Common Core Math...

[jammindude]

When I went to school (Class of '88...but dropped out in '86) I was one of the best in my entire class at math.  I didn't get good grades, because I was just lazy.  But I was very quick to understand it.  Math always just made sense to me.   Once the teacher explained how to do a problem...I understood it immediately, and I didn't want to go home and do it 50 times.  All my homework would be listed as "Incomplete", but I would always ace my tests...so I passed with a D. 

That's just a brief background.   I've never even heard of "common core" math.   This article was the first I've ever heard of it.  Are there any math wizzes here who can give a brief explanation of "common core" math, and then give their opinions on whether or not it has any real value?   It sounds like most people...even those that are really into math...think it's pretty stupid..

https://allenwestrepublic.com/2014/03/21/angry-mother-destroys-common-core-by-writing-this-on-her-sons-test/

[theseoafs]

I'm sorry, did you open up the OP by bragging about getting D's in your math class and dropping out of school in your sophomore year? 

Anyway.  I am not an expert in common core stuff, but I can tell you the motivation.  The idea is that with the older math, you learn algorithms to do little problems (453 minus 299, 643 divided by 6, and so on and so forth), but understanding is limited.  Kids learn the long division algorithm, but they don't actually get how it works; they know the steps by heart, but they don't understand the steps.  The sense among educators is that knowing how to mechanically do long division isn't really useful in the real world, but having an intuitive sense of how numbers actually work is a much more innately valuable thing.  So the problems might look kind of fluffy or weird, but the idea is to give students a good, strong, intuitive number sense.

Here's a link to a blog post with pictures making fun of Common Core math problems.  I don't think all of them should be made fun of, though.  Here's number 7, which I think sums everything up in a nice way:



The blog post makes fun of the language in this email, but actually the changes make sense.  What the fuck is "borrowing", anyway?  Walk into a math class in 1986 and you'll probably find that all of them can do a subtraction problem with borrowing, but if you ask them what borrowing is and why you're allowed to do it, you'll probably struggle to get a decent informative answer out of the bunch.  By taking away the meaningless name "borrowing" and giving it a name that actually makes sense, you give students an idea of how subtraction actually works.  Same with carrying.  "Carrying" and "borrowing", in the old language, are two operations that are exactly opposite, but the words "carrying" and "borrowing" aren't related in English -- they should probably be called "borrowing" and "lending", but they're not.  However, by calling one "regrouping ten ones as a ten" and the other "regrouping a ten as ten ones", their status as opposite operations is immediately clear.  The example problem on the bottom has the same motivation.  You can line up the two numbers and add the columns, but what does that all mean?  By framing 62 + 26 as 60 plus 2 plus 20 plus 6 (which it is), you get a sense of why lining the numbers up by the columns works like it does.  Moreover, if you were going to subtract 26 from 62, you would understand that 62 is actually 60 + 2, and that you can subtract 10 from the 60 and add it to the 2 when the time comes for you to "borrow".  And so on and so forth. 

Here is a Wikipedia link summing up some of the responses to the Common Core standards initiative.  You will see that many of them are positive, and some of the quantitative results (the stats for Kentucky dropouts) are actually very encouraging.

[jammindude]

I kinda figured that I was just an example of how the system was broken....but maybe I just didn't want to do the footwork.   

I *completely* understand the concept of "borrowing".    You mean there are people who don't?    Heck, I even use "borrowing" when I'm making a mix CD and I'm trying to total up song track lengths.    (If I'm doing subtraction, I sometimes have to "borrow" a minute, turn it into 60 seconds, and add it to 13 seconds so that I can subtract 73 from 55...blah blah blah)    So "borrowing" always made sense to me.    Although "stealing" would probably be a more accurate term....because those 10 1's don't get returned to the 10's column once you take them. 

[theseoafs]

Yeah, you've got it.  You understand borrowing, and you understand it well enough to apply it to other number systems (minutes and seconds, etc.).  The argument you'd get from the supporters of this curriculum is that that kind of understanding is uncommon in the old system, at least among the students who are learning these algorithms.  The idea is that "in this situation, I have to subtract 1 here and add 10 here, because teach told me to" is unacceptable, and that the approach should be understanding-first rather than algorithm-first.  If you genuinely, truly understand how subtraction works in the abstract, then the old subtraction algorithm should be obvious to you, but if you spent the second grade just following instructions about lining up numbers and carrying ones like a computer, then you might be at a disadvantage when the time comes to learn more difficult concepts.

So the reasoning makes sense.  Having said that, I am not an educator and can only refer you to outside resources about whether the new standards have been successful.

[jammindude]

What's stupid to me about that is that why don't you have TEACHERS...TEACH!   I mean, borrowing is not a difficult concept to grasp, and I personally never had a teacher that would simply say, "do this and don't ask why, just follow the instructions".    Like I said, once the teacher put it on the board and said, "We're taking 10 1's and putting them over here..." I got it.   I mean, a freakin 6 year old could wrap his head around that.    What is 10?  Well, it's 10 1's.   DUH....I don't get it.      I'd like to think that most kids are at least smart enough to understand that.    All you have to do is *TEACH* that.

IDK...seems like they are making it more difficult than it has to be...but what you're really doing is admitting that teachers don't teach, so we have to try to teach for them....which, in a bureaucracy situation never ceases to become more convoluted than it needs to be.

[rumborak]

I read a book the other day by Richard Feynman, about Quantum Electrodynamics. In the preface he explained his approach for teaching the subject, which is somewhat similar to the way Common Core goes about it. His argument was (paraphrased): "When you are done with this book, you will have an understanding of Quantum Electrodynamics on the same level as a graduate level physics student. The difference being, while what I explain in this book is correct, it is not the most efficient way of doing things. That is something graduate students learn. I could try to teach you that, but given limited time and attention span, you would have to learn it by rote, thus understand nothing, and forget about it a week later. With my approach, you can read an article about Quantum Electrodynamics and understand it, and reason about it. "

I wholeheartedly agreed with Feynman on his approach.

[theseoafs]

IDK...seems like they are making it more difficult than it has to be...but what you're really doing is admitting that teachers don't teach, so we have to try to teach for them....which, in a bureaucracy situation never ceases to become more convoluted than it needs to be.

You're sorely misunderstanding me if you think that's what I'm suggesting.  Teachers are teaching just fine.  I am not suggesting that anybody teach for teachers.  That doesn't make any sense.  However, teachers don't write their own curricula, and what they actually teach is an extremely contentious issue that's entirely up for debate.

What is 10?  Well, it's 10 1's.   DUH....I don't get it.      I'd like to think that most kids are at least smart enough to understand that.    All you have to do is *TEACH* that.

Well, yeah.  That's the point.  If you teach it, the kids will get it... but just learning the algorithm probably isn't enough to make the kids "get it".  The Common Core is an attempt to get these ideas into the curriculum.

[kári]

I read a book the other day by Richard Feynman, about Quantum Electrodynamics. In the preface he explained his approach for teaching the subject, which is somewhat similar to the way Common Core goes about it. His argument was (paraphrased): "When you are done with this book, you will have an understanding of Quantum Electrodynamics on the same level as a graduate level physics student. The difference being, while what I explain in this book is correct, it is not the most efficient way of doing things. That is something graduate students learn. I could try to teach you that, but given limited time and attention span, you would have to learn it by rote, thus understand nothing, and forget about it a week later. With my approach, you can read an article about Quantum Electrodynamics and understand it, and reason about it. "

I wholeheartedly agreed with Feynman on his approach.

True.

Look for example at this way of subtracting numbers, let's try 43-14.
First, pick a round number close to the ones you are subtracting. Let's say 50.
Then we do 50-14 = 36.
Then add that result to the other number: 36 + 43 = 79.
Now subtract the number you picked from the result you got: 79 - 50 = 29.
Which is the result of the original subtraction.

This may seem like a lot of work, but it is WAY faster for subtracting long numbers in your head, like maybe
75434 - 42878
50000 - 42878 = 7122
7122 + 75434 = 82556
82556 - 50000 = 32556.

Since the addition is easier in your head than the original subtraction this method saves a lot of time.
However, it doesn't give you any additional insight into subtraction... If anything it can make it seem more complicated. But knowing the regular way of subtracting you can use this method to obtain fast results.

It is the same for the "common core" method vs. the method you learned. The "common core" one seems like more work, while the one you know is way faster.
 

[El Barto]

Well I'll be damned. So the way I was doing math in 3rd grade, and getting tormented by the teachers for it, is actually how smart kids are learning it now. The reason I was always failing math was because teachers insisted that I show every step of their tedious process which would always screw me up; funny brain wiring. If they would have just let me figure it out my way and show them the damn answer everything would have been fine.

However, I can see why some people hate this. What I took away from my educational experience was that different people do things different ways. What worked for most (the old method) didn't work well for me, but a lot of them wouldn't have been able to work out the reasoning behind Kari's example there. Frankly, it seems like they're making math hard to give people a better understanding of it, and while some will benefit, others will be completely mindfucked.

[orcus116]

What is the most criminal part of this is not the rewired teaching of the subjects but the sudden evaluation of teachers and students based on this newer curriculum and style of teaching. I mean there is no easing either student or pupil into it and gradually assessing the outcome, there are people that are in danger of losing their jobs for not adapting to a completely new line of thinking that they haven't gotten time to prepare for.

What's sad is that while this may turn into the better way of teaching kids, the desparation for the DOE to attempt to accelerate the process of turning the US from a middling education country to a higher one will create a huge stumbling block that will probably end up backfiring, at least in the short term.

[rumborak]

I was talking to a German friend of mine the other day (he also lives in Boston). He has a kid, and he pointed out that summer break here in the US is 3 months. I was stunned; in Germany it's 6 weeks. My suggestion to the US education system: Maybe send your kids to school a bit more. You can optimize your curriculum all you want, you just can't counteract 1.5 months of "missed" school per year.

[kári]

Yeah but don't you have longer winter breaks and fall/spring breaks? And doesn't school end kind of early in Germany? I thought most countries had about the same of school time.

[jammindude]

I was talking to a German friend of mine the other day (he also lives in Boston). He has a kid, and he pointed out that summer break here in the US is 3 months. I was stunned; in Germany it's 6 weeks. My suggestion to the US education system: Maybe send your kids to school a bit more. You can optimize your curriculum all you want, you just can't counteract 1.5 months of "missed" school per year.

Our summer breaks out here have gotten FAR shorter than they used to be.   I think our summer break now is down to around 2 months.   But there are also more weeks off during the year than there used to be.

[rumborak]

This graph puts Germany at 193 days of school, the US at 180. That's 13 days less, which is about 3 weeks. So, maybe not as bad as 6 weeks less, but there's also this thing called "Summer Learning Loss", which is the idea that the 3 months of vacation causes students essentially having to relearn a lot of stuff because they did not have it in their mind for 3 months.

[Fiery Winds]

However, I can see why some people hate this. What I took away from my educational experience was that different people do things different ways. What worked for most (the old method) didn't work well for me, but a lot of them wouldn't have been able to work out the reasoning behind Kari's example there. Frankly, it seems like they're making math hard to give people a better understanding of it, and while some will benefit, others will be completely mindfucked.

This is especially true when you have EL (English Learners) in your class.  With the old method, as long as they memorized the steps, they could generally keep up.  Now, EL students need to combine reading comprehension, writing, and math into a single problem. 

Teaching Common Core math is more challenging for the teacher as well.  Rather than teach a procedure and have students memorize by rote, you need to use multiple modalities.  This takes more time, planning and resources that may or may not be available.

This isn't to say that I don't agree with the goal set by Common Core.  My thesis was written on a related topic, suggesting that students tend to be more successful in math if they are taught through contextual-based problem solving as opposed to memorization and adherence to procedure.  However, this is still radical shift in the way that math is taught and learned, and it will be a challenge for both students and teachers to adapt.

I was talking to a German friend of mine the other day (he also lives in Boston). He has a kid, and he pointed out that summer break here in the US is 3 months. I was stunned; in Germany it's 6 weeks. My suggestion to the US education system: Maybe send your kids to school a bit more. You can optimize your curriculum all you want, you just can't counteract 1.5 months of "missed" school per year.

I had a great math teacher in college who would start off the Fall semester with, "The amount of math that you remember is inversely proportional to the amount of fun you had this summer."  It's absolutely true, and summer break is increasingly seen as a break from learning, which makes me sad.

[kári]

This graph puts Germany at 193 days of school, the US at 180. That's 13 days less, which is about 3 weeks. So, maybe not as bad as 6 weeks less, but there's also this thing called "Summer Learning Loss", which is the idea that the 3 months of vacation causes students essentially having to relearn a lot of stuff because they did not have it in their mind for 3 months.

Wow, France.

[El Barto]

I'm a pretty firm believer that kids need to have an opportunity to stop being students for a while and just be kids. If you want to distribute time off better, then that's fine. Maybe a separate Summer and Winter break equally divided or something. It just needs to be something more than the standard weekend/occasional holiday time off. You don't stop being a student just because it's Saturday.

[rumborak]

Oh, absolutely, and looking at that graph, Indonesian kids must have a miserable time. I think the way to go is to distribute it more, i.e. not have the kids' education come to a full stop for a whopping 2-3 months, but instead have 6 weeks in summer, and maybe 6 weeks in winter. Or 4+4. At least my German friend would like the idea; he is a soccer coach for kids, and there's barely any time to coach them, because during summer break they're gone, and spring/fall often is either dark early or too cold.

[El Barto]

The French do four 7-week terms with a break in between them. Seems to me like a 2 month on, 3 weeks off type of thing would work pretty well. While I certainly enjoyed a 3 month vacation, it just seemed like the rest was one giant year of hell. Shorter terms would have been a great thing.

[Implode]

When I was younger, I thought that teaching math in a way similar to this would be better, but now I'm not so sure. Yes, it more accurately teaches what's going on when you operate through math, but it will alien some kids with its seemingly over complication. As EB pointed out, not all people learn the same way. Sure it'll make more sense to some, but then it'll make less sense to others. I bet it'll just even out. Results are yet to be seen, but I bet if this continues, when we look at the numbers, there won't be a significant increase in understanding of how math works by the time those kids are college age. By then, most people figure that stuff out on their own anyway. That's my bet, but I can't predict the future.

All of this applies to music theory too. When I actually studied formal music theory, I thought, "Why couldn't they teach all of this when I first started to learn how to read music when I was like 7?" The answer is probably the same as this core math stuff. Yes, there are some benefits to building a subject for the ground up, but maybe it just isn't worth it. Sometimes knowing the answers to problems will help you learn why those are the answers a little bit later on, rather than learning the what and the why at the same time.

[BlobVanDam]

Oh, absolutely, and looking at that graph, Indonesian kids must have a miserable time. I think the way to go is to distribute it more, i.e. not have the kids' education come to a full stop for a whopping 2-3 months, but instead have 6 weeks in summer, and maybe 6 weeks in winter. Or 4+4. At least my German friend would like the idea; he is a soccer coach for kids, and there's barely any time to coach them, because during summer break they're gone, and spring/fall often is either dark early or too cold.

Over here we have about 6 weeks off at Christmas/New Year, then a 2 week break at the end of every other quarter, giving us 4 terms of 10 weeks. I liked that distribution. Enough of a break to get things done, plus the long break after Christmas to start the new year, and each term didn't feel too long.
I really can't imagine having all of that time off in one big hit, and then having to get back into it. Even after 6 weeks it was tough to get back into the school routine, so I can't imagine how bad it would be after double that. I also think shorter individual breaks better prepare kids for the workforce where you're not getting a huge block of time off each year.

As for the common core math idea, I was always about understanding the problem as opposed to just doing it, because I need to understand it to remember it and adapt it to new situations, so it's a good principle.
But with the older approach, I had no problem understanding what was going on, and I don't think the new language here makes it any easier at all. It's mostly just needlessly verbose imo, and I think it focuses on the wrong part of the issue. The newer approach to the math itself looks fine though.

[orcus116]

One state has already opted out:

https://www.indystar.com/story/news/education/2014/03/24/gov-mike-pence-signs-bill-ditch-common-core/6829927/

[rumborak]

The problem is also the implementation of the standards. Check out this Louisiana math question:

https://www.wired.com/wiredscience/2014/03/good-math-question/

[Tick]

Stupid fucking shit.

[El Barto]

The problem is also the implementation of the standards. Check out this Louisiana math question:

https://www.wired.com/wiredscience/2014/03/good-math-question/

I agree with the author. This would be a great question in a normal class setting, or even a normal test graded by a human being rather than Professor Scantron. In fact, I'd make that the bonus question, with extra points for anybody who drew it correctly or explained what was wrong with it. I'm fine with it in principle since I'm a big fan of understanding the basis of something rather than the mechanics.

[rumborak]

I just looked at this thing from the LA practice tests:

https://www.louisianabelieves.com/docs/assessment/practice-test-math-grade-5.pdf?sfvrsn=4

Check out question 12. Oh man, fraction hell.

9 7/12 cups?

 

I will probably never understand the US' obsession with fractions.

[Neon]

I just looked at this thing from the LA practice tests:

https://www.louisianabelieves.com/docs/assessment/practice-test-math-grade-5.pdf?sfvrsn=4

Check out question 12. Oh man, fraction hell.

9 7/12 cups?

 

I will probably never understand the US' obsession with fractions.
[/quote


I quickly glanced through the questions, and I don't even think I could pass this test.   
Well, maybe I'm exaggerating...but yeah it would take me awhile to remember how to do all of that shit. 

And you're right about the stupid fractions thing.  And really, you're never going to encounter goofy shit like that in "real life."  (Unless you've got some sort of math/science related job, of course).  The craziest fraction I encounter in a day might be 1/8 or 2/3 or something....you know...basic shit.



EDIT I ALSO APPARENTLY CAN'T MANAGE TO PROPERLY QUOTE SOMEONE...