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Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong

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Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong

#41

Post by Al-Khwarizmi »

pohl wrote: post #34
tomrod wrote: post #5

What a defense of nonsense. The marking punishes a student for achieving a correct answer in an appropriate way, regardless of pedagogical justification.

"Use the repeated addition strategy..." Critics of this are missing that the teacher is not asking the student to find the correct result. Instead, the teacher is asking the student to apply a specific algorithm. If the teacher asks to apply Merge Sort to a list, but the student applies Insertion Sort, both strategies will result in the same sorted list. But only one will demonstrate what the teacher asked the studen…

The student wrote 5+5+5, isn't that a repeated addition strategy?

Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong

#42

Post by ontoillogical »

1) When I was learning what "5 times 3" was I don't think I could even pronounce "commutative," let alone understand what it meant. I did know that 3 x 5 was the same as 5 x 3, but 5 / 3 was not 3 / 5 though!

2) Javascript's equality operators can confuse even longtime practitioners and bringing them up muddles the point.

I think the author is trying to say that 5 x 3, 3 x 5, and 30 / 2 are equivalent but not equal because they represent different operations, which he is somehow equating to types in computer science? This is nonsense, all three expressions are obviously the same type, and they are referentially transparent mathematical expressions, so they would be equal not just equivalent.

3) Setting students up for matrix multiplication? Really?

Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong

#44

Post by pohl »

Al-Khwarizmi wrote: post #41
pohl wrote: post #34

Earlier quoted context omitted.

"Use the repeated addition strategy..." Critics of this are missing that the teacher is not asking the student to find the correct result. Instead, the teacher is asking the student to apply a specific algorithm. If the teacher asks to apply Merge Sort to a list, but the student applies Insertion Sort, both strategies will result in the same sorted list. But only one will demonstrate what the teacher asked the studen…

The student wrote 5+5+5, isn't that a repeated addition strategy?

It certainly is a repeated addition strategy, but is it the repeated addition strategy given to the students?

The definition of the algorithm given to the student may involve language like "take the first number and..."

The steps are the steps.

Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong

#45

Post by Comaleaf »

I'm not sure why this argument tries to use programming as a justification but then uses a different example from programming as the evidence. Yes, in JS, 4 === "4" is false. But 3+3+3+3+3 === 5+5+5 is true. Because they are mathematically identical. It's a universal truth that 3+3+3+3+3 will always be equal to 5+5+5. If the idea is that the kid needs to understand the difference between equality and identity then actually it seems important that the kid does understand that 3+3+3+3+3 is identical to 5+5+5.

Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong

#46

Post by tomrod »

luckystarr wrote: post #10

In the number-fields used outside university multiplication is commutative (it even is for complex numbers!). So I can't imagine why this should not be correct. There are algebraic structures where multiplication is not commutative, but I don't think this was the case here.

On that point, matrix multiplication is not commutative (and oh that it were!).

Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong

#48

Post by lucio »

I almost stop reading at the first paragraph: He makes a difference between "Equals" and "Equivalency" and then he gives overlapping definitions:

Equal is defined as, “being the same in ...value.” Whereas equivalent is defined as, “equal in value...”

If you can't be precise in what you write yourself...

Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong

#49

Post by jonsen »

QuantumRoar wrote: post #18

There are just too many assumptions in this article. It says: Use the repeated addition strategy to solve 5x3. That is clearly what the student did. The argument about bundles and bananas is besides the point. But even then it works because 3x(5 bananas) = (3x5) bananas = 5 x (3 bananas) Of course, if I define my own special multiplication, then 3x5 != 5x3. If I put enough concepts on top of it an operate in obscure…

  3 bundle x 5 banana/bundle =
  5x3 bundlexbanana/bundle =
  5 bundle x 3 banana/bundle =
  15 banana

Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong

#50

Post by JoeAltmaier »

scintill76 wrote: post #40
howeman wrote: post #2

Sure, Wikipedia defines it as 3+3+3+3+3, but the Oxford English dictionary defines it the other way (as 5+5+5). They are both correct.

> I did something today I’ve never done before, I looked up the definition of multiplication. > And as I suspected in the definition of multiplication, the first factor is is the number of copies and the second is the number being repeated. Yeah, something seems off if an educated adult has to look up something (on the site that's always harped on for being untrustworthy in school) in order to convince us that it's b…

They are being multiplied, as in drawing a rectangle with one side equal to each number. There's no 'first' and 'second'; the idea that one is a count and the other being copied shows a fundamental misconstruction.
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