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

#61

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

#62

Post by [deleted] » Sat, Oct 31, 2015, 3:24 PM UTC

[deleted]

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

#63

Post by lips » Sat, Oct 31, 2015, 3:24 PM UTC

I'd be fully ok with this if the kid in question was actually learning about "Equals Versus Equivalency," but all of my school experience says that's unlikely. I hope I'm wrong.

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

#64

Post by jmilloy » Sat, Oct 31, 2015, 3:24 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.

I agree with you. The learning objective is stated as "I can use multiplication strategies to help me multilpy", but it's important that the question asks about a specific multiplication strategy, and marks the question as partially correct because the specific multiplication strategy desired is used only partially correctly.

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

#65

Post by sparkie » Sat, Oct 31, 2015, 3:24 PM UTC

JoeAltmaier wrote: post #43

Its a trivial mistake; we don't know the context; the kid could (and maybe was) tutored on the difference. All about nothing.

It's the tutor who needs tutoring on the non-difference.

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

#66

Post by phamilton » Sat, Oct 31, 2015, 3:28 PM UTC

JoeAltmaier wrote: post #43

Its a trivial mistake; we don't know the context; the kid could (and maybe was) tutored on the difference. All about nothing.

Precisely. Is this a homework assignment? Did the teacher explicitly teach it the way it was marked? Did the teacher follow up with the student to understand why the student strayed from the path taught? Who knows, but if they did then good job. Broken foundations have huge consequences, and if being pedantic makes it easier to spot broken foundations, then it's the right approach.

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

#67

Post by jmilloy » Sat, Oct 31, 2015, 3:30 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…

> 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".

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

#68

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

JoeAltmaier wrote: post #50

scintill76 wrote: post #40

Earlier quoted context omitted.

> 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 b…

They are being multiplied, as in drawing a rectangle with one side equal to each number. There's no 'first' and 'second'; the idea that one is a count and the other being copied shows a fundamental misconstruction.

I don't really support the pedantry that's going on in the grading, but I'm not sure I agree with you. To the observer looking at a non-moving rectangle, "length" and "width" are not interchangable. In the same way, there are indeed a "first" and "second" by simple definition of the way English/math notation work (in other words, "left" and "right".) The student was asked to use the "repeated addition strategy" and an "array" -- if the algorithm for doing those was taught using a specific order of the operands, the student is technically wrong to swap them. Whether or not it's fair or useful to deem them wrong when they are giving an equal but non-equivalent answer, or whether or not the algorithm should care about order when the underlying mathematical operation is commutative, are other issues.

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

#69

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

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, and work on equivalence down the line….

  Brett Berry's Answer:
  I agree! Great opportunity for learning!!

... I would say that this author has no idea what's he talking about. Saying "I agree" to a refutation of your article is dangerously close to agreeing that your article is more rhetoric than substance. Especially when considering the self-righteous tone, this article seems little more than your garden-variety mental gymnastics: dressed up in pretty rhetoric which barely obscures the lesions of condescension, defensiveness, and disdain for others.

Flagged.

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

#70

Post by jmilloy » Sat, Oct 31, 2015, 3:34 PM UTC

ryandrake wrote: post #58

pohl wrote: post #44

Earlier quoted context omitted.

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.

When are practising skills in school, sometimes we practice creativity and sometimes we practice techniques. Both are useful, and it's clear which is which.

Secondly, a student that knows the difference between different techniques and can call them up at will (such as the difference between 5 sets of 3 and 3 sets of 5) is better off than a student that only knows how to produce a particular answer for a particular question.