Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong • Hacker News Board

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

#31

Post by TeMPOraL » Sat, Oct 31, 2015, 3:05 PM UTC

pbreit wrote: post #23

signal11 wrote: post #19

Earlier quoted context omitted.

I found this link interesting. Under this "Common Core" curriculum, apparently, students are trained to read 5x3 as "five groups of three" which is why 3+3+3+3+3 is right and 5+5+5 is wrong. http://www.businessinsider.com/why-55515-is-wrong-under-the-... It's hilarious because I read 5x3 as "5, 3 times". Anyhow, just goes to show Maths teachers have now been replaced by box tickers who refuse to apply their brain. In…

How do you not read it "5 times 3"? Why would you re-arrange where the "times" is?

You're joking, right?

GP read it as: "5 x3", like he would read "copy x3", or "copy, three times". It's a natural way of reading "5x3", though I personally read it as "5x 3".

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

#32

Post by jules » Sat, Oct 31, 2015, 3:05 PM UTC

This is how you ensure that somebody will never like math.

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

#33

Post by xworld21 » Sat, Oct 31, 2015, 3:06 PM UTC

signal11 wrote: post #19

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.

I found this link interesting. Under this "Common Core" curriculum, apparently, students are trained to read 5x3 as "five groups of three" which is why 3+3+3+3+3 is right and 5+5+5 is wrong. http://www.businessinsider.com/why-55515-is-wrong-under-the-... It's hilarious because I read 5x3 as "5, 3 times". Anyhow, just goes to show Maths teachers have now been replaced by box tickers who refuse to apply their brain. In…

Funnily enough, the traditional formal definition of product is due to Peano and it would say 5x3=5+5+5: https://en.m.wikipedia.org/wiki/Peano_axioms#Multiplication

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

#34

Post by pohl » Sat, Oct 31, 2015, 3:06 PM UTC

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 student to demonstrate.

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

#35

Post by dznkorxt76qb » Sat, Oct 31, 2015, 3:07 PM UTC

jasode wrote: post #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 co…

> "you'll see in Question #2 that the child had a "different rectangle orientation" than the teacher"

Vectors can be considered identical for the same reason... [1, 0] and [9, 0] are the same arrow if you move your head in the latter case. Here, the teacher is assuming the kid's head is at [0,0], when rotation (or translation) doesn't change the arrow any more than the rectangle. Neither is wrong. The lesson: memorize the teacher's poor use of language; ignore objective reality.

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

#36

Post by emsy » Sat, Oct 31, 2015, 3:07 PM UTC

I may have bought the explanation if the answer below hadn't been marked incorrect as well, because the axis on an imaginary array are arbitrary.

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

#37

Post by newjersey » Sat, Oct 31, 2015, 3:08 PM UTC

tremendo wrote: post #30

jasode wrote: post #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 co…

When I learned English (second language) I remember thinking "wow, wonderful, the language of multiplication tells you exactly what to do!" which I read as, in this case 5 × 3 => "[five times] three" 3+3+3+3+3, as the teacher illustrated, but here the student apparently answered "five [three times]". In my first language (Spanish) the multiplication is read as "five by three" which conjures up rectangles or lists, wh…

If you look at the next question, they go over the five by three in a rectangle approach.

Maybe we should do away with grading students based on exam performance altogether.

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

#38

Post by adrusi » Sat, Oct 31, 2015, 3:09 PM UTC

53 is pronounced "5 times 3", synonymous with "3, 5 times in sequence". So if the problem given had been presented as "5 times 3" I would agree that that means "3+3+3+3+3".

However, just becuase 53 is pronounced "5 times 3" doesn't mean that it's exactly the same thing. We pronounce it that way because it's convenient, "times" is a one syllable word that we can inject right where the multiplication sign goes, and have it be a meaningful, representative sentence. But that doesn't mean that "53" derives its semantics from "5 times 3". "53" is an abstract mathematical expression that has no concept of "grouping". It can't have a concept of grouping --- how would you extend grouping to something like matricies.

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

#39

Post by Retric » Sat, Oct 31, 2015, 3:09 PM UTC

pbreit wrote: post #23

signal11 wrote: post #19

Earlier quoted context omitted.

I found this link interesting. Under this "Common Core" curriculum, apparently, students are trained to read 5x3 as "five groups of three" which is why 3+3+3+3+3 is right and 5+5+5 is wrong. http://www.businessinsider.com/why-55515-is-wrong-under-the-... It's hilarious because I read 5x3 as "5, 3 times". Anyhow, just goes to show Maths teachers have now been replaced by box tickers who refuse to apply their brain. In…

How do you not read it "5 times 3"? Why would you re-arrange where the "times" is?

(5, times 3) or (5 times, 3) both work.

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

#40

Post by scintill76 » Sat, Oct 31, 2015, 3:10 PM UTC

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 basic knowledge a grade-schooler should know. It implies there's not an actual consensus (as indicated by my parent comment), and/or that the fact in question does not really matter at all. I have no memory of whether I was originally taught an order that's "right." It's possible the student already learned it the opposite/"wrong" way -- what purpose is served by forcing them to change? As illustrated by the more complete photo here (https://imgur.com/gallery/KtKNmXG), the student seems to understand the geometric difference between 7x4 and 4x7, when it's more explicitly stated and the two are non-equivalent in the context.