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Post by Deleted on Mar 28, 2014 10:52:16 GMT -5
But we were essentially "catering" to those kids' way of learning.
ETA: My niece and nephew are those kids that were getting A's and are now getting C's. My sister is EXTREMELY against common core and has joined some lobby group in her town to try and get it reversed. She has also "opted out" of any testing being performed this year, even though my niece has said that she wants to take the standardized tests.
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Post by Deleted on Mar 28, 2014 10:54:04 GMT -5
I'm not conceding anything Walk But one problem i have had with algebra is getting son to write down anything. We do so much mental math, that it was difficult for him to move to a process of having to write down the steps as algebra progressed. It took awhile. It was hard because he could still do 2 out of 3 in his head, so he didn't want to write stuff down, but getting a third wrong just because you can't keep track of all the little things is not an option. BUT I never said there wasn't a place for formula and function. And it is in higher level math and AFTER you learn the concept. One of the reasons my kids do so well in math though, i think, is because they weren't hemmed in by algorithms and memorization early on. They were encouraged to explore numbers and relationship, etc. in lots of different ways. And most of the processes like the numberline are actually a pathway to mental math. Its much easier to argue with a teenager, who can reason, about the importance of writing down a process just so... than it is to reason with one who can't understand the concept behind the algorithm...
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Miss Tequila
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Post by Miss Tequila on Mar 28, 2014 11:00:05 GMT -5
The thing is, advanced math is based on the simple functions of adding, subtracting, multiplication and division. So you learn how to subtract using a number line, which does make sense in my brain but other than simple principles, exactly how are you going to use this when you are taking algebra, when you are stacking function on function?
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shanendoah
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Post by shanendoah on Mar 28, 2014 11:08:31 GMT -5
And I'll be honest, I'm not offended easily. And for the most part, I like you Miss Tequila, but I am offended at you claiming that people who are visual learners are "dumb". They aren't dumb. They learn in a different method than you do, but that doesn't make them dumb. They will arrive at the same answer you do, maybe a little more slowly, or maybe, given some problems, a little more quickly. What method they take to get there does not matter.
However, in order to be able to teach kids the different methods, and for the kids to figure out which one works for them, guess what ALL the different methods have to be taught. And so yes, for a few nights, your kid is going to have to do math in the method that does not work best for them. The number line method is infinitely better for Pop Tart, but that doesn't mean I don't make her use the "stacking" method on nights when her homework requires her to use that method. I don't say that method is stupid and overly complicated (when she has to borrow across 0) and tell her that she doesn't need to learn it. Instead, I sit with her and try to help her understand it.
And that's the point. People learn differently. It's that simple. To me, it's like this cartoon:
Being a visual learner doesn't make someone dumb. Teaching the visual method of doing something isn't "dumbing it down", it's teaching a different method. But this idea that it is dumbing down, while making it overly complicated, is what makes the memes like the one that started this OP so powerful.
And once more this is a rant against Singapore math, NOT COMMON CORE.
Common Core is just a list of skills kids should have when the finish each grade. It does not, in any way, tell teachers how they have to teach those skills. The state board of Ed, or the school district, or the school may then tell teachers how they should teach those skills, but that is NOT Common Core. That is a decision by their state, district, or school, and if you have a problem with that- then complain to the correct entity. Don't blame the idea that all 3rd graders should be able to do simple division.
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NomoreDramaQ1015
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Post by NomoreDramaQ1015 on Mar 28, 2014 11:11:40 GMT -5
I'd probably get Singapore math if I was younger. But I've been doing it the old school way for 30 years. It's going to require a complete retooling of my brain to figure out Singapore math. I have no clue what any of you people are talking about. I do wonder if it would have been easier for me. I'm numbers dyslexic so I had a horrible time in math class growing up. I've learned to overcome it and adapt but it would have been a lot easier to just learn a method that fits how my brain is wired to begin with.
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Post by Deleted on Mar 28, 2014 11:13:04 GMT -5
Actully, i never saw a question like that in my Singapore books... i'm not sure its Singapore specifically, but a singapore-like method...
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shanendoah
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Post by shanendoah on Mar 28, 2014 11:37:53 GMT -5
oped - I don't think I've seen a problem exactly like that in Pop Tart's singapore math book either, but we do have problems that are- look at these answers. We've circled the ones that are wrong. Tell us why they are wrong. And they aren't all obvious. She's currently doing geometry, so in one case, the math was correct but the unit of measurement written with the answer was wrong, or it was area and they forgot to put the squared after the unit of measurement (or perimeter and they did put the squared after the unit of measurement). So while I haven't seen a problem exactly like this, we just did problems this week that were- this is wrong, tell us why.
The Walk of the Penguin Mich - The point is, they learned subtraction. Once you learn it, the method you took to learn it doesn't matter as much. But the truth is, the number line method, especially for subtraction, is actually much closer to what most of us use in our daily lives, when doing math in our head. We use it "backwards" but it's what we use.
Say we're at a craft fair booth and we have $50 to spend. I've picked out something that costs $19.21 and want to know how much more I have to spend. I've been doing basic math in my head for a really long time, so without thinking hard, I know the answer is $30.79, but when figuring that out, I don't use the stacking method in my head. All the borrowing would be too much to keep track of. Instead, I know the difference between $50 and $20 is $30. And that the difference between 19.25 and 30 is .75, and the difference between .25 and .21 is .04, giving me 30.79. The number line method isn't so much about drawing pictures, though the pictures help, it's about dividing problems up into simple chunks. Do I actually do all those steps consciously each time I am figuring out math in my head- no, because I've been doing them long enough that I don't have to think about it. That's how this translates to algebra. Once kids get addition, subtraction, multiplication and division, it doesn't matter how they learned it, they know it. What mental process they used to get there doesn't matter. (Goes back to the earlier conversation about mentally figuring 30%- some people do the straight 30, while others find it much easier to figure 10 and multiply by 3. Officially it has more steps, but for me, at least, I'll get to the right answer a whole lot more quickly going 10x3 than trying to figure 30% out directly in my head.)
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Post by Deleted on Mar 28, 2014 11:47:08 GMT -5
I have wanted to post a rant to some of DD's homework and I have heard that some of the parents have. However I just google it. I realize it isn't common core, which I actually like, but the way it is being implemented. DD's math teacher was saying that he is being forced to show the students at least 2 ways of doing things and one has to be visual. This work well for some things, number lines and such. There is one example though that we never figured out and DH is an engineer and I have gotten A all the way through college calc 2. It was multiply and dividing negative/positive numbers and there were red and black chips. It was a total convoluted mess. So dd can multiply and divide - and + numbers great. It is easy, but she gets answers wrong because she can't use this chip method. It was wrong on the quiz, then wrong on the test, then wrong on the mid term, and I am sure it will be wrong again on the final.
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souldoubt
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Post by souldoubt on Mar 28, 2014 11:55:36 GMT -5
But we were essentially "catering" to those kids' way of learning. Of course and that's kind of the point I was hitting on. Now they're catering to kids who think another way while we'll have other types of thinkers who struggle. It's not more fair one way or the other but if it makes the US feel all warm and fuzzy because we test a bit better down the line I guess that's at least an improvement internationally. I appreciate people in this thread showing different ways to approach a problem but that outlines the bigger issue that not everyone thinks or processes information the same way. If kids are taught one way and expected to do it that one way we're still going to have others who ultimately struggle because of the way their thought process work.
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Post by Deleted on Mar 28, 2014 12:02:21 GMT -5
But we were essentially "catering" to those kids' way of learning. Of course and that's kind of the point I was hitting on. Now they're catering to kids who think another way while we'll have other types of thinkers who struggle. It's not more fair one way or the other but if it makes the US feel all warm and fuzzy because we test a bit better down the line I guess that's at least an improvement internationally. I appreciate people in this thread showing different ways to approach a problem but that outlines the bigger issue that not everyone thinks or processes information the same way. If kids are taught one way and expected to do it that one way we're still going to have others who ultimately struggle because of the way their thought process work. They're not trading one for another. They're trading one for several, and by casting a wider net they are going to reach more students.
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raeoflyte
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Post by raeoflyte on Mar 28, 2014 12:02:54 GMT -5
I know I've said this before, but my mom read something when I was in highschool that said that girls typically did great in math at the elementary level and then did worse and worse through middle and highschool and the reasoning was that girls were more likely to do what they were told to do and so in basic math they learned/memorized the answers, not because they actually understood the concepts that go to the correct answer. That works well in basic math, but really starts to fall apart once you get farther along. The theory definitely held true for me which is why I do plan to have tutors with my kids even if they are doing well. Are they doing well because they really get it or are just better than the crowd or not a trouble maker.
And parents having trouble with kids homework isn't new. I remember my dad trying to help me with algebra homework in 7th grade and while he knew the answer, he couldn't figure out how to come up with the answer the right way. That was over 20 freaking years ago, so nothing new. Just like how kids today behave terribly and the world is coming to an end. blah, blah, blah.
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Miss Tequila
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Post by Miss Tequila on Mar 28, 2014 12:07:44 GMT -5
And I'll be honest, I'm not offended easily. And for the most part, I like you Miss Tequila, but I am offended at you claiming that people who are visual learners are "dumb". They aren't dumb. They learn in a different method than you do, but that doesn't make them dumb. They will arrive at the same answer you do, maybe a little more slowly, or maybe, given some problems, a little more quickly. What method they take to get there does not matter.
However, in order to be able to teach kids the different methods, and for the kids to figure out which one works for them, guess what ALL the different methods have to be taught. And so yes, for a few nights, your kid is going to have to do math in the method that does not work best for them. The number line method is infinitely better for Pop Tart, but that doesn't mean I don't make her use the "stacking" method on nights when her homework requires her to use that method. I don't say that method is stupid and overly complicated (when she has to borrow across 0) and tell her that she doesn't need to learn it. Instead, I sit with her and try to help her understand it.
And that's the point. People learn differently. It's that simple. To me, it's like this cartoon:
Being a visual learner doesn't make someone dumb. Teaching the visual method of doing something isn't "dumbing it down", it's teaching a different method. But this idea that it is dumbing down, while making it overly complicated, is what makes the memes like the one that started this OP so powerful.
And once more this is a rant against Singapore math, NOT COMMON CORE.
Common Core is just a list of skills kids should have when the finish each grade. It does not, in any way, tell teachers how they have to teach those skills. The state board of Ed, or the school district, or the school may then tell teachers how they should teach those skills, but that is NOT Common Core. That is a decision by their state, district, or school, and if you have a problem with that- then complain to the correct entity. Don't blame the idea that all 3rd graders should be able to do simple division. Sorry..I didn't mean any offense by it. I can see how you were offended and I do apologize for it. I have one kid who is very bright and one who is special needs so I certainly understand all kids learning at different paces. I don't have a kid in the middle (who struggles but gets it) so to me this method seems ludicrous (probably more so because I am not a visual learner).
Way back before the "if you don't get it you don't understand higher level skills" I did state several times that I knew all kids learned in different ways. I still don't think I am in agreement with making visual learning the first choice for all students (for math) but if a kid is struggling and this works, great.
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souldoubt
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Post by souldoubt on Mar 28, 2014 12:08:32 GMT -5
Of course and that's kind of the point I was hitting on. Now they're catering to kids who think another way while we'll have other types of thinkers who struggle. It's not more fair one way or the other but if it makes the US feel all warm and fuzzy because we test a bit better down the line I guess that's at least an improvement internationally. I appreciate people in this thread showing different ways to approach a problem but that outlines the bigger issue that not everyone thinks or processes information the same way. If kids are taught one way and expected to do it that one way we're still going to have others who ultimately struggle because of the way their thought process work. They're not trading one for another. They're trading one for several, and by casting a wider net they are going to reach more students. I hope you're right but only time will tell. Others have posted before about how the US has issues educating that some of the countries we test against don't - language barriers for example and educating every kid. We've got an office in one of the countries that tests real well and the emphasis placed on education at home by parents is something you don't always see here. Maybe that's why despite the scores US kids who took the last big test countries partake in reported being quite a bit happier than kids in some of the best testing countries.
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8 Bit WWBG
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Post by 8 Bit WWBG on Mar 28, 2014 12:10:03 GMT -5
As a systems/business process designer, I constantly deal with folks who just plain don't want to learn a new way. No matter how much "better" the new way is, and how much time could be saved, they know what they know and don't want to change.
Think of the ribbon menus introduced in Office 2007. M$ took time to analyze the most commonly used functions, and made them easily accessible. People are used to them now, but the griping when they first launched was incredible. People would rather continue to rely on their memorization of something in a menu, than appreciate how much easier it is to access now.
I think I'd been using a variation of this "common core" idea. I do the same thing with percents -- I am not a savant and can't just "do" it. So if its something complicated, I break it down by 10s and 1s. What is 8% of 76? I know 1% of 76 = .76, so 2% must be (.76x2) = 1.52, and 4 x 1.52 = 6.08. Even then its not easy, as I made a mistake the first time I did this.
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Miss Tequila
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Post by Miss Tequila on Mar 28, 2014 12:12:20 GMT -5
As a systems/business process designer, I constantly deal with folks who just plain don't want to learn a new way. No matter how much "better" the new way is, and how much time could be saved, they know what they know and don't want to change. Think of the ribbon menus introduced in Office 2007. M$ took time to analyze the most commonly used functions, and made them easily accessible. People are used to them now, but the griping when they first launched was incredible. People would rather continue to rely on their memorization of something in a menu, than appreciate how much easier it is to access now. I think I'd been using a variation of this "common core" idea. I do the same thing with percents -- I am not a savant and can't just "do" it. So if its something complicated, I break it down by 10s and 1s. What is 8% of 76? I know 1% of 76 = .76, so 2% must be (.76x2) = 1.52, and 4 x 1.52 = 6.08. Even then its not easy, as I made a mistake the first time I did this. but that is where we disagree. I do not believe using visual methods to learn math concepts is better.
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Post by Deleted on Mar 28, 2014 12:13:09 GMT -5
It's not "better" than any other way. It's just different.
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8 Bit WWBG
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Post by 8 Bit WWBG on Mar 28, 2014 12:24:27 GMT -5
That being said, I am a proud, sarcastic, and downright immature individual and could totally see myself writing something along the lines of "Jack's Dad".
Dearest Lucien,
Sometimes in life, we are forced to subordinate our superior knowledge in order to secure a desirable outcome. There are those who are ridiculously closed minded when it comes to method, and though we may pity them, we must be adept at recognizing when they are also gatekeepers. Know that we live in a results oriented world. Be true to yourself, but know that many people will lash out negatively at what they don't understand or appreciate. You are learning a lot more with this lesson than just "math".
- Daddy.
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8 Bit WWBG
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Post by 8 Bit WWBG on Mar 28, 2014 12:29:30 GMT -5
...:::"The higher level skill has nothing to do with drawing a picture.":::...
What happens if the kid is horrible at math, but draws an absolute masterpiece? Like, better than a Miyazaki film?
Or crap, what if I have a real emo daughter and she draws some incredibly sad scenario.
"Desdemona cried one thousand and one tears yesterday, because endangered baby walruses are being clubbed to death senselessly for their ivory. Today, she only cried eight hundred and sixty four tears, because of the rampant hunger and disease in Eritrea. Though all pain is beautiful and sad, and we are defined through our suffering, how many less tears did she cry today?"
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8 Bit WWBG
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Post by 8 Bit WWBG on Mar 28, 2014 12:36:51 GMT -5
...:::"but that is where we disagree. I do not believe using visual methods to learn math concepts is better.":::...
"Better" was in quotes. I do get your point and its different with learning than with systems, but also has overlap.
I'm prejudiced, because in my process design world, sometimes the new way really is better. Or at least, it reduces level of effort, it increases accuracy, it eliminates the possibility of mistakes or incomplete submissions, and it speeds up a process from several hours to several seconds.
Now for the math... If you are so used to doing math one way, and that works for you, then do it. I get there are many reasons one wouldn't want to change. Maybe the new way is utterly ridiculous to you. Maybe you have no desire to change.
Its also a drastically different proposition when dealing with a "blank slate" vs. re-training someone.
I was taught 2 ways to read music. One by memorization and one by interval. With practice, I'm sure either would become "natural" to me.
Here is another example: the DVORAK keyboard layout is vastly better designed than the QWERTY layout. It puts many words right on the home row, and most words can be typed through an alternating left/right, and out/in methodology.
But man, I don't want to invest the time it would take to re-learn typing! I can type very quickly with fantastic accuracy. Ultimately I'm sure DVORAK would enhance that even further. But until it is more widespread, and I want to make the investment, I'm not going to try.
Someone just starting to type might smoke me on DVORAK.
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Virgil Showlion
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Post by Virgil Showlion on Mar 28, 2014 12:44:23 GMT -5
I always found the canonical subtraction algorithm ridiculously simple, but if a student doesn't "get it", it seems like a good idea to have a graphical analogy like a number line waiting as a backup. The main problem I'd have with teaching the number line primarily (or even exclusively) is that it obviously can't be applied to large numbers. 86298301927 - 72634918274 = ? can very easily be computed using the canonical subtraction algorithm, but can't realistically be represented on a number line. And let's face it, the subtraction algorithm isn't exactly rocket science. It has three rules: i) if top digit >= bottom digit, subtract bottom from top ii) otherwise add 10 to top digit and decrement it's left neighbour by 1 iii) if a left neighbour is 0 and can't be decremented, add 10 to it and decrement it's left neighbour by 1; rinse, lather, repeat We're saying this is too hard for US kids to learn?
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8 Bit WWBG
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Post by 8 Bit WWBG on Mar 28, 2014 12:50:20 GMT -5
Well geez virgil, you just start by taking away 70 billion from 80 billion. That leaves us with 16 billion. Now you take away 2 billion from 16 billion and you have 14 billion...
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whoisjohngalt
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Post by whoisjohngalt on Mar 28, 2014 12:50:30 GMT -5
hey hey hey don't you all rag on Singapore - I am LOVING that book. I am from the "old country" and math was a biggy and we learned it in all kinds of different ways and I never heard of "number line" but I think Singapore approach is excellent. For the record, they don't just do a number line - they address the same problem from 3-4 different angles, which I think what should be done in schools. Now, anyone who disagrees with what I am saying is just too dumb to get it!!!
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Post by Deleted on Mar 28, 2014 12:57:50 GMT -5
I'm an English educator and a long way from being a parent of children learning math, but this number line method just sounds like a step backwards to me. Our ancestors used an abacus to do math. Isn't that all a number line is? Isn't counting on your fingers a primitive and portable form as well? Should reinventing the wheel be heralded as if it were something new?
For what it's worth, we used a number line in the primary grades back in the very early 1960s. It was used primarily to help you visualize what happens when you add and subtract with negative numbers, but I guess it would help with positive numbers as well if that were a problem. But you got past it fairly quickly because speed and accuracy were what were expected of us. You basically internalized the various combinations of 0-9. I won't even call it memorizing since no one drilled us on them like the multiplication tables. It's like how you internalize the irregular verb forms by virtue of being a native speaker. You just practice the combinations so much that they are wired into your brain. That just seems a faster way of doing basic arithmetic.
I'm just confused as to why this is considered new. Yes, I get that we want to teach kids critical thinking skills. But 2+2 doesn't need analysis. Like I said, it is arithmetic. Those word problems should be enough to foster critical thinking skills.
You can make fun of me. That's one of the perks of being old. Nothing is ever really new.
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Post by Deleted on Mar 28, 2014 12:59:05 GMT -5
I always found the canonical subtraction algorithm ridiculously simple, but if a student doesn't "get it", it seems like a good idea to have a graphical analogy like a number line waiting as a backup. The main problem I'd have with teaching the number line primarily (or even exclusively) is that it obviously can't be applied to large numbers. 86298301927 - 72634918274 = ? can very easily be computed using the canonical subtraction algorithm, but can't realistically be represented on a number line. And let's face it, the subtraction algorithm isn't exactly rocket science. It has three rules: i) if top digit >= bottom digit, subtract bottom from top ii) otherwise add 10 to top digit and decrement it's left neighbour by 1 iii) if a left neighbour is 0 and can't be decremented, add 10 to it and decrement it's left neighbour by 1; rinse, lather, repeat We're saying this is too hard for US kids to learn? No, i'm saying a baboon could probably learn it. And even if he couldn't, my cell phone can do that... What i want is people who can approach a problem, analyze it, utilize their knowledge and solve it, including trouble shooting for themselves and others when errors might naturally occur...
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Post by Deleted on Mar 28, 2014 13:00:42 GMT -5
Once again, a number line is an excellent early tool for visualizing what becomes a mental process...
And yes, its one way. And the new method is to teach multiple ways. But also to focus on numbers and relationships, etc. rather than rote memorization and algorithm...
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Post by 973beachbum on Mar 28, 2014 13:19:22 GMT -5
oped I think this actually gets back to a pet peeve of yours. We are trying to force kids to learn things before they are actually ready. Common core is a list of things students should have learned at the end of particular grade. Where I may have learned multiplication in 4th grade now they are teaching it in 2nd. Because of this IMO it needs to be way more broken up to help the kids understand things that if taught when they were older wonuldn't be quite that difficult. I am not talking about visual vs other types of learners, just the age that they learn it at. And I would LOVE to see you guys trying to do adding, subtracting and mult/dividing in Everyday math. I think a few heards would explode at the process of going from left to right.
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Post by Deleted on Mar 28, 2014 13:24:28 GMT -5
Its probably a bit that Its also that i've always been a left to right kind of person in math and its finally nice to have that method acknowledged by something other than a blank look
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raeoflyte
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Post by raeoflyte on Mar 28, 2014 13:26:28 GMT -5
oped I think this actually gets back to a pet peeve of yours. We are trying to force kids to learn things before they are actually ready. Common core is a list of things students should have learned at the end of particular grade. Where I may have learned multiplication in 4th grade now they are teaching it in 2nd. Because of this IMO it needs to be way more broken up to help the kids understand things that if taught when they were older wonuldn't be quite that difficult. I am not talking about visual vs other types of learners, just the age that they learn it at. And I would LOVE to see you guys trying to do adding, subtracting and mult/dividing in Everyday math. I think a few heards would explode at the process of going from left to right. omg--this drives me nuts. We are starting to learn how to write sentences in kindergarten now (which I thought was bad, but my super religious friends preschool had to talk to her because her 4 year old wasn't using complete sentence structure yet so what do I know...) Is there anything backing up that earlier academics is better? I knew another couple from India who said their 4 year old would be terribly behind if they wanted to move back to India because our preschools were so lax. I know India has tested well and probably better than the US in math/science, so maybe that is the system we are emulating? My 4 year old does seem ready for more academics so I guess I can't argue it from that stand point, but I really don't think that he would be suffering if we waited either. If we get to kindergarten and they aren't learning all of these academics through playing we are going to have to seriously re-evaluate our education plans.
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Post by Deleted on Mar 28, 2014 13:29:19 GMT -5
No. Nothing backs up earlier academics are better. In fact if anything research backs up less formal early academics as better.
But the educational system isn't generally a picture of whats better...
Thus why i homeschool...
Now, that is not to say young children shouldn't be given stimulation and challenge and read to, etc. ... and that they shouldn't be offered the opportunities to explore and gain skills in areas that interest and engage them...
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Post by Deleted on Mar 28, 2014 13:31:35 GMT -5
oped I think this actually gets back to a pet peeve of yours. We are trying to force kids to learn things before they are actually ready. Common core is a list of things students should have learned at the end of particular grade. Where I may have learned multiplication in 4th grade now they are teaching it in 2nd. Because of this IMO it needs to be way more broken up to help the kids understand things that if taught when they were older wonuldn't be quite that difficult. I am not talking about visual vs other types of learners, just the age that they learn it at. And I would LOVE to see you guys trying to do adding, subtracting and mult/dividing in Everyday math. I think a few heards would explode at the process of going from left to right. You don't get scratch paper? Stacking them is actually to make sure that the ones all stay in one column, the tens in another, and so on. It's another form of visualization. Ditto, with multiplication and even the dividing thingamajig. I think we could do it linearly, but it would slow us down in the same sense of typing on the non-Qwerty keyboard would. Once we got used to it, it would be probably be no big deal. But the horizontal method makes sense because it allows you to hyperfocus on one column at a time if the number of things to be added are many.
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