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

#51

Post by mattmcknight » Sat, Oct 31, 2015, 3:17 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…

I feel the opposite way about the English reading "5 times 3". In English, the subject comes first, so I would expect the sentence to mean take 5, use "times" as a verb, and 3 as the adverb. Likewise, if you read it as "5 multiplied by 3", you would expect to take five, three times.

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

#52

Post by NathanKP » Sat, Oct 31, 2015, 3:18 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 Anyhow, just goes to show Maths teachers have now been replaced by box tickers who refuse to apply their brain.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…

Personally the way I learned to think of it was to read it in the order that organizes it into the fewest number of "groups". Afterall it is easier (and faster) to visualize three groups of five items, than it is to visualize five groups of three items.

For example what if it was 11 x 3. It would make no sense to try to think of it as eleven groups of three, when you can easily derive the answer far quicker as 11 + 11 = 22 + 11 = 33.

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

#53

Post by ja27 » Sat, Oct 31, 2015, 3:19 PM UTC

natmaster wrote: post #9

Multiplication 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.

But the students aren't supposed to know that yet. That's literally two topics later in the Common Core Standard, so they won't learn that for another day or two. Smh.

http://www.corestandards.org/Math/Content/3/OA/

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

#54

Post by ecspike » Sat, Oct 31, 2015, 3:19 PM UTC

kator wrote: post #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 do…

Yep. My dad taught me a bunch of math on his own and I would also get in trouble for "not showing my work" on tests.

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

#55

Post by lucio » Sat, Oct 31, 2015, 3:19 PM UTC

A 5x3 rectangle is exactly the same as a 3x5 rectangle. It is not a bundle of bananas, silly. It's just a rectangle, regardless of orientation.

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

#56

Post by jmilloy » Sat, Oct 31, 2015, 3:20 PM UTC

I am surprised to see exclusively negative reactions here. For one, the question wasn't marked wrong so much as partially incorrect (and partially correct). Secondly, the question is not "What is 5x3?" and the test is not about multiplication. It's explicitly about a specific process, which the teacher has presumably taught and which the student unequivocally got wrong.

If you were asked in the wood shop to make a drawer using dovetail joins and you instead make a drawer using a rabbet joins, well you shouldn't get full credit because the task wasn't about producing a drawer but about dovetail joins.

The learning objective may read "I can use control structures to solve tasks involving repetition", but if the question is "Use a for-loop to print the numbers from 1 to 10", and you used a while-loop, well again you would get partial credit but not full credit.

Many of us are computer programmers, and we know that many successful code solutions to the same problem are of equal quality. The worst code I work with is by people who never seem to care what the code looks like as long as it produced a correct result. Maybe they were only ever taught by teachers who would mark this 100% correct because they thought that answers matter and concepts don't.

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

#57

Post by gherkin0 » Sat, Oct 31, 2015, 3:20 PM UTC

I like how all of the comments "Recommended by Brett Berry [the author]" are the few that agree with him. What an ass.

The worst teachers I've had graded like this this one did: demanding regurgitation of the precise idiosyncratic procedure they use, while refusing to recognize equivalent methods or equivalent terminology.

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

#58

Post by ryandrake » Sat, Oct 31, 2015, 3:22 PM UTC

pohl wrote: post #44

Al-Khwarizmi wrote: post #41

Earlier quoted context omitted.

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.

"The steps are the steps". Great advice if the purpose of school is to train people for rote factory work (we have robots for that). Not such a great way to prepare future leaders or creative problem solvers.

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

#59

Post by vixen99 » Sat, Oct 31, 2015, 3:22 PM UTC

newjersey wrote: post #37

tremendo wrote: post #30

Earlier quoted context omitted.

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.

As against what happens out there in the tough world of work.

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

#60

Post by netheril96 » Sat, Oct 31, 2015, 3:22 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?

I just consider "times" the name of the multiplication operator.