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#1
09-10-2018, 02:27 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Common Core Math

This has probably been covered already but...

WTF is this bullshit!!!

It seems like math for people who can't grokk math.

Can't they just put all the slower kids in a different class and teach them common core?

Question: 7*3

7+7+7=21 WRONG

3+3+3+3+3+3+3=21 RIGHT

Has common core eliminated the commutative property of multiplication?

Also acceptable is making 7 rows of three dots (bit not making 3 rows of 7 dots) and then counting the number of dots.

What the fuckity fuck fuck?
#2
09-10-2018, 02:37 PM
 manson1972 Member Join Date: Jan 2004 Posts: 8,350
Dude, what decade are you living in?

Also, who told you that was Common Core?
#3
09-10-2018, 02:37 PM
 andros Member Join Date: Sep 1999 Location: Dejagore Posts: 10,067
Depends on the context and how one wishes to integrate mathematics into young peoples' lives.

7*3 == 3+3+3+3+3+3+3 == 21

3*7 == 7+7+7 == 21

They equal the same thing, yes. But having seven three dollar bills is obviously not the same as having three seven dollar bills, even when your total is 21 dollars.

Unless, of course, you're suggesting that the commutative property is never introduced or explored at all in CC math.
#4
09-10-2018, 02:38 PM
 friedo Guest Join Date: May 2000 Location: Brooklyn Posts: 24,022
Quote:
 Originally Posted by Damuri Ajashi WTF is this bullshit!!!
Angry idiots who have no idea what "common core" actually entails, and are pissed off at badly-written worksheets.
#5
09-10-2018, 02:45 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by manson1972 Dude, what decade are you living in?
I'm not sure what you're getting at. This is my first exposure to Common Core Math. I didn't realize how dumbed down it was.

Quote:
 Also, who told you that was Common Core?
The school district, I think. Am I wrong somehow because other posters seem to think that this is indeed representative of common core.
#6
09-10-2018, 02:47 PM
 manson1972 Member Join Date: Jan 2004 Posts: 8,350
Quote:
 Originally Posted by Damuri Ajashi I'm not sure what you're getting at. This is my first exposure to Common Core Math. I didn't realize how dumbed down it was
Sorry, just this complaint is like 10 years old now

Quote:
 The school district, I think. Am I wrong somehow because other posters seem to think that this is indeed representative of common core.

Quote:
 Originally Posted by friedo Angry idiots who have no idea what "common core" actually entails, and are pissed off at badly-written worksheets.
Who exactly told you that what you were looking at is mandated by the Common Core standards?
#7
09-10-2018, 02:49 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by andros Depends on the context and how one wishes to integrate mathematics into young peoples' lives. 7*3 == 3+3+3+3+3+3+3 == 21 3*7 == 7+7+7 == 21 They equal the same thing, yes. But having seven three dollar bills is obviously not the same as having three seven dollar bills, even when your total is 21 dollars. Unless, of course, you're suggesting that the commutative property is never introduced or explored at all in CC math.
OK, so explain to me why 7*3 need be be seven groups of 3 rather than 7 repeated three times? You are creating an arbitrary convention and calling it math. And in the process you are ignoring the commutative property. One of the first and most fundamental conceptual mathematical notions.

AFAICT, this is waving the white flag on math and just dumbing it down to the lowest possible denominator.
#8
09-10-2018, 02:49 PM
 bobot Member Join Date: Jan 2009 Location: Chicago-ish Posts: 6,449
Quote:
 Originally Posted by Damuri Ajashi I'm not sure what you're getting at. This is my first exposure to Common Core Math. ....
Also, at least the kiddies are counting dots, there's a logic to that. In my day Sr. Doris just made us memorize them and recite them aloud. Over and over again.
#9
09-10-2018, 02:50 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by friedo Angry idiots who have no idea what "common core" actually entails, and are pissed off at badly-written worksheets.
So explain to me why one is wrong and the other is right?
#10
09-10-2018, 02:51 PM
 manson1972 Member Join Date: Jan 2004 Posts: 8,350
Quote:
 Originally Posted by Damuri Ajashi So explain to me why one is wrong and the other is right?
First you explain why you think that is representative of the Common Core standards.
#11
09-10-2018, 02:59 PM
 Strassia Guest Join Date: Jul 2007 Posts: 1,585
As others have said, I think you are confusing one badly written worksheet with the whole of Common Core. Common Core Third Grade requirements for multiplication:
Quote:
 Represent and solve problems involving multiplication and division. CCSS.MATH.CONTENT.3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. CCSS.MATH.CONTENT.3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. CCSS.MATH.CONTENT.3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 CCSS.MATH.CONTENT.3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ? Understand properties of multiplication and the relationship between multiplication and division. CCSS.MATH.CONTENT.3.OA.B.5 Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) CCSS.MATH.CONTENT.3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Multiply and divide within 100. CCSS.MATH.CONTENT.3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Solve problems involving the four operations, and identify and explain patterns in arithmetic. CCSS.MATH.CONTENT.3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
The only part that comes close is the part I bolded in red. The intent of the section is to ground the symbols that are being taught to real world situations. That should be applied to word problems and not just a number problem with no context.

Overall, I like the direction common core is going. It integrates algebraic concepts throughout, rather than springing on them in grade 9. It also strives to improve number sense and finding strategies as opposed rote algorithm application.

ETA: The bolded green part covers teh commutative property as well.

Last edited by Strassia; 09-10-2018 at 03:02 PM.
#12
09-10-2018, 02:59 PM
 Cheesesteak Charter Member Join Date: Jan 2001 Location: Lovely Montclair, NJ Posts: 12,589
The fact that one lousy teacher demands that 7x3 be 3+3+3+3+3+3+3 and not 7+7+7, does not mean all teachers teach the same way, nor does it mean that "common core" math demands this.

Anyway, what does 7 times 3 mean if not "7 times" the number "3?"
#13
09-10-2018, 03:02 PM
 crowmanyclouds Guest Join Date: Sep 2005 Location: ... hiding in my room ... Posts: 4,415
Quote:
 Originally Posted by Damuri Ajashi OK, so explain to me why 7*3 need be be seven groups of 3 rather than 7 repeated three times? You are creating an arbitrary convention and calling it math. {...}
IIRC later on, algebra and such, you apply commutative property at the risk of getting the whole equation wrong.

CMC fnord!
#14
09-10-2018, 03:04 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by manson1972 Sorry, just this complaint is like 10 years old now
I'm just learning what common core is now.

So in the last ten years have we seen improvement in the US global math rankings?

NOPE! We have been sliding even further behind.

https://www.politifact.com/virginia/...math-and-scie/

Quote:
So then why are we sliding further behind those countries that are using the old outdated antiquated math?

Quote:
 Who exactly told you that what you were looking at is mandated by the Common Core standards?
The teacher told me that this is the methodology required by the school district.

Apparently learning the multiplication table is a waste of time.

Memorization generally is not regarded as learning.

Memorization is essential to learning. In much the same way that muscle memory slows down the game or slows down a fight (see martial arts), brain memory also slows down the math game and lets you operate at a higher level.
#15
09-10-2018, 03:05 PM
 bobot Member Join Date: Jan 2009 Location: Chicago-ish Posts: 6,449
Quote:
 Originally Posted by Damuri Ajashi ... This is my first exposure to Common Core Math. ...
Quote:
 Originally Posted by bobot May I ask what your exposure to it entailed? ...
I only ask because you weren't clear about where you saw this. It could have been on a child's homework assignment. It could have been on rightwingoutrage dot com, how do I know?
#16
09-10-2018, 03:07 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by bobot May I ask what your exposure to it entailed? Also, at least the kiddies are counting dots, there's a logic to that. In my day Sr. Doris just made us memorize them and recite them aloud. Over and over again.
My kid just started bringing home homework that included this stuff. I don't know if Common Core gets less stupid later on.

Once you understand what multiplication is, there is really no need to keep making graph papers full of dots and counting them out.

After that it is in fact about memorization.

My kid's math homework looks like an art project.
#17
09-10-2018, 03:08 PM
 Thudlow Boink Charter Member Join Date: May 2000 Location: Lincoln, IL Posts: 25,505
Quote:
 Originally Posted by Damuri Ajashi Question: 7*3 7+7+7=21 WRONG
In order for me to be properly outraged, I'm going to need to see the context in which this is marked "WRONG."
#18
09-10-2018, 03:08 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by friedo Angry idiots who have no idea what "common core" actually entails, and are pissed off at badly-written worksheets.
That is true scottsman bullshit.

If that is the way it is being taught then that is common core.
#19
09-10-2018, 03:10 PM
 bobot Member Join Date: Jan 2009 Location: Chicago-ish Posts: 6,449
Quote:
 Originally Posted by Damuri Ajashi ... Question: 7*3 7+7+7=21 WRONG 3+3+3+3+3+3+3=21 RIGHT ...
Well if they actually grade it like this then I can see why you're upset. Do they really mark the first answer as wrong?
#20
09-10-2018, 03:11 PM
 Anny Middon Guest Join Date: Oct 2012 Posts: 924
Quote:
 Originally Posted by Cheesesteak Anyway, what does 7 times 3 mean if not "7 times" the number "3?"
Why can't it mean "7 three times"?
#21
09-10-2018, 03:11 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by manson1972 First you explain why you think that is representative of the Common Core standards.
Because that is what is being taught. It doesn't matter if there is some better theoretical way of teaching it. That is the way they are actually teaching it.

Is this complaint specific to this particular teacher who is blaming common core for this travesty? Why are some of the posters defending this idiocy as common core if this is not representative of common core?
#22
09-10-2018, 03:12 PM
 crowmanyclouds Guest Join Date: Sep 2005 Location: ... hiding in my room ... Posts: 4,415
No link to Tom Lehrer: New Math yet? Yous people is getting slow!

CMC fnord!
#23
09-10-2018, 03:14 PM
 bobot Member Join Date: Jan 2009 Location: Chicago-ish Posts: 6,449
Does it have the Common Core stamp in the corner of it?
#24
09-10-2018, 03:18 PM
 Thudlow Boink Charter Member Join Date: May 2000 Location: Lincoln, IL Posts: 25,505
Quote:
 Originally Posted by Damuri Ajashi That is true scottsman bullshit. If that is the way it is being taught then that is common core.
IIUC correctly, "Common Core" is a What, not a How. Common Core defines what children are learning, not the way it's being taught.

Previous thread in GQ: What Common Core math technique was that check mocking?

In that thread, even sven said
Quote:
 Originally Posted by even sven Just a clarification, but the Common Core is a set of standards, along the lines of "by grade X, children shall be able to do Y". It does not specify any particular method or teaching technique. ... So this is not a "Common Core" technique, because such a thing does not exist.
But other posters are disputing this, including Joey P, who seems to have the same complaint you have.
#25
09-10-2018, 03:26 PM
 The Lurker Above Guest Join Date: Jan 2009 Location: Calgary, AB Canada Posts: 756
Quote:
 Originally Posted by Anny Middon Why can't it mean "7 three times"?
The last time I looked into this, I found cites for mathematicians defining it both ways.

So if a teacher is marking one way or another wrong they're enforcing an arbitrary and non-universal convention. And they're just going to have teach the commutative property soon anyway...
#26
09-10-2018, 03:29 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by Strassia As others have said, I think you are confusing one badly written worksheet with the whole of Common Core. Common Core Third Grade requirements for multiplication: The only part that comes close is the part I bolded in red. The intent of the section is to ground the symbols that are being taught to real world situations. That should be applied to word problems and not just a number problem with no context.
That seems to be how it is being applied in the real world.

Quote:
 Overall, I like the direction common core is going. It integrates algebraic concepts throughout, rather than springing on them in grade 9. It also strives to improve number sense and finding strategies as opposed rote algorithm application. ETA: The bolded green part covers teh commutative property as well.
What you seem to be saying is that this is just a bad teacher who doesn't understand common core, right? Well, let me suggest that there is a reasonably large population of 3rd grade teachers who are too fucking dumb to implement common core the way that education policymakers think it ought to be implemented.

Once you understand multiplication as a concept it is largely a waste of time to NOT use the algorithms.

Algebraic concepts have been a part of 3rd grade math for at least half a century. Division is mostly accomplished through algebraic concepts, it also requires you to have almost memorized the multiplication tables to do quickly and effectively.

KNOWING that 7*8=56 and 7*9=63 makes it a lot easier to know that 60/7=8 plus some remainder. You don't have to sit there and do 60-7=53-7=46-7=39-7=32-7=25-7=18-7=11-7=4, then count up all the 7s you subtracted to get the number 8. You stop doing division that way after the first week or so.

What the common core people call memorization can also be referred to as knowledge.
#27
09-10-2018, 03:32 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by Cheesesteak The fact that one lousy teacher demands that 7x3 be 3+3+3+3+3+3+3 and not 7+7+7, does not mean all teachers teach the same way, nor does it mean that "common core" math demands this.
This is the way it is being taught. My kid's teacher is not unique.

Quote:
 Anyway, what does 7 times 3 mean if not "7 times" the number "3?"
7 times 3 mean 21 to me. What does it mean to you? IN what way does it matter if you get 7 groups of 3 or 7 repeated 3 times?
#28
09-10-2018, 03:33 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by crowmanyclouds IIRC later on, algebra and such, you apply commutative property at the risk of getting the whole equation wrong. CMC fnord!
The thing about math is that it is frequently true that if you apply ANY concept incorrectly, you get the wrong answer.
#29
09-10-2018, 03:35 PM
 Bryan Ekers Guest Join Date: Nov 2000 Location: Montreal, QC Posts: 57,707
If common core upsets the OP this much, I can only imagine how he'll react to aristocratic core.
__________________
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#30
09-10-2018, 03:35 PM
 Strassia Guest Join Date: Jul 2007 Posts: 1,585
Quote:
 Originally Posted by Damuri Ajashi That is true scottsman bullshit. If that is the way it is being taught then that is common core.
Did you read what I posted? That is Common Core. A list of objectives that lesson plans need to accomplish. If your district is misunderstanding them, or your child's teacher misunderstands the district mandates, that is not on Common Core.

Look at the two sections of third grade requirements that I highlighted. If the are working on the red section and it is a word problem about something that only comes in groups of 3, and they did but adding 7 three times, they missed the point of the exercise. If it is just a written problem of 3x7, then it is poorly written.

One of the issues/features of Common Core is that the implementation is entirely up to the the states.

Last edited by Strassia; 09-10-2018 at 03:36 PM.
#31
09-10-2018, 03:37 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by Thudlow Boink In order for me to be properly outraged, I'm going to need to see the context in which this is marked "WRONG."
You have the context.

My kid was asked to answer math questions and to show his work. One of them was:

7*3=

If you were to try to find the answer to this, you might think that the easiest way to get this answer while showing all your work would be to add 3 numbers together. Nope that would be wrong. You have to add 7 numbers together.
#32
09-10-2018, 03:37 PM
 CurtC Guest Join Date: Dec 1999 Location: Texas Posts: 6,698
Damuri Ajashi, lots of people have asked how you know this is Common Core, without explaining why they're asking. Modern math teaching is trying to actually teach kids the math concepts and not just memorize tables. There's good reason for doing this, even though I find it amusing when I give a clerk \$20.12 when the tab is \$9.87, and watching the bewildered look on their face after they've entered into the register that I simply gave them \$20.00 even.

When I learned math back in the 60s, there was starting to be some of that Tom Lehrer "new math" where we learned about sets and different number bases, but lots of the basics were still memorizing multiplication tables for the single-digit numbers and rote learning of a mechanism to adapt those to numbers with more digits. Those work for getting the right answer, but don't do much for acquiring a numbers sense. And is the old way really important? If I want to multiply a couple of multi-digit numbers, there's never a calculator more than two feet away from me.

So modern math teaching is trying to give kids a sense of how numbers work, not just having them memorize an opaque and nearly obsolete process that can yield the correct answer.

And finally, this has been going on for quite a few years, while "Common Core" is just standardizing the best practices across the states.
#33
09-10-2018, 03:40 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by bobot Well if they actually grade it like this then I can see why you're upset. Do they really mark the first answer as wrong?
He got partail credit for getting the right answer but lost points for getting it the wrong way. I don't care about the actual grade, its third grade. I care about the confusing and incorrect message its sending to my kid that there is some significance to the order in which two numbers are multiplied.
#34
09-10-2018, 03:41 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by bobot Does it have the Common Core stamp in the corner of it?
You're kidding right? There is a common core stamp? How does that prevent the teacher from applying stupid standards to the answers. I think she got the homework straight out of a teacher's edition book and she was following the answer key.
#35
09-10-2018, 03:49 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by Thudlow Boink IIUC correctly, "Common Core" is a What, not a How. Common Core defines what children are learning, not the way it's being taught. Previous thread in GQ: What Common Core math technique was that check mocking? In that thread, even sven said But other posters are disputing this, including Joey P, who seems to have the same complaint you have.
The principles of Common Core may make sense but there certainly seem to be implementation issues. And this is a decade later. I will have to check again but I think the "answer key" to 7*3 is:

7*3=3+3+3+3+3+3+3=21

Perhaps we need to teach the teachers a bit better. Because they seem to be turning Common Core into a very rote form of math where 7*3=7+7+7=21 is wrong.
#36
09-10-2018, 03:51 PM
 Chronos Charter Member Moderator Join Date: Jan 2000 Location: The Land of Cleves Posts: 78,537
What you have there is a bad teacher. And she was a bad teacher even before Common Core, and was probably teaching in exactly the same way. The fact that she's a bad teacher has nothing to do with the fact that 42 states got together and agreed that it'd make sense for all of them to teach the same things at the same grade levels.
#37
09-10-2018, 03:54 PM
 Ravenman Charter Member Join Date: Jan 2003 Location: Washington, DC Posts: 24,217
I've watched a few YouTube videos on how math is being taught these days. Though I had no freaking clue what all the squiggles and dots meant when they were just put in front of me, after some explanation I think it's pretty clear that these are novel ways to explain math in ways I rather wish I had some exposure to when I was in school.

The comparison to martial arts is apt. Martial arts is not simply about repetition and rote memorization of various techniques. If you want to execute some kind of takedown, it's reasonable to expect a decent student to show not only that they can execute the technique if the attacker starts in ready position; steps forward with a single punch; and basically pauses until the defender can execute the technique they have memorized. They should understand both how to adapt the technique to unplanned situations, and grok why the technique works to begin with.

Learning how imbalances among several axes on someone's body will make them fall down -- that is, the basic principle of a takedown -- adds context to the action and allows a person to tinker with their technique and experiment with the principles in order to become better.

So, in the same manner -- teaching kids some of the principles behind math in order for them to know how to solve the problem in various ways seems like a good idea; demanding that the multiplication tables AND NOTHING ELSE DAMMIT be pounded into their head seems like a poor idea.

Last edited by Ravenman; 09-10-2018 at 03:55 PM.
#38
09-10-2018, 03:55 PM
 Strassia Guest Join Date: Jul 2007 Posts: 1,585
Quote:
 Originally Posted by Damuri Ajashi This is the way it is being taught. My kid's teacher is not unique. 7 times 3 mean 21 to me. What does it mean to you? IN what way does it matter if you get 7 groups of 3 or 7 repeated 3 times?
If you are working in pure math sure. In the real world sometimes it matters. Take eggs.

Eggs come in cartons of 12. If you are just counting cartons and figuring out how many eggs you have then you can do X*12 or 12*X and get the right answer. But if have a more complex question it matters if they understand how the concept is being applied.

Common core shifts some of the emphasis from memorizing math facts (they are still taught, just not as emphasized) to math sense. Understanding how numbers work and why. There are a lot of math algorithms that are either no longer taught or emphasized. My algebra teacher showed us the algorithm for finding square roots once, just so we could see it. I have never used or or seen it since. Is that problem?

My 6th grade just brought home a worksheet on factoring. When I did it, I would have had to shown how I divided each large number by the possible factors to determine if there was a remainder. His wanted him to explain how he eliminated each one: Didn't end in 0 or 5, added digits and weren't divisible by 3, etc. Those were "tricks" I learned in SAT prep. He even had ones that I never saw before. His way was much faster and, if done properly, will give him a better basis for understanding how bases work later on.
#39
09-10-2018, 03:57 PM
 Thudlow Boink Charter Member Join Date: May 2000 Location: Lincoln, IL Posts: 25,505
Quote:
 Originally Posted by Damuri Ajashi You have the context. My kid was asked to answer math questions and to show his work. One of them was: 7*3=
I wondered whether they had been given specific instructions on how to carry out the multiplication.

Quote:
 Originally Posted by Damuri Ajashi The principles of Common Core may make sense but there certainly seem to be implementation issues. And this is a decade later. I will have to check again but I think the "answer key" to 7*3 is: 7*3=3+3+3+3+3+3+3=21 Perhaps we need to teach the teachers a bit better. Because they seem to be turning Common Core into a very rote form of math where 7*3=7+7+7=21 is wrong.
It could just be that the answer key shows a way to do it, and the teacher is wrongly interpreting it as the only way to do it. In which case, yeah, we need smarter or better-trained teachers.

Or it may be that the children are being explicitly taught that X*Y means X Y's added together, and not Y X's added together, though by the magic of the commutative property these turn out to have the same value. In which case, okay, but I'm not sure there's a standard, generally-understood meaning of what the order in multiplication is supposed to signify.
#40
09-10-2018, 03:58 PM
 SingleMalt Guest Join Date: Jan 2017 Location: Front Range Posts: 239
Keep in mind that this is an approach used when first learning multiplication. For those newly exposed to the concept of multiplication, the associative, commutative, and distributive properties of multiplication are a foreign concept.

It is perfectly natural, then, to present the expression "3 x 7" as "three groups of seven" and "7 x 3" as "seven groups of three". Remember, these kids don't know that multiplication commutates, so they don't intuitively know that "3 x 7" is equivalent to saying "7 x 3". This concept is yet to come.

"Seven groups of three" and "three groups of seven" may have the same total, but they are not the same.
#41
09-10-2018, 04:02 PM
 Apollyon Guest Join Date: Feb 2000 Location: Auckland, New Zealand Posts: 2,584
Quote:
 Originally Posted by andros But having seven three dollar bills is obviously not the same as having three seven dollar bills, even when your total is 21 dollars.
I dunno, in both cases you have \$21 of rather poorly thought out counterfeit currency.
#42
09-10-2018, 04:04 PM
 Buck Godot Guest Join Date: Mar 2010 Location: MD outside DC Posts: 4,990
What is missing for those parents who complain about these sorts of problems is that none of them actually attended the lesson where these concepts and methods were taught.

This problem wasn't just spring out of the blue on their precious little angel, from a vengeful teacher who takes pleasure marking papers wrong. It was done at the end of a hour long lesson describing the method they want to kids to use on that worksheet along with a whole host of examples. Today we will learn that 3 times 7 means the addition of 7 threes in a row. Next week we might point out that this is the same as 3 sevens in a row, but that is not what we are learning today. Today we are working on this particular understanding of what multiplication means.

If they just wanted to know the answer the kids could google it on their cell phones.

Now I can understand if your sweet little nugget of blessedness spent the whole lesson watching Jim in the next chair over to play with his booger, and then came home to ask you to do their homework you might not guess the lesson plan correctly and feel the wrath of a thousand suns that the teacher had the temerity to mark it wrong. But for the purpose of that lesson, it was indeed wrong, and your adorable dumpling of innocence needs to spend less time looking a boogers and more time paying attention in class.
#43
09-10-2018, 04:12 PM
 Buck Godot Guest Join Date: Mar 2010 Location: MD outside DC Posts: 4,990
It also might be easier to see it from the point of view of higher mathematics. If I was teaching factoring polynomials, I might ask

Solve X^2 - X -12 = 0 for X. The correct was would be to factor it into (X-4)(X+3) = 0 so that X = 4 or -3

If the student solved this using the quadratic formula, I would mark it wrong because he didn't demonstrate an understanding of factoring polynomials.
#44
09-10-2018, 04:20 PM
 Johnny Bravo Guest Join Date: Jan 2003 Location: The Swamp Posts: 7,440
Quote:
 Originally Posted by Buck Godot If the student solved this using the quadratic formula, I would mark it wrong because he didn't demonstrate an understanding of factoring polynomials.
Right. Education isn't always about getting the "right" answer - it's about learning specific processes or skills.

Last edited by Johnny Bravo; 09-10-2018 at 04:22 PM.
#45
09-10-2018, 04:33 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by Ravenman I've watched a few YouTube videos on how math is being taught these days. Though I had no freaking clue what all the squiggles and dots meant when they were just put in front of me, after some explanation I think it's pretty clear that these are novel ways to explain math in ways I rather wish I had some exposure to when I was in school. The comparison to martial arts is apt. Martial arts is not simply about repetition and rote memorization of various techniques. If you want to execute some kind of takedown, it's reasonable to expect a decent student to show not only that they can execute the technique if the attacker starts in ready position; steps forward with a single punch; and basically pauses until the defender can execute the technique they have memorized. They should understand both how to adapt the technique to unplanned situations, and grok why the technique works to begin with. Learning how imbalances among several axes on someone's body will make them fall down -- that is, the basic principle of a takedown -- adds context to the action and allows a person to tinker with their technique and experiment with the principles in order to become better. So, in the same manner -- teaching kids some of the principles behind math in order for them to know how to solve the problem in various ways seems like a good idea; demanding that the multiplication tables AND NOTHING ELSE DAMMIT be pounded into their head seems like a poor idea.
Who is demanding the memorization of multiplication tables and NOTHING ELSE DAMMIT be pounded into their heads?
#46
09-10-2018, 04:35 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by Strassia If you are working in pure math sure. In the real world sometimes it matters. Take eggs. Eggs come in cartons of 12. If you are just counting cartons and figuring out how many eggs you have then you can do X*12 or 12*X and get the right answer. But if have a more complex question it matters if they understand how the concept is being applied. Common core shifts some of the emphasis from memorizing math facts (they are still taught, just not as emphasized) to math sense. Understanding how numbers work and why. There are a lot of math algorithms that are either no longer taught or emphasized. My algebra teacher showed us the algorithm for finding square roots once, just so we could see it. I have never used or or seen it since. Is that problem? My 6th grade just brought home a worksheet on factoring. When I did it, I would have had to shown how I divided each large number by the possible factors to determine if there was a remainder. His wanted him to explain how he eliminated each one: Didn't end in 0 or 5, added digits and weren't divisible by 3, etc. Those were "tricks" I learned in SAT prep. He even had ones that I never saw before. His way was much faster and, if done properly, will give him a better basis for understanding how bases work later on.
If this is an improvement then why in the world is our relative math proficiency dropping relative to countries that are teaching math the "old" way.
#47
09-10-2018, 04:41 PM
 Chronos Charter Member Moderator Join Date: Jan 2000 Location: The Land of Cleves Posts: 78,537
This is "the old way".
#48
09-10-2018, 04:44 PM
 Measure for Measure Charter Member Join Date: Oct 2000 Location: Twitter: @MeasureMeasure Posts: 13,714
As of 2012, math scores in the 9 year old set were growing by leaps and bounds. So I'm dubious about the evils of common core.

The problem is that the gains dissipate in high school. https://www.motherjones.com/politics...ts-kevin-drum/

Ok, but how are we doing internationally?
In 8th grade math, American students ranked ninth out of the 56 educational systems that participated in the testing, behind five Asian countries and three others. Average scores are up 17 points since 1995.

Last edited by Measure for Measure; 09-10-2018 at 04:44 PM.
#49
09-10-2018, 04:46 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
 Originally Posted by Buck Godot What is missing for those parents who complain about these sorts of problems is that none of them actually attended the lesson where these concepts and methods were taught. This problem wasn't just spring out of the blue on their precious little angel, from a vengeful teacher who takes pleasure marking papers wrong. It was done at the end of a hour long lesson describing the method they want to kids to use on that worksheet along with a whole host of examples. Today we will learn that 3 times 7 means the addition of 7 threes in a row. Next week we might point out that this is the same as 3 sevens in a row, but that is not what we are learning today. Today we are working on this particular understanding of what multiplication means. If they just wanted to know the answer the kids could google it on their cell phones. Now I can understand if your sweet little nugget of blessedness spent the whole lesson watching Jim in the next chair over to play with his booger, and then came home to ask you to do their homework you might not guess the lesson plan correctly and feel the wrath of a thousand suns that the teacher had the temerity to mark it wrong. But for the purpose of that lesson, it was indeed wrong, and your adorable dumpling of innocence needs to spend less time looking a boogers and more time paying attention in class.
Do you have kids? If doubt anyone would fuck you other than yourself but if you did somehow manages to impregnate someone else without that person immediately swallowing a tub of Plan B and getting their uterus removed, they probably gave birth to really dumb kids that NEED common core to understand simple math. We are dumbing down America in an effort to avoid reinforcing your kids well deserved feelings of inadequacy. If you think Trump is bad, your kid is probably going to be one of the dumb fucks that vote for someone even worse than Trump in order to "fix" social security and Medicare.

TLDR: Why the fuck are you insulting my kid in a discussion of common core you fucking waste of sperm?
#50
09-10-2018, 04:50 PM
 Damuri Ajashi Guest Join Date: Jul 2006 Posts: 19,995
Quote:
http://www.pewresearch.org/fact-tank...-math-science/

It was never great but it used to be better. So tell me again how great common core math is. I don't really notice a difference in common core reading except they seem to be teaching more critical reading skill earlier. its not that hard to fuck that up I suppose.

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