreed to it. But it can’t be derived in a vacuum as that other dude contends it should be.

              • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.dev
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                5 hours ago

                But +, -, *, and / are all binary operators?

                No, only multiply and divide are. 2+3 is really +2+3, but we don’t write the first plus usually (on the other hand we do always write the minus if it starts with one).

                As far as I know, the only reason multiplication and division come first is that we’ve all agreed to it.

                No, they come first because you get wrong answers if you don’t do them first. e.g. 2+3x4=14, not 20. All the rules of Maths exist to make sure you get correct answers. Multiplication is defined as repeated addition - 3x4=3+3+3+3 - hence wrong answers if you do the addition first (just changed the multiplicand, and hence the answer). Ditto for exponents, which are defined as repeated multiplication, a^2=(axa). Order of operations is the process of reducing everything down to adds and subtracts on a number line. 3^2=3x3=3+3+3

          • barsoap@lemm.ee
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            27 days ago

            Nothing. And that’s why people don’t write equations like that: You either see

                 4
            6 + ---
                 2
            

            or

             6 + 4
            -------
               2
            

            If you wrote 6 + 4 / 2 in a paper you’d get reviewers complaining that it’s ambiguous, if you want it to be on one line write (6+4) / 2 or 6 + (4/2) or 6 + ⁴⁄₂ or even ½(6 + 4) Working mathematicians never came up with PEMDAS, which disambiguates it without parenthesis, US teachers did. Noone else does it that way because it does not, in the slightest, aid readability.

            • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.dev
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              15 hours ago

              And that’s why people don’t write equations like that

              Says someone who clearly hasn’t looked in any Maths textbooks

              If you wrote 6 + 4 / 2 in a paper you’d get reviewers complaining that it’s ambiguous

              Only if their Maths was very poor. #MathsIsNeverAmbiguous

              Working mathematicians never came up with PEMDAS

              Yes they did.

              which disambiguates it without parenthesis

              It was never ambiguous to begin with.

              Noone else does it that way

              Says someone who has never looked in a non-U.S. Maths textbooks - BIDMAS, BODMAS, BEDMAS, all textbooks have one variation or another.

    • dohpaz42@lemmy.world
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      27 days ago

      You might be smart, but you’re still wrong about the importance of order of operations; especially in algebra.

      As far as teachers go, you’re being a dick by generalizing all (US) teachers are lazy and do not understand math.

      Pro tip: opinions are like assholes; you too have one, and yes it too stinks.

    • baines@lemmy.cafe
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      27 days ago

      just say you like the smell of your own farts, it would be less text for us to read for the same result