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
#2Sure, 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.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#3The wikipedia definition includes commutativity. Multiplication is defined as inherently commutative there.
This is just wrong. It teaches children to hate this type of math, where even the correct answer is wrong.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#4> Equal is defined as, “being the same in quantity, size, degree, or value.” Whereas equivalent is defined as, “equal in value, amount, function, or meaning.”
Nonsense. By those definitions, equality is a special case of equivalence - one that simply neglects to strongly emphasize function (which could be taken as value; the latter still doesn't mean 'identical').
5 x 3 = 3 + 3 + 3 + 3 + 3 and 5 x 3 = 5 + 5 + 5
are both numerically equal and functionally equivalent. The student at least understands the commutative property of multiplication, unlike the teacher.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#5What a defense of nonsense. The marking punishes a student for achieving a correct answer in an appropriate way, regardless of pedagogical justification.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#6[deleted]
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#7What a Kafkaesque non-explanation. It is exactly as correct to say that the second factor is the number of copies.
People who don't understand a subject should not teach it. If they understand education but not math, then let them teach education.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#8>For example, 3 bundles of 5 bananas is different from 5 bundles of 3 bananas although they total to the same number of bananas. Their structures are different.
I don't fully buy into this justification. The "5x3" problem on the test had "pure" numbers with no annotation of "objects". It's the blog writer that inserted an additional interpretation of "bananas" or "bundles".
Instead, the "5x3" can be interpreted as counting iterations of "rows" -- or -- "columns" of a rectangle. Whichever orientation the child picked in his head can yield 5+5+5 or 3+3+3+3+3. In fact, take a closer look at the photo and you'll see in Question #2 that the child had a "different rectangle orientation" than the teacher! The Q1 & Q2 should not have been marked as incorrect.
As for the other justification about possibly using a commutative law that's out of sequence with the learning curriculum, it still seems possible to interpret "5x3" using plain English as "take 5 and copy it out 3 times". No jumping ahead to Commutative Law required.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#9Multiplication is commutative. I don't care if you can rewrite the definition on wikipedia, this is a fundamental truth of math. Far more important than your semantic nonsense.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#10In 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.