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

#71

Post by jasode » Sat, Oct 31, 2015, 3:35 PM UTC

jmilloy wrote: post #67

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…

> The "5x3" problem on the test had "pure" numbers with no annotation of "objects" It's not the "5x3" problem but the "repeated addition strategy" problem. I think that's part of the problem. Similarly, the bananas example isn't about the 5 and the 3 but about a difference between counting " x sets of y " and " y sets of x ".

>a difference between counting "x sets of y" and "y sets of x".

You're making the same mistake as the blog writer by overlaying a difference between "x" and "y" that was not on the test.

The child did do the repeated addition strategy. It's just that the child's "shape" of the addition didn't exactly match the teacher's. If the point of the problem was the "repeated addition" instead of the final answer "15", the child still did it correctly. He/she showed his work of repeated addition!

The actual test problem was stated as "5 times 3" and not "5subscriptX times 3subscriptY" or "5subscriptBundles times 3subscriptBananas". You're arguing about a test the child didn't actually take.

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

#72

Post by drtz » Sat, Oct 31, 2015, 3:35 PM UTC

The author forgets to mention that in mathematics = represents equivalency.

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

#73

Post by jmilloy » Sat, Oct 31, 2015, 3:37 PM UTC

88e282102ae2e5b wrote: post #12

> They are qualified experts on child education. This is absolutely false. Becoming a 3rd grade teacher is not that hard ( being a third grade teacher, on the other hand, surely is). > It’s more important than ever for students to understand the difference between equal as a result and equivalence in meaning from a young age because it is a fundamental computer science concept. It's not though, because you can learn…

> What exactly is lost if you don't have this figured out on your 9th birthday?

Not much. But what exactly is lost if you get 1 out of 2 instead of 2 out of 2 on a quiz in 3rd grade?

If there is a problem, it's that we can't be told that we were partially correct instead of fully correct on silly problems without it being a big deal and a failing.

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

#74

Post by husam212 » Sat, Oct 31, 2015, 3:38 PM UTC

But the question is asking the student to find a solution not something equivalent, I will agree with what this article says if the question is "Find the equivalent repeated addition form of the following multiplication problem" but it is not.

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

#75

Post by ryandrake » Sat, Oct 31, 2015, 3:39 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, the "erase your brain of that technique because we haven't gotten to that part of the book yet" reasoning was the most frustrating part of math (and science) classes in high school. It's a miracle I got through my teen years still interested in STEM. Contrast with how they treat these situations at the university level:

University: "Ahh, you seem to be pretty far ahead for MATH 140! You might as well go test out of the class and enroll in 141 instead! Save some time."

High School: "Conform to the curriculum. Repeat this technique. Obey the rules or fail."

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

#76

Post by signal11 » Sat, Oct 31, 2015, 3:39 PM UTC

hitekker wrote: post #69

After reading this article, reading the comments here and then reading the author's follow-up to a direct message: Comment: This approach seems a great way to discourage smart young kids.Do we expect geometry students to grasp integrals? Want to convert kids to be math people? Laud the child for grasping the connection between multiplication and addition, use it as an opportunity to introduce the commutive property,…

I think the meta-lesson for the child is that there'll always be people like the teacher who marked "5+5+5" wrong and this guy who defends it with bullshit reasoning, and part of learning to deal with the world involves learning that sometimes one can be absolutely right and still be penalised/marked wrong/disagreed with, and you have to deal with that, sometimes by just answering the way they expect you to answer.

It's a pretty rough lesson to learn during a math test, though. :-\

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

#77

Post by phamilton » Sat, Oct 31, 2015, 3:39 PM UTC

Potentially a straw man, but:

5*(1 + 1 + 1) is equivalent. If the student had written (1 + 1 + 1) + (1 + 1 + 1) + (1 + 1 + 1) + (1 + 1 + 1) + (1 + 1 + 1), should the teacher have marked it correct? It's essentially the approach in question 2.

I'd argue that in this example, it doesn't demonstrate an understanding of "repeated addition" and at the very least should warrant follow-up by the teacher. The commutative example is more subtle and context would be nice to understand, but if this was a no consequence homework assignment that led to a quick follow-up by the teacher then it seems like a good move.

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

#78

Post by 3pt14159 » Sat, Oct 31, 2015, 3:40 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…

I was leaning that way, but when I tried to the plain English way, I defaulted to "Five threes" not the backwards "take five and copy it out three times".

Once he made the tie back to programming he was able to change my mind that this was important enough. Although it does seem unfair for the individual child.

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

#79

Post by maxerickson » Sat, Oct 31, 2015, 3:40 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 ought to be a bridge to understanding the arithmetic as an abstraction.

Teaching and requiring that a commutative operation be ordered doesn't seem like it is going to contribute to that.

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

#80

Post by ricardobeat » Sat, Oct 31, 2015, 3:41 PM UTC

"Common Core Math problem" - yes, it does look like a special kind of math. Marking that answer wrong is the equivalent of "you are not allowed to think about this just yet". I sure hope that teacher at least sat him down to explain how multiplication is commutative.

Does anyone have a more sane explanation of what the goal is? I can't think of any way this is going to be helpful to the student.