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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

#131

Post by jmilloy »

chris_wot wrote: post #120
jmilloy wrote: post #114

Earlier quoted context omitted.

That's not part of the definition . That's a separate property . I'm not sure we should care about that in elementary school, so the point is not to defend the teacher but only that you can't use the definition as an argument against the teacher.

No, I'm afraid you've not given a complete definition of multiplication. You need to also show that multiplication is commutative, which is indeed a property of multiplication but MUST be included in the definition. At the child's level (primary age child, NOT high-school) then it is unnecessary to introduce the distributive property. But you honestly have to make the associative property very, very clear of the chil…

Well, maybe you can find a source, but I can only find sources that define multiplication as I have and then mention that multiplication of, say, real numbers, is commutative.

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

#132

Post by scintill76 »

JoeAltmaier wrote: post #101
scintill76 wrote: post #68

Earlier quoted context omitted.

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 a…

Then we can only conclude, the syllabus is teaching nonsense. They are structuring things that don't need (and shouldn't be) structured; they are instilling fake rules in plastic young minds that will take enormous effort to unlearn later. Math is important. Teaching some witchcraft-inspired rote math is destructive to real learning. And rectangles exist regardless of how you view them. If I approach your desk and se…

Yes, the difference between length and width is only one of perception or orientation. I emphasized it because I felt like you went too far in the other direction, almost implying that which axis is which doesn't matter geometrically. A 5x3 rectangle drawn in 2D space with labeled axes is not the same as a 3x5 rectangle, even if they have equal perimeter and area. There might be some value in trying to make sure the student understands that.

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

#133

Post by pohl »

ryandrake wrote: post #94
pohl wrote: post #34

Earlier quoted context omitted.

"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 studen…

I don't think "merge sort vs. insertion sort" is a good analogy in this case. This seems more like the teacher is deducting points because of a wrong indentation or brace style.

It's not an analogy.

I was giving a different example of an algorithm than the one denoted by the assignment. "Use the repeated addition strategy..." is a clear call to demonstrate the application of a named procedure.

This is no accident, by the way. This is a deliberate design decision of those who created the common core standards. One of the goals is to teach algorithmic thinking.

It's pretty easy to google about if you can find your way through the reactionary hissy-fit memes.

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

#134

Post by scrollaway »

jmilloy wrote: post #130
scrollaway wrote: post #124

Earlier quoted context omitted.

> But what exactly is lost if you get 1 out of 2 instead of 2 out of 2 on a quiz in 3rd grade? Spoken like someone truly unaware of how children think! You should work in education, there's plenty of people like that there. The child could in fact become horribly confused about multiplication because of a bullshit technicality, and this could set them back months. Or the child could be certain they're right and this…

I think you would find we agree much more than we disagree. Though what I find most infuriating is the blanket assumption (with similar level of disconnect) that what is being taught is mindless or confusing with no value, often simply because it's labeled as a "curriculum" or a "learning objective". You're not automatically right because you "experienced similar BS"; instead you have to realize that you, too, are co…

You're still stuck in the theory, talking about how the people in this thread feel when none of them matter. The child matters, that's it.

> It's so important for young students to feel like they understand and will continue to understand, in order for them to then achieve new understanding. I don't know how to write that without sounding like a theorist, but I sincerely believe it to be true. You've got to get rid of that fear of red ink.

None of what has been applied in the photo is pedagogical and will lead to "getting rid of the fear of the red ink". Seriously man, take a step back, punishing a child for being right will make it worse if anything. Even if what you were talking about was a thing (it's not - the closest thing that comes to it is fear of failure and it's dealt with outside of tests), this would NOT help it.

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

#135

Post by jmilloy »

scrollaway wrote: post #134
jmilloy wrote: post #130

Earlier quoted context omitted.

I think you would find we agree much more than we disagree. Though what I find most infuriating is the blanket assumption (with similar level of disconnect) that what is being taught is mindless or confusing with no value, often simply because it's labeled as a "curriculum" or a "learning objective". You're not automatically right because you "experienced similar BS"; instead you have to realize that you, too, are co…

You're still stuck in the theory, talking about how the people in this thread feel when none of them matter . The child matters, that's it. > It's so important for young students to feel like they understand and will continue to understand, in order for them to then achieve new understanding. I don't know how to write that without sounding like a theorist, but I sincerely believe it to be true. You've got to get rid…

The child isn't being punished.

The child wasn't right.

That's okay.

They child might not know it's okay. In that case, they should receive support.

Getting marked wrong doesn't help get rid of the fear of failure; we agree about that. Not sure why you got the impression I thought otherwise.

Many people in the thread are reacting against the lesson and grading because of how they feel, not about how the child feels. That's why how they feel matters, when discussing it in an ultimately irrelevant forum.

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

#136

Post by Someone »

jmilloy wrote: post #70
ryandrake wrote: post #58

Earlier quoted context omitted.

"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 q…

I seriously doubt this student "only knows how to produce a particular answer for a particular question". Are you claiming he could compute 3 times 5 but not 5 times 3?

On the contrary, I think this student may be showing that he knew the two techniques, and that he is smart enough to pick the easier computation.

But yes, if your goal is to kill any creativity in intelligent should punish kids that deviate from the lines hard.

If a teacher asked "compute 1000 x 1", no sane kid would do "1 plus 1 equals 2; 2 plus 1 equals 3;...; 999 plus one equals 1000".

This teacher would have failed Carl Friedrich Gauss, too, for computing sum(1,100) in seconds.

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

#137

Post by aninhumer »

jmilloy wrote: post #135
scrollaway wrote: post #134

Earlier quoted context omitted.

You're still stuck in the theory, talking about how the people in this thread feel when none of them matter . The child matters, that's it. > It's so important for young students to feel like they understand and will continue to understand, in order for them to then achieve new understanding. I don't know how to write that without sounding like a theorist, but I sincerely believe it to be true. You've got to get rid…

The child isn't being punished. The child wasn't right. That's okay. They child might not know it's okay. In that case, they should receive support. Getting marked wrong doesn't help get rid of the fear of failure; we agree about that. Not sure why you got the impression I thought otherwise. Many people in the thread are reacting against the lesson and grading because of how they feel, not about how the child feels.…

The purpose of marking a test is to communicate to the child whether they understand the topic. Marking an almost correct answer wrong (without elaboration) is bad feedback.

The problem that people are raising here isn't how the child feels, it's how the child thinks. And one thing they might think as a result of this answer is "Oh, I guess multiplication isn't the same both ways. I must have been mistaken." and it might take some time for this misunderstanding to clear up.

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

#138

Post by aninhumer »

sophacles wrote: post #86
learnstats2 wrote: post #13

This article defends multiplication marked incorrectly because of a semantic difference between 5x3 and 3x5. I recognise there is semantic difference (although I don't think the Wikipedia reference is correct about its nature). If the marker's motivation is to identify that difference, then this is horribly misguided. In my opinion the marker has just made an error. Note the stated goal of the exercise: "I can use mu…

Teaching necessarily forces a rigor not seen in most actual usage. This is because there is a need to build concepts on top of one another. So while 3x5 and 5x3 are the same in practical usage, it this method helps in later steps like algebra: 5x = x + x + x + x, i can't rearrange that into terms of 5+ without involving even more concepts (like recursion etc)

>Teaching necessarily forces a rigor not seen in most actual usage. This is because there is a need to build concepts on top of one another.

To be honest, what I take away from this is "It's easier for the teacher to keep track of progress if everyone takes the same path to understanding". This might be true, but is precise knowledge of progress more important than the benefits of allowing different paths? I'm inclined to think it will stunt their creativity and exploration in ways that slow them down overall.

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

#139

Post by chris_wot »

jmilloy wrote: post #131
chris_wot wrote: post #120

Earlier quoted context omitted.

No, I'm afraid you've not given a complete definition of multiplication. You need to also show that multiplication is commutative, which is indeed a property of multiplication but MUST be included in the definition. At the child's level (primary age child, NOT high-school) then it is unnecessary to introduce the distributive property. But you honestly have to make the associative property very, very clear of the chil…

Well, maybe you can find a source, but I can only find sources that define multiplication as I have and then mention that multiplication of, say, real numbers, is commutative.

What are your sources?

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

#140

Post by JoeAltmaier »

scintill76 wrote: post #132
JoeAltmaier wrote: post #101

Earlier quoted context omitted.

Then we can only conclude, the syllabus is teaching nonsense. They are structuring things that don't need (and shouldn't be) structured; they are instilling fake rules in plastic young minds that will take enormous effort to unlearn later. Math is important. Teaching some witchcraft-inspired rote math is destructive to real learning. And rectangles exist regardless of how you view them. If I approach your desk and se…

Yes, the difference between length and width is only one of perception or orientation. I emphasized it because I felt like you went too far in the other direction, almost implying that which axis is which doesn't matter geometrically. A 5x3 rectangle drawn in 2D space with labeled axes is not the same as a 3x5 rectangle, even if they have equal perimeter and area. There might be some value in trying to make sure the…

The act of calculating the area surely does mean they are the same rectangle. Because they can be written down in more than one way is a weakness of the notation; the math is independent of that.
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