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Comment on A fake Facebook event disguised as a math problem has been one of its top posts for 6 months

barsoap@lemm.ee ⁨2⁩ ⁨months⁩ 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.

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AbidanYre@lemmy.world ⁨2⁩ ⁨months⁩ ago
What fundamental property of the universe says that

6 + 4 / 2 is 8 instead of 5?

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- barsoap@lemm.ee ⁨2⁩ ⁨months⁩ 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 0.5 (6 + 2) 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.
  
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  - SmartmanApps@programming.dev ⁨1⁩ ⁨month⁩ 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 textbook - BIDMAS, BODMAS, BEDMAS, all textbooks have one variation or another.
    
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- SmartmanApps@programming.dev ⁨1⁩ ⁨month⁩ ago
  
  6 + 4 / 2 is 8 instead of 5?
  
  The fundamental property of Maths that you have to solve binary operators before unary operators or you end up with wrong answers.
  
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  - AbidanYre@lemmy.world ⁨1⁩ ⁨month⁩ 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 he contends it should be.
    
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    SmartmanApps@programming.dev ⁨1⁩ ⁨month⁩ 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.
    
    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.
    
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SmartmanApps@programming.dev ⁨1⁩ ⁨month⁩ ago

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.

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