gooddecisions
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Post by gooddecisions on Mar 27, 2014 15:38:34 GMT -5
What's weird is that almost the exact same response from a mother, also to "Jack" has been making its rounds. Two thoughts: 1. I'm going to have to take a class if I need to learn to do math using a number line instead of simple subtraction. 2. Since when do parents have to write essays on where their kid made a mistake?
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Wisconsin Beth
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Post by Wisconsin Beth on Mar 27, 2014 15:47:15 GMT -5
Here's an explanation of the number line used in the link The Captain originally posted, which is slightly different than the method I mentioned earlier, but works just as well.
427-316 You start your number line at 427. You then look at what you need to subtract. Unlike "traditional" methods, you start on the left (once again, the way westerners are naturally taught to read) instead of the right, which, in my experience, eliminates some of the most common mistakes.
You have 3 hundreds that you need to take away. The number line shows going in 3 jumps of 100 each, taking us to 127. You then have 1 tens that you need to take away (and this is what you were supposed to find wrong in the question). We do one jumps of 10, taking us to 117. Finally, we have 6 ones that need to be taken away, that takes us to 111.
Again, with answers like 111, it always seems simpler to do it the old fashioned way, especially since there would be no borrowing. So let's look at the more complicated problem I posed.
765-478 Start our number line at 765 Take away 4 hundreds. That leaves us at 365. Take away 7 tens. That leaves us at 295. Take away 8 ones. That leaves us at 287.
Remember this compares to 765 - 478 _____
Start on the right, in the ones place. You can't take 8 from 5, so borrow from the 10s place giving us 15-8 is 7 Move to the 10s place. Remember, the 6 is now a 5. You can't take 7 from 5, so borrow from the 100s place, giving us 15-7 is 8 Move to the 100s place. Remember, the 7 is now a 6. 6-4 is 2. That gives us 287.
Now, I am biased in that my 4th grader still does addition and subtraction on her fingers (she has a very solid grasp of multiplication and division, but based on what her life was like when she was learning addition and subtraction, that didn't stick as well), so she'd like use a number line or count on her fingers to get 15-8 anyway.
Now, you may look at the number line example and say there's "borrowing" when you take away the tens and the ones, but there's not really, because you're just moving down a number line. The jump from 305 to 295 is not any harder than the jump from 315 to 305 was, as long as you understand counting. And again, this is just my experience, but kids seem to "get" moving down the number line in a way they don't "get" why they are borrowing or how that really works. I have to do math the 2nd way, most of the time. I also need to do it on paper. I get too confused and incorrect when I do math in my head.
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shanendoah
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Post by shanendoah on Mar 27, 2014 16:06:45 GMT -5
gooddecisions - this isn't something the parent has to do. This is part of the kid's homework- as in, look at this problem, what was done wrong (my daughter just had math in her workbook like that last night for area/perimeter) and then write a note explaining what was wrong.
I would guess that the kid was having a hard time understanding, went to their parent for help, and this is what the parent wrote to the teacher on their child's homework. Except that if you actually look at the number line (and the answer "jack" got), it's pretty easy to see he missed subtracting 10. And if you look at the notes supposedly written by the kid/dad, you can see that instead of just just making one "tens" jump, they just kept making 10s jumps and never got to the "ones".
I know this isn't math the way we learned it. And again, I only seem to see examples of about how awful this method of teaching is when answers are of the all 1s variety, but it's a number line. We all know how number lines work. And taking 5 minutes to actually look at it and think about it, I don't believe that adults can't get it, even ones that struggle with math.
The problem with letting people like those with BS in Electrical Engineering tell us how we should teach our kids is that they use the "old" way pretty much every day, and it works for them, and so they don't see why it shouldn't work for everyone. (And I've yet to meet an electrical engineer who wasn't a micro manager by nature.) They are also so caught up in the way they have "always done it" that it can be harder for them to break out of their habit and see something new. But that's a general problem with highly educated people, especially when you're doing something new in what they consider their area of expertise.
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justme
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Post by justme on Mar 27, 2014 16:09:41 GMT -5
I could see how that type of math would work on visual learners. But geeze, that sounds so convoluted. Then again, I'm one that easily grasped the borrowing situation so I don't get how it's confusing. Borrowing from the 10 column gives you ten 1s to add to the top line.
ETA: I could probably logic my way to figure it out, it's just counter intuitive. I saw the problem and got an answer in my head and went to the end and saw he was off by 10. Count the 10s on the number line wasn't on my radar. But I've always been a start at the end and work you way back. I'd do all the math in my head and go through it, then once I was done I'd scribble in the steps to get the full points.
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The Captain
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Post by The Captain on Mar 27, 2014 16:12:08 GMT -5
gooddecisions - this isn't something the parent has to do. This is part of the kid's homework- as in, look at this problem, what was done wrong (my daughter just had math in her workbook like that last night for area/perimeter) and then write a note explaining what was wrong.
I would guess that the kid was having a hard time understanding, went to their parent for help, and this is what the parent wrote to the teacher on their child's homework. Except that if you actually look at the number line (and the answer "jack" got), it's pretty easy to see he missed subtracting 10. And if you look at the notes supposedly written by the kid/dad, you can see that instead of just just making one "tens" jump, they just kept making 10s jumps and never got to the "ones".
I know this isn't math the way we learned it. And again, I only seem to see examples of about how awful this method of teaching is when answers are of the all 1s variety, but it's a number line. We all know how number lines work. And taking 5 minutes to actually look at it and think about it, I don't believe that adults can't get it, even ones that struggle with math.
The problem with letting people like those with BS in Electrical Engineering tell us how we should teach our kids is that they use the "old" way pretty much every day, and it works for them, and so they don't see why it shouldn't work for everyone. (And I've yet to meet an electrical engineer who wasn't a micro manager by nature.) They are also so caught up in the way they have "always done it" that it can be harder for them to break out of their habit and see something new. But that's a general problem with highly educated people, especially when you're doing something new in what they consider their area of expertise. Shane - and I honestly mean this in the most affectionate, sincere way - I appreciate your responses but it's not easy to see Jack missed subtracting 10. I'm honestly going to go home, sit in a quite room, and try to understand what you've been trying to each us. I'm a bit smarter than the average bear but I'm not getting it.
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973beachbum
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Post by 973beachbum on Mar 27, 2014 17:29:30 GMT -5
I don't understand any of the remarks about common core in this thread or in the internet at large. Common core is a law that says what all students should have learned by the end of a particular grade. It isn't a method of teaching. It isn't a book manufacturer. It doesn't give any specific methods of teaching. My kids schools have had the verson of standards that is very similar to common core. Sometimes the schools have purchased curriculum that was crazy convoluted to understand for the lay person. But the fault of buying that particular curriculum is solely the fault of the local school district, not the standards they were trying to achieve when they bought that curriculium. And for the record was designed by the goveners association not the dept of education.
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Deleted
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Post by Deleted on Mar 27, 2014 17:49:51 GMT -5
Shane's explanation actually made sense to me. It still seems overly complicated (probably just because it's not what I'm familiar with), but I understood how it works, FINALLY. lol Good job shanendoah!
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shanendoah
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Post by shanendoah on Mar 27, 2014 18:26:20 GMT -5
I probably have an advantage in that I've been doing number line math with my daughter, so I've had the workbook in front of me.
Part of the problem may be reading what is on the paper presented- figuring out what was the original problem, and what is the "work" being done by our BS and his son. But the first step is to look and see, as we easily can, that the answer would be 111. The answer given on the sheet is 121. So, the answer is obviously off by 10. The sheet shows the jumps labeled as 100s, but doesn't label any of the others, so that does make it harder. But if I subtracted 306 from 427, I'd get 121, so knowing he forgot to skip subtracting the 10 perhaps is an intuitive leap, but not one that I think most parents could not make. (But again, the scanned copy has a lot of info, so it's harder to read.)
You can then look at the hand written notes. There's a typed number at 127, and someone then wrote the following series "107, 97, 87, 77, 67, 57". So the first thing I notice is that their first jump was by 20 (from 127 to 107) and then the proceeded to jump by 10s. And again, whether that's the kid or the dad, I don't know, but the first question to ask is- why would it ever make sense to jump by 20? But if we look at the number line, and look at what we're subtracting- look, we've made 3 100 jumps. If we're subtracting 316, what is the next, rather obvious jump? How about 1 10. And then 6 1s.
Here's the thing, this is presented this way SPECIFICALLY to be confusing. The intent of posting this "picture" is NOT to inform, but to persuade, so it's purposefully meant to look confusing to people who will go- "OMG, can't you just teach them the traditional way, because the answer is 111, and the traditional way is SOOOO easy. This is awful and complicated." This is presented specifically to get the response you are having. And there's nothing wrong with that. I very much doubt this was done by a random "dad", and instead was put together by an organized opponent of Common Core.
But they don't show you how it looks when you have to double borrow, or borrow across a zero (something my daughter, at least, still struggles with).
I get that some people totally get the "borrowing". And that's good. That's how I learned it, and it made sense to me then and it makes sense to me now. But I KNOW it did not make sense to all of my classmates. And I KNOW it doesn't make sense to my daughter. And that's why I am very happy that she is being taught BOTH ways to do the math- so she can use the one that works for her, and other kids can use the one that works for them, when they are at a point to make that choice. But they do have to learn both ways. What bothers me is the parents who aren't supportive of that, because one isn't what they were taught. To me, that's undermining their child's teachers and making the job of the teachers much harder, and also giving their child an excuse not to learn. "My dad has a degree in Engineering and he says this doesn't make sense to him, so how can it ever make sense to me. I'll just ignore it." You aren't doing the teacher or your kid any favors.
And The Captain, explaining it over the internet is hard. I would bet that if I could sit down next to you and go over it, you'd get the number line theory pretty quickly.
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Deleted
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Post by Deleted on Mar 27, 2014 18:37:43 GMT -5
We can't both bitch about the dumbing down of our education and complain about efforts to improve it...
The fact is the father wasn't even close to the right answer. The right answer was NOT 111. The right answer was not possible to achieve by the application of an algorithm.
The question was about understanding how a process works, examining how it was used, identifying the steps in which it was employed correctly, identifying the error, and being able to articulate that to someone...
That's higher level skills people. If you want people to just plug in an algorithm... well frankly, a calculator can handle that... we don't need more people who can just as easily be replaced by machines.
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Deleted
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Post by Deleted on Mar 27, 2014 18:41:25 GMT -5
Honestly, and i mean no disrespect, but the fact that people couldn't easily see that the issue there was that he skipped subtracting 10 is because they were taught to think about algorithms and not mathematics. That is what we need to change.
A lot of this isn't just an employment of 'common core' ... which is little more than a list of common performance standards which are not that complicated... There is not common core CURRICULUM... just curriculums which are developed to be compliance with common core standards.
But when you look at other countries that are beating our bottoms in math... they teach math this way. THAT is why we have been moving towards different curriculum.
I loved Singapore Math because it taught the kids in this manner, the way i always did math in my head/own way anyway...
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Deleted
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Post by Deleted on Mar 27, 2014 18:52:13 GMT -5
Honestly, and i mean no disrespect, but the fact that people couldn't easily see that the issue there was that he skipped subtracting 10 is because they were taught to think about algorithms and not mathematics. That is what we need to change. A lot of this isn't just an employment of 'common core' ... which is little more than a list of common performance standards which are not that complicated... There is not common core CURRICULUM... just curriculums which are developed to be compliance with common core standards. But when you look at other countries that are beating our bottoms in math... they teach math this way. THAT is why we have been moving towards different curriculum. I loved Singapore Math because it taught the kids in this manner, the way i always did math in my head/own way anyway... So you love it because it matches the way you think. Can't people dislike it because it doesn't match the way they think?
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Deleted
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Post by Deleted on Mar 27, 2014 19:01:35 GMT -5
It actually provides many different options for 'thinking'... It is about more than an algorithm. It is about unspderstanding how numbers work, come together and apart, etc... Not just the employment of algorithms.
Is that more clear?
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Knee Deep in Water Chloe
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Post by Knee Deep in Water Chloe on Mar 27, 2014 23:17:50 GMT -5
shanendoah, you are my new favorite person.
Couple of things... I have read the actual documents of the CCSS from front to back and sideways multiple times over the past four years. However, it is my job. While I don't believe those who wrote it acknowledged cognitive development, I think it's important that the United States has a common goal for what high school graduation means. The CCSS is one huge step towards it. The CCSS is not a law in and of itself. They are set of ELA, math, and literacy for content areas academic standards. Each state has the choice to adopt the standards or not. It is NOT how to teach. You will read that in page of the link I put above. There are suggestions for reading in the ELA. There are suggested problems, and the eight math skills are really life skills. It is much more about critical thinking than the short cuts we learned as students. We cannot be the most creative country in the world without consistently critically thinking. I'm not able to be here as much as many of you, but I can try to answer your questions about it from an educator's perspective if you want. Many states and districts have not done a good job training their teachers about the CCSS and how to change their teaching. That is imperative and where much of the frustaration lies. Another portion lies, again, with the science of cognitive development. That could be fixed if we started down the path of disregarding grade levels, but that's another topic.
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Knee Deep in Water Chloe
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Post by Knee Deep in Water Chloe on Mar 27, 2014 23:21:03 GMT -5
Honestly, and i mean no disrespect, but the fact that people couldn't easily see that the issue there was that he skipped subtracting 10 is because they were taught to think about algorithms and not mathematics. That is what we need to change. A lot of this isn't just an employment of 'common core' ... which is little more than a list of common performance standards which are not that complicated... There is not common core CURRICULUM... just curriculums which are developed to be compliance with common core standards. But when you look at other countries that are beating our bottoms in math... they teach math this way. THAT is why we have been moving towards different curriculum. I loved Singapore Math because it taught the kids in this manner, the way i always did math in my head/own way anyway... So you love it because it matches the way you think. Can't people dislike it because it doesn't match the way they think? But, there's nothing that will be match everyone's thinking. That's the point of the CCSS--we must, to positively perpeuate our society, learn to think critically. Not everyone is intellectually capable of that, and the rest of us are able to do so at varying levels. Regardless of the academic standards we choose to strive for, not everyone will ever be able to meet all of them. Does that mean we drop the expectation down to the lowest level? I hope not, or my life's work (outside of my own children) is senseless.
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Knee Deep in Water Chloe
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Post by Knee Deep in Water Chloe on Mar 27, 2014 23:32:28 GMT -5
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. www.corestandards.org/Math/Practice/This is what the end game is for CCSS math. I really don't mean to trivialize anyone's feelings about this. I understand the reaction of not knowing what this is all about. I don't understand dismissing CCSS completely without understanding what the end game is. Is this really not something we want fully functional adults to be able to do when it comes to math--or even life? The problem that was originally posed is addressed in #s 1, 2, 3, 4, 5, and 6 easily and I could probably make arguments for 7 and 8 if I thought about it. Again, I completely empathize with those of you who are just starting to deal with this with your kids and with teachers who are frustrated. No, it's not perfect. And no way has the presentation of it to the general public been good. I just ask that you understand the bigger picture before dismissing it. Again, I'm happy to answer questions both on the math and ELA sides. Please tag me in your post so I know to check it. I'm not on here on a daily basis.
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shanendoah
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Post by shanendoah on Mar 28, 2014 0:44:37 GMT -5
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happyhoix
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Post by happyhoix on Mar 28, 2014 7:33:52 GMT -5
Actually what the person with the BS in Engineering does every day is use a really fancy calculator.
I'm in the same boat. I'm in a STEM field and have to do math a lot, which I do either through excel sheets that do the calculations for me, or I use an engineering calculator that does the math for me. I only have to be able to understand how to correctly put the numbers into the calculator.
Even though I had trig and geometry and calculus way back in the day when calculators could only add and subtract, I still wasn't able to help DS with his trig and geometry and calculus classes when he was going through middle and high school - I didn't remember the classroom math. And it's been such a long time since I did long division in my head, I would really struggle trying to do it without a calculator.
It's like typing - I type everything, everywhere. The only things I hand write anymore is my signature and grocery lists. Consequently, my hand writing has gotten worse and worse over the years so the point that even I have trouble reading it.
You don't use it, you lose it, and that goes for basic math and basic penmanship.
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NomoreDramaQ1015
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Post by NomoreDramaQ1015 on Mar 28, 2014 8:15:07 GMT -5
I'm in a STEM field and have to do math a lot, which I do either through excel sheets that do the calculations for me, or I use an engineering calculator that does the math for me. I only have to be able to understand how to correctly put the numbers into the calculator. Same here, I have software that does all the number crunching for me. I'd be here all night if I had to sit and crunch all the numbers by hand like I did in math class. Nobody does their data analysis by hand anymore. I can do stuff that requires a fancy calculator but ask me to calculate the slope of a line from memory and I'm in trouble. It's not that I can't do it, it's that I haven't done it on paper in years. I drive DH insane, he's always saying "But you do math every day!" No I work with analytical software every day, with my software I just need to understand where the numbers go, the computer does the actual analyizing.
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CarolinaKat
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Post by CarolinaKat on Mar 28, 2014 8:32:41 GMT -5
Math is still math, the answer is the same no matter what way you get it. But we should be celebrating new ways to learn, so that we can help our kids find the way that works best for them, regardless of whether it works best for usMy Alegra III teacher in High School took that approach. If there were two ways to do a problem he'd show you both and leave it up to you which one you preferred since both methods were considered acceptable. I really struggle with math. Being able to choose between two acceptable methods really helped me out. that's why engineering school was awesome. You have so many ways to get to the answer. As long as you don't apply concepts incorrectly (like eliminating a constant with no justification) they didn't care. You just have to get there.
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Miss Tequila
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Post by Miss Tequila on Mar 28, 2014 8:37:00 GMT -5
Maybe my brain just works differently but that problem seems like a ridiculous way to do math. I don't use basic math but I do have to have a strong understanding of the concepts so that I can develop formulas and calculations. I still think this problem is taking a simple concept and making it much more complicated than it needs to be.
ETA: I just re-read what I wrote...of course I use basic math, we all do. I just meant that in my job I am using concepts more than math. Apparently my brain also works differently when it comes to writing clearly
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CarolinaKat
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Post by CarolinaKat on Mar 28, 2014 8:37:57 GMT -5
I'm in a STEM field and have to do math a lot, which I do either through excel sheets that do the calculations for me, or I use an engineering calculator that does the math for me. I only have to be able to understand how to correctly put the numbers into the calculator.
Same here, I have software that does all the number crunching for me. I'd be here all night if I had to sit and crunch all the numbers by hand like I did in math class. Nobody does their data analysis by hand anymore. I can do stuff that requires a fancy calculator but ask me to calculate the slope of a line from memory and I'm in trouble. It's not that I can't do it, it's that I haven't done it on paper in years. I drive DH insane, he's always saying "But you do math every day!" No I work with analytical software every day, with my software I just need to understand where the numbers go, the computer does the actual analyizing. I tell my husband all the time ' I'm an engineer, I don't do math with numbers.' Which is pretty accurate. We do math with concepts, but the actual numers? Ask Excel or mini-tab or JMP
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Deleted
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Post by Deleted on Mar 28, 2014 8:40:32 GMT -5
Again, that problem was not about 'doing math'... It was about analyzing someone's process to identify their mistake and articulate it that mistake to them...
Higher level skill set.
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Miss Tequila
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Post by Miss Tequila on Mar 28, 2014 8:43:08 GMT -5
Again, that problem was not about 'doing math'... It was about analyzing someone's process to identify their mistake and articulate it that mistake to them... Higher level skill set. But why the heck should there be a picture to do basic math? And is the writing the person that didn't understand the problem, versus the typed? And if the big hump represents the 100's spot (not sure if I am using the terms correctly...I just remember my oldest having to do stuff with 100's spots, 10's spots, and 1's spots) why are the other humps all the same? It looks like there should be a medium spot for the 10's spot and then smaller ones for the 1's spots.
This isn't a higher level skill set...it is a ridiculous way of figuring out a very simple concept. Teaching addition and subtraction should include drawing pictures.
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Post by Deleted on Mar 28, 2014 8:47:19 GMT -5
I was taught to do math the old way but to my surprise I do it the new way when I'm coming up with an answer off the top of my head. The thing I see about Shane's explanation is that it requires more memorization. I only have to memorise subtracting from 9. With the new way you need to memorize subtracting from 20's, 30's etc.
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NomoreDramaQ1015
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Post by NomoreDramaQ1015 on Mar 28, 2014 8:50:38 GMT -5
It was about analyzing someone's process to identify their mistake and articulate it that mistake to them... And I can't do that anymore unless we're talking about someone plugging things into the software/excel wrong. I can tell you what numbers go where in y = mx+b but I can't tell you WHY they go there or break down the method of how to the answer. My HPLC software does the heavy lifting, I just give it the raw numbers. My kid is doomed, we're going to have to hire her a tutor.
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Deleted
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Post by Deleted on Mar 28, 2014 8:51:02 GMT -5
As I said earlier, I don't have a problem with Common Core, so I don't have a dog in this fight.
I think the idea behind it is to not have the kids just get "the answer" but to think about how they figured out the answer as well. Which is a good thing, IMO.
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Deleted
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Post by Deleted on Mar 28, 2014 8:52:19 GMT -5
There is a picture for several reasons. First, you teach young children to do math in many different ways, with many kinds of pictures, including number lines.
Most importantly in this problem, the number line is illustrating the INTERNAL PROCESS of another student. If you are going to understand where they made their mistake, you are going to have to be able to 'see' their process. The number line illustrates the process the student used to address the problem.
In most cases this problem would actually be done by mental math, not an algorithm... and the number line illustrates the process so that the child can identify the error.
There is no medium hump for the 10... because the student forgot to deduct the 10... that was the error....
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whoisjohngalt
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Post by whoisjohngalt on Mar 28, 2014 8:54:41 GMT -5
Don't you just all love the phrases "the old way" when it comes to math.
What the heck does it mean? Has 2+2 has changed over the years?
And I will never understand how trying to make everyone learn it the same way will ever work.
Teach the concepts. Teach the foundation. Who cares if "you" use a number line or do it in your heard or whatever.
Common Core is not about trying to improve education. Not at all
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Miss Tequila
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Post by Miss Tequila on Mar 28, 2014 8:59:55 GMT -5
Don't you just all love the phrases "the old way" when it comes to math. What the heck does it mean? Has 2+2 has changed over the years? And I will never understand how trying to make everyone learn it the same way will ever work. Teach the concepts. Teach the foundation. Who cares if "you" use a number line or do it in your heard or whatever. Common Core is not about trying to improve education. Not at all I agree with this. I do not learn by looking at pictures. To me, this is a crazy ass way to teach the concept. Can't we agree that some kids learn by looking at this picture while others would find this a more difficult way to understand the concept? And to say that not wanting to draw pictures means you dont' have higher level skills is just crazy.
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Miss Tequila
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Post by Miss Tequila on Mar 28, 2014 9:03:10 GMT -5
As I said earlier, I don't have a problem with Common Core, so I don't have a dog in this fight. I think the idea behind it is to not have the kids just get "the answer" but to think about how they figured out the answer as well. Which is a good thing, IMO. I agree...but I can do that without drawing a picture. Heck, writing out 100+100+100+10+1+1+1+1+1+1 (I can't see the actual problem so I am making up an answer) makes much more sense to me than drawing humps...and would accomplish the same thing.
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