Requiring students to blindly memorize and regurgitate arbitrary definitions and punishing the use of intellect and common sense is the worst possible way to teach math. Or anything else for that matter.
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
#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 these things later in life and still understand them just as well. What exactly is lost if you don't have this figured out on your 9th birthday?
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#13This 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 multiplication strategies to help me multiply".
Using commutativity is a multiplication strategy and it's an essential goal for students at this level to learn this as part of their work with number.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#14Mathematics education should embrace discovery as well as memorizing definitions. The commutative property for multiplication does not necessarily need to be taught before a student discovers it. They may not be able to rigorously prove it. Early on mathematics education should be about to discover and curiosity and lighter on rigor.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#15The answers were wrong. But I would have given the student at least 1/2 point if not a full point with an explanation.
Would probably depend on how how much the concept was presented in class and the books, etc.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#16What a defense of nonsense. The marking punishes a student for achieving a correct answer in an appropriate way, regardless of pedagogical justification.
Agreed. Few children are going to get to the point where the commutative property is a concern, anyway.
If we're going to be pedantic, use this as a learning opportunity. "Actually, 5x3 is slightly different than 3x5. Multiplication has this property..." Some of the kids won't care, but some will be intrigued.
Teaching it this way is a gotcha.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#17The leap from the implied definition on Wikipedia to the authoritative "by definition" one sentence later is truly stunning, surpassed only by the sudden parachuting of bundles and bananas into the unsuspecting 3s and 5s.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#18There are just too many assumptions in this article. It says: Use the repeated addition strategy to solve 5x3. That is clearly what the student did.
The argument about bundles and bananas is besides the point. But even then it works because
3x(5 bananas) = (3x5) bananas = 5 x (3 bananas)
Of course, if I define my own special multiplication, then 3x5 != 5x3. If I put enough concepts on top of it an operate in obscure mathematical domains, sure, I'll need to be careful about things being accidentally equal but not equivalent. But I bet the student expected that multiplication behaves just like the multiplication an elementary student knows. Or do you expect them to define the operations they're working with?
When I grade the work of students, I will accept any answer that is in accordance with the question. Who cares how often they commute things that commute, or if they picked an entirely different approach that was never even discussed. If it says solve X using Y and they solved X using Y, they deserve the points.
If the teacher didn't make it clear enough in his question, then it's not the student's fault.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#19What 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 my book, the kid demonstrated repeated addition and should have got the mark.
Re: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
#20A similar discussion rescued from about 15 years ago: http://mathforum.org/library/drmath/view/58567.html from which I quote:
"To my mind, it makes no difference at all which is which. In fact, today it is more common to call them both "factors" and not make such a distinction. I wouldn't fight over this, on either side."