FSTDT Forums
Community => Society and History => Topic started by: Askold on October 29, 2015, 10:13:03 am
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(http://i.imgur.com/KtKNmXG.png)
http://www.businessinsider.com/why-55515-is-wrong-under-the-common-core-2015-10?ref=yfp&IR=T
I ran into a debate on another site where people were arguing about this. Some felt that 3x5 and 5x3 are COMPLETELY DIFFERENT THINGS and anyone who doesn't understand this is a moron while others were arguing that "OBAMA DID THIS" and his satanic-atheist-math is ruining USA. Which of course lead to the earlier group using this as a proof that Common core is great since the only people who oppose it are Republicans and therefore they are wrong, because Republicans are always wrong and anything that they oppose must be right. Both sides then complain about trying to put politics into math.
...A rare few insisted that no matter which way you frame it, 5+5+5 or 3+3+3+3+3, the answer will be the same and there is no mathematical difference in 3x5 and 5x3.
Though apparently this article is missing the point:
http://finance.yahoo.com/news/common-core-math-quiz-everyone-190806618.html
Apparently the teacher wasn't following the Common core standards, which makes me question why those defending this are claiming that this is how Common core does it? Are they wrong and defending this because they don't know what they are talking about but want to defend Common core or does it mean that people teach Common core the wrong way and all those defending it did learn it like that?
Still... Even if this method is trying to explain something that is used in more advanced math they are still claiming that correct answer is wrong because if it had been a different type of question then it would have been wrong.
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Argument about Common Core detected, deploying relevant link (http://www.patheos.com/blogs/friendlyatheist/2015/10/21/why-would-a-math-teacher-punish-a-child-for-saying-5-x-3-15/?ref_widget=popular&ref_blog=friendlyatheist&ref_post=theres-a-reason-non-christians-dont-share-evangelical-morals)
Hemant has written a shit-ton about common core on his blog, I'll try to find the rest of the links
EDIT:
Here (http://www.patheos.com/blogs/friendlyatheist/2015/09/21/the-dad-who-wrote-a-check-using-common-core-math-doesnt-know-what-hes-talking-about/) are (http://www.patheos.com/blogs/friendlyatheist/2014/03/07/about-that-common-core-math-problem-making-the-rounds-on-facebook/) some (http://www.patheos.com/blogs/friendlyatheist/2014/10/01/this-is-how-you-do-common-core-subtraction/) more (http://www.patheos.com/blogs/friendlyatheist/2015/03/17/its-worth-taking-a-full-minute-to-learn-how-to-add-9-and-6-a-response-to-the-common-core-critics/), not sure if I'm missing any, Hemant used to be a Math Teacher and is still certified as one, so he likes to write about this stuff a lot, you can check through the tags on his blog
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I had to learn common core about 3 years ago when I started helping my kids with homework. There was a lot of "Hold up, what?" It seems like a very complicated way of learning math.
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Bob... I am still going to disagree with most of what I've seen from Common core. In the latter link they say that the strength in Common core is that although the method is slower it is easier as the kids understand what they are doing while "The OLD way" is hard to explain. To me that just sounds like the teachers have a trouble explaining how math works.
I suppose that does showcase a problem but rather than designing a slower and more complicated method of adding and substracting things you could just explain the kids how it works.
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Especially in the days of calculators and mobile apps that do practically everything for you. Though, knowing how to do up to regular algebra is relatively useful for most careers.
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I would have to have more information about how this was taught. If the teacher very carefully went over about how the standard notation for repeated addition is [multiplier] * [multiplicand] (in this case, "5 of 3" or "5 3's"), I can understand taking a point off.
To take the commutative property for granted you have to understand the mathematical framework you're working within and that, on the most basic level, it's an assumption -- an assumption that can be shown to give different answers, by the way, when you're doing transformations with matrix multiplication.
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Argument about Common Core detected, deploying relevant link (http://www.patheos.com/blogs/friendlyatheist/2015/10/21/why-would-a-math-teacher-punish-a-child-for-saying-5-x-3-15/?ref_widget=popular&ref_blog=friendlyatheist&ref_post=theres-a-reason-non-christians-dont-share-evangelical-morals)
I have to disagree with Hemant Mehta here. Given the questions asked on the test, the answers were exactly correct. Not just the result! The actual method used was exactly correct too.
Marking such an answer as wrong suggests that, in class, the teacher has insisted that n x m means the number m, added n times. OK. That's a good definition of integer multiplication. But math also involves looking at the implications of definitions, see what they imply and how they can be extended and how they can be used more easily. In the case of multiplication, commutativity is one of the more important things to learn, and many kids who actually learn multiplication internalise commutativity to the point that asking them whether 5x3 is 5+5+5 or 3+3+3+3+3 sounds meaningless (I know it does to me).
There are settings in which multiplication isn't commutative, to be sure. And if that kid was studying quaternions or matrices or cross products this could be an issue. But they were not. They were studying integer fucking multiplication. The kid knew how to multiply and had the right intuitions built up. Don't punish them for that.
All that being said, show me one study that says that insisting on order of operations for multiplication as kids helps them do better work with non-commutative multiplication in the future, and I'll shut up (until I can find better evidence to the contrary). But this "well, it might help them when they look at matrices later on..." bullshit does not justify taking marks away.
Finally, anecdote is not data, but in my experience the sort of people who use correct-but-not-the-one-the-teacher-likes methods are much more likely to follow up with studying math-heavy subjects. Mathematical intuition is important. I don't like the idea of telling kids they are not allowed to use it.
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Where's the L when you really need her sexy ass.
Ironbite-she's got a lot to say about Common Core if I recall.
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On the other hand, it's just 2 points taken off a 6-point test. I'm of the opinion it's not the end of the world.
Putting excessive pressure on kids by telling them they need to ace everything is probably more damaging to mathematical aptitude than a little clarification every now and then.
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On the other hand, it's just 2 points taken off a 6-point test. I'm of the opinion it's not the end of the world.
Putting excessive pressure on kids by telling them they need to ace everything is probably more damaging to mathematical aptitude than a little clarification every now and then.
Chewie actually has a point here. Excessive pressure to succeed can cause a lot of problems. Much as we like to talk up school systems in East Asia, their approach has its own drawbacks.
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On the other hand, it's just 2 points taken off a 6-point test. I'm of the opinion it's not the end of the world.
Putting excessive pressure on kids by telling them they need to ace everything is probably more damaging to mathematical aptitude than a little clarification every now and then.
I'm not sure how it works in America, but when I was in primary school 66% was a failing grade. Is it the end of the world? Of course not. Few things are. But that seems like a shitty excuse for bad testing practices.
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On the other hand, it's just 2 points taken off a 6-point test. I'm of the opinion it's not the end of the world.
Putting excessive pressure on kids by telling them they need to ace everything is probably more damaging to mathematical aptitude than a little clarification every now and then.
I'm not sure how it works in America, but when I was in primary school 66% was a failing grade. Is it the end of the world? Of course not. Few things are. But that seems like a shitty excuse for bad testing practices.
I'm assuming this test was a tiny portion of their overall grade for the class. If it were 100 points taken off a 300-point test I'd be more horrified.
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I have, on occasion, been told to do this when marking for university courses. (That is, the question specified some method or other, the student used some other method that--in my view--demonstrated a deeper understanding of the material, and the instructor ordered me to dock points.) Suffice it to say that I did not like that at all, and docked the points only because I was specifically told I had to.
EDIT: Thankfully, I've also had the reverse experience, where I was allowed to give students who stumbled onto a more advanced method some points simply for displaying that insight even though if I had been marking a course where that method was actually done they would not have received points.
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I find some of the crazy shit said about Common Core to be funny as hell(I don't have an opinion either way on it), best one I heard was when I was working at the Office Supply store last year around back to school, had this one guy telling parents that the tests are used by Obama and the FBI to spy on your kids. I was doing my best not to laugh in the guy's face.
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sigma, i've got an "artistic eye", or so my teachers told me. i struggle with basic algebra, but i've been known to intuition complex trigonometry in my head without being able to explain it, with enough consistency to write out dumb luck. complex geometry, no problem. ask me to calculate the volume of said geometric figure, and i'm a fish out of water. what i always did was find the way that seemed the easiest for me. let's just say i was not my many math teachers' favorite student. on the contrary, the added pressure for being math dumb in a society that prizes scientists made me develop a near-phobia to math more evolved than basic operations. to this day, the teachers saying "it's not hard to get, try harder", or worse "yeah, you're just litterary" and brushing me off left me with a very stunted level in mathematics. nevermind that i can aim a trebuchet precisely (ok, ballistics is technically physics, but it's applied trig). i'm still very leery of math in general.
perhaps you saw the opposite, but in my case, it discouraged me more than anything. and partly the reason why i studied the humanities and languages, and not ballistics, physics, or chemistry.
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I HAVE BEEN SUMMONED!
Frankly, I think if the teacher wanted those specific addends, she should have said, "by adding 3's." (Personally, I would have said, "Use addition to show that 5x3 and 3x5 both equal 15," thus having the child write both 3+3+3+3+3 and 5+5+5. This also makes it more clear that, while the result is the same, the order of numbers can be important.) But then, unlike most elementary-school math teachers, I majored in math for undergrad, so I actually have a decent understanding of how numbers work beyond basic fucking arithmetic.
You have to be able to recognize patterns in the way numbers work, or algebra is going to be really fucking hard to learn. The traditional algorithms are useful, but they don't make it easy to see those patterns. I've taught adults who can't look at a number and know whether or not it's divisible by 2. (This is also why I support a lot of "counting by twos, threes, fives, etc." exercises in the primary grades too--put charts on the wall of all the twos, threes, or fours up to 100* and the patterns for multiples and factors get much easier to see.) Students have to learn what happens when you add 2 even numbers, or one odd number and one even number, or 2 odd numbers. They have to see how multiplication works, or the times table is just a bunch of meaningless disconnected facts. This is why arrays and repeated-addition are used so much in common-core math classes--they make the concept of multiplication more intuitive, so that they realize that there are probably patterns to it. If you don't understand what it means to multiply, or that multiples of a number form recognizable patterns, then how are you going to be able to remember that x * x = x2?
Plus, by encouraging exploratory methods, you give students room to discover interesting math facts for themselves. I remember the "Eureka" moment I had when I realized that terminating decimals terminate in the decimal system because if you make them fractions, the denominator is a power of 2, 5, or 10. Other denominators make repeating decimals. This doesn't seem relevant to real life, but the sense of accomplishment from realizing this fact, and that the rule is based on the factors of the "base" of the number system, was huge.
That said, I do disagree with Hemant Mehta on the array thing, but that may also be because I despise matrices with a flaming passion. I failed so-called "Linear Algebra" twice because it was literally nothing but working with matrices. I'd work them out on paper, then check with my TI-83+, and every single problem would be wrong, and I wouldn't be able to find the error.
* Naturally, this would have to only go up to 99 for the threes, since 100 isn't a multiple of 3.
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I am not a maths teacher, nor have I studied maths, but I have provided some tutoring on the side.
For me, its always been about what works. Some kids may need to see an array of digits to understand multiplication, some need to have it operate in a very specific order. However some may need something else entirely. I find the whole idea behind this narrowness of thinking on the teachers part abhorrent. I dont think it is an intrinsic failure on common core, but on a failure of a teacher with far too rigid thinking. When I tutored I would try and use lots of different examples and lots of different ways of describing and explaining how something works. All in the hopes that something sticks and resonates with the student. Anything else they manage to pick up just helps them to understand all the more.
Personally I believe in screw any special mandated system. Teach what works. Understanding something properly is way more important than some government mandated method to robotically repeat.