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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

#21
I think the argument of the article is flawed. Reason being, the "=" sign denotes equality and not equivalence. And the argument hangs on the observation that while 5+5+5 and 3+3+3+3+3 may be equal, they're not equivalent. Yeah, right, but that wasn't asked here, was it?

Edit: Also, "5"x3 or 5x"3"?

How many fingers do you see?

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

#23
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 Anyhow, just goes to show Maths teachers have now been replaced by box tickers who refuse to apply their brain.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…

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

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

#25
Here's a view of why it might make sense for a teacher to emphasize one way over the other that doesn't focus on "it's the definition and definitions are important":

> The teacher obviously knows (I’m assuming) that 5 + 5 + 5 is the same as 3 + 3 + 3 + 3 + 3.

> So why would one method be preferred over the other?

> Because thinking of 5 x 3 as, literally, “five groups of three” will help them when they learn how to divide. (That’s what the Common Core standard here is getting at.)

from http://www.patheos.com/blogs/friendlyatheist/2015/10/21/why-...

Also notable is the explicit assumption of good faith:

> Let’s assume for a second that this teacher isn’t an idiot. (I know. I know. Bear with me for a minute.)

> What possible explanation could there be for deducting points from this poor child’s exam?

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

#26
I hope this kid goes to school and tells the teacher that they were just using the Peano axioms of arithmetic.

    x * 0 = 0
    x * S(y) = x + (x * y)
So the original 5 * 3 would be

    5 * S(2) = 5 + 5 * 2
             = 5 + 5 + 5 * 1
             = 5 + 5 + 5 + 5 * 0
             = 5 + 5 + 5 + 0
             = 5 + 5 + 5

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

#27
Funny when I read the image I thought the student was optimizing to less work. His way was faster "I can use multiplication strategies to help me multiply." Seems the student's strategy was to do less work by adding 5+5+5.

When I took geometry I often was burned by my teacher when she'd ask me to come to the board and solve a problem. She'd say "You can't do that we haven't gotten to that part of the book yet, sit down already!" It all just seemed to logical to me. Maybe I didn't know what "it" was called but it was logical and easy to work out.

Most of my math teachers treated me this way, they'd be upset with me because I didn't write 100 copies of the problem on my homework but I'd pass all my tests. I was constantly in trouble with my teachers often being reported to the administration as a cheater. One teacher made me take my shirt off he was so convinced I must have written the answers on a sleeve or something. All because I didn't miss a single problem on his test but never turned in a single page of homework to his class.

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

#30
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, which can be vertical or horizontal oriented, and in either case, less clear and unambiguous than the English version.

Still I believe it's certainly teaching the wrong lesson to mark the answer as incorrect, especially when the red mark comes without explanation. Even if the problem states "Use the repeated addition strategy". The author mentions it's crucial to understand this but I don't believe important enough to discourage a young student this way. The explanation of what was requested and the method of arriving at it should be made explicit, and it may have happened in class, we just don't know.

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