Post by irishbride2 on Oct 19, 2014 17:19:19 GMT -5
People are idiots.
That's all I've got. There are valid concerns with any art of curricula but Jesus Christ most of the common core math comments just illustrate how most people seem to lack critical thinking skills.
That's all I've got. There are valid concerns with any art of curricula but Jesus Christ most of the common core math comments just illustrate how most people seem to lack critical thinking skills.
#crankyMathTeacher
That method makes no sense to me. Do you start on the left or the right? Is he counting up from 316 or down from 427. Also, what exactly are we trying to learn from using this method to find the difference between the numbers? I'm honestly asking.
That's all I've got. There are valid concerns with any art of curricula but Jesus Christ most of the common core math comments just illustrate how most people seem to lack critical thinking skills.
#crankyMathTeacher
That method makes no sense to me. Do you start on the left or the right? Is he counting up from 316 or down from 427. Also, what exactly are we trying to learn from using this method to find the difference between the numbers? I'm honestly asking.
I don't teach this method so I don't know. My issue is with the argument that another way is faster, so what? Our goal isn't just to have kids memorize short cuts. We want them to understand it. I'm not some big common core proponent. I'm just over peoples stupid arguments of "that's not how I learned it so it sucks" or "a different way is faster."
That method makes no sense to me. Do you start on the left or the right? Is he counting up from 316 or down from 427. Also, what exactly are we trying to learn from using this method to find the difference between the numbers? I'm honestly asking.
I don't teach this method so I don't know. My issue is with the argument that another way is faster, so what? Our goal isn't just to have kids memorize short cuts. We want them to understand it. I'm not some big common core proponent. I'm just over peoples stupid arguments of "that's not how I learned it so it sucks" or "a different way is faster."
Post by litebright on Oct 19, 2014 17:37:13 GMT -5
See, having seen my daughter's common core math sheets, I actually do understand this.
The number line could be used to count up or down 316 from the answer that "Jack" got. I'll use it to count down from 427. First by the biggest units, the 100s. So there's the three big swoops. But Jack forgot to count down by the 10s (in this case, just 10) and went straight to counting down by the ones (the six little swoops). That's how he ended up at 121 instead of 111.
I don't get the common core hate. My DD1's teachers are really optimistic about it and say the expectations more rigorous. My first grader comes home talking about writing equations -- yeah, it's just things like 1+1=2, but the way they build them is more like 1+y=2 and so when actual equations come along, it's not an "OMG, this is totally unlike how I memorized my numbers!"
One of the things I do to help out her teacher is tear out the math workbook pages so that they can pass them out as homework, and as a literature major, I see common core math as actually more like a language. It's about understanding how numbers work, and their relationship to each other, and that no matter what "things" you're counting or calculating, the relationship is what's important. I dunno, to me as a writer it seems like the basis of it is to be able to understand and use numbers in a similar way that you would use words.
Common core math? Common core is not a curriculum. CCSS is a set of standards. A state, district, school, teacher can teach those standards by using a curriculum. We want kids to think.we are teaching kids multiple strategies to find an answer and asking them the how? Why? Are you sure? Etc., to make sure they know how to problem solve.
For this problem, instead of using a number line to solve this problem, I would use a place value mat and base 10 blocks. I would model using the place value mat and the standard algorithm right alongside each other, so kids know what it means to subtract the ones, tens and hundreds. I would use language like, the first step is to subtract the ones, 7 ones - 6 ones = 1 one. 2 tens -1 ten= 1 ten, etc.
I agree that the number line is not efficient and there are better ways. But having a tool kit of strategies and knowing which strategy to use and when, helps kids to become more efficient problem solvers.
Post by game blouses on Oct 19, 2014 17:48:09 GMT -5
It's less about the number line and more about having kids practice critical thinking skills by finding both the correct and incorrect steps in the process.
All these different models (ten frames, base ten, etc), which are different from what we might call 'stacking' (usually referred to as the traditional algorithm) , are important because rather than focusing just on the rote skill of addition and subtraction, they focus on manipulating numbers and extending number sense. As students continue through the math continuum it is more important that they have flexible thinking when it comes to numbers, that they be able to decompose, split and make numbers in a variety of ways, that they understand the relationship between numbers, than to simply be able to stack two or three-digit numbers and add or subtract them, carrying or borrowing as needed.
I really dislike that people claim that is inefficient or more complicated. The traditional algorithm is fast or less complicated because that is what you are familiar with. A good math teacher shows multiple ways to solve a problem. Just because it confuses more parents doesn't mean the kids aren't getting it. In fact, I think it reaches more kids and helps them develop a better understanding of what the standard algorithm actually means.
Personally I have taught in the classroom, and I have worked with my DD. My DD really struggled with multi-digit addition on paper. She used partial sums to solve it mentally, but she could not "show her work." Once I showed her that partial sums was a real way to do it and to write that down, she felt much more comfortable with multi-digit. It helped her to realize what the traditional method was symbolizing.
This looks insane. I am nervous about having to teach my kid that psycho math at night. Again. After she's supposed to learn it at school. Because it makes no sense.
Sure blah blah critical thinking.* But I already know how to add and subtract. I have no desire to learn a new way. Which I will, because every parent has to relearn everything as their elementary kids learn it.
*eta. Not sure I buy this explanation but I will accept it as true for the sake of argument.
So, I get some of the explanations in here. It makes more sense to me now, although I still think the method is a bit screwy. But, here's my thing with it: making a change like this almost seems to require a re-education of the parents, no? Because I look at that and think, "well now Jack has to count down to 316 by using the number line and in specific amounts. THEN he has to add all the individual numbers he counted down by to come up with the correct answer." I really did require someone to explain to me HOW to use the number line to solve the problem. If my 5 year old is coming home and needs help with his homework, how the heck am I supposed to help teach him the method if I don't understand it either?
I'm all for advancement of techniques and trying to help kids have different ways of learning and understanding basic concepts, but this just feels off to me. Then again, I'm having a hard time remembering how exactly I learned the method of subtraction because I have such an innate understanding of it now, so maybe I should just shut up about it.
This looks insane. I am nervous about having to teach my kid that psycho math at night. Again. After she's supposed to learn it at school. Because it makes no sense.
Yes, this is exactly my concern when I look at this! "Um, I don't know, kid, it doesn't make any sense to me either. Go ask your dad." lol
This looks insane. I am nervous about having to teach my kid that psycho math at night. Again. After she's supposed to learn it at school. Because it makes no sense.
LOL. It makes sense, but I'm still not convinced that this is a superior way to learn math.
Can somebody please explain why rote learning is so discouraged?
This looks insane. I am nervous about having to teach my kid that psycho math at night. Again. After she's supposed to learn it at school. Because it makes no sense.
LOL. It makes sense, but I'm still not convinced that this is a superior way to learn math.
Can somebody please explain why rote learning is so discouraged?
This looks insane. I am nervous about having to teach my kid that psycho math at night. Again. After she's supposed to learn it at school. Because it makes no sense.
LOL. It makes sense, but I'm still not convinced that this is a superior way to learn math.
Can somebody please explain why rote learning is so discouraged?
Seems to work all around the rest of the world.
rote learning isn't discouraged, it simply isn't the only thing taught anymore. It is about meeting the needs of different thinkers AND, more importantly, extending critical thinking skills beyond the rote operation and into more complex thinking.
Here is one example...
Mental math is considered an important life skill and a great way to assess number sense vs. operational skill. The ability to work flexibly with numbers in your head (vs. pen/paper or calculator) is a really easy way to tell how well someone can manoeuvre numbers to work in the most efficient way.
Example…if the only way you know how to add and subtract is using the traditional algorithm, 8744-1298 would involve borrowing and would be tough to do in your head. But if you can manipulate numbers easily in your head because you have strong number sense you would see that 1298 is essentially 1300. But since you added 2 to the subtrahend you need to add 2 to the minuend…so if you add 2 to 1298 to get 1300, you need to add 2 to 8744 to get 8746. It is really easy to subtract 3000 from 8746 in your head, it is 8446.
This is just one strategy for mental math (I want to say the strategy is called compensation but I would have to check)…there are many others (front end estimation, friendly numbers, etc). But these strategies all require more than a rote understanding of how to do the standard algorithm.
I still don't understand. (Irrelevant qualification, I'm a Cpa and got a 790 on my math SAT).
I agree with all of the theory being said, but I still don't understand how to do the problem.
Can someone please explain it even more than above?
Jack used counting backward to solve the problem. He used a number line to help him keep track of how much he counted back. When he had counted 316 worth backwards then that would be his answer. He started counting back by hundreds 427, 327, 227, 127, then by ones 126, 125, 124, 123, 122, 121.
His error was he only counted back 306 worth. He should have counted back by 3 hundreds, then 1 ten, then 6 ones. 427, 327, 227, 127 (300), 117 (10), 116, 115, 114, 113, 112, 111 (6).
I would be willing to bet that before this lesson there were other place value lessons, including expanding a number (316= 300+10+6)
Post by UMaineTeach on Oct 19, 2014 18:51:52 GMT -5
I think part of the answer to this is sending the learning target home with the homework.
The parents should know what the goal of the lesson is, so they understand that the purpose of this lesson what critical thinking about numbers and not about how to solve a subtraction problem.
Post by chickadee77 on Oct 19, 2014 18:53:59 GMT -5
Kind of funny, because I'm as old-school as they come, but this is kind of how I do math in my head. I've just never thought to draw it out or analyze it. Believe me, if I'm adding or subtracting (in my head, not on paper), I'm certainly not visualizing carrying the one or borrowing a ten - I'm essentially doing what is shown here!
Ok, so I see the big jumps are 100, but why are the small jumps 1s when they are labeled 10s?
So I see 100 200 300 310 320 330 340 350 360. I think that's why I'm so confused. Or is that part of the solution, that the number line is labeled incorrectly?
Post by irishbride2 on Oct 19, 2014 19:09:19 GMT -5
As a higher math teacher I can spot a memorizer a mile away.
Route learning only at a young age hampers higher level thinking later. And generally it becomes very apparent around algebra 1. Cue anecdotes of people only memorizing but being math geniuses.
Math at its core is about learning how to problem solve and approach a problem from multiple ways. That's really the point of learning math beyond simple arithmetic. You are learning skills that will enable you to solve hard problems of all sorts as an adult. So learning multiple approaches and deeper meaning is important. And many of you who think you just learned by pure memorization probably did not. You just didn't notice the higher level methods your teacher used.
Most of the CC methods aren't even new lol. Many are based on very old methods.
Again I'm not pro or anti CC. I just hate the argument that memorization is better or that new ways are automatically bad.
Ok, so I see the big jumps are 100, but why are the small jumps 1s when they are labeled 10s?
So I see 100 200 300 310 320 330 340 350 360. I think that's why I'm so confused. Or is that part of the solution, that the number line is labeled incorrectly?
That threw me too. I think the parent/student wrote that part in and it wasn't in the original worksheet.
As a higher math teacher I can spot a memorizer a mile away.
Route learning only at a young age hampers higher level thinking later. And generally it becomes very apparent around algebra 1. Cue anecdotes of people only memorizing but being math geniuses.
Math at its core is about learning how to problem solve and approach a problem from multiple ways. That's really the point of learning math beyond simple arithmetic. You are learning skills that will enable you to solve hard problems of all sorts as an adult. So learning multiple approaches and deeper meaning is important. And many of you who think you just learned by pure memorization probably did not. You just didn't notice the higher level methods your teacher used.
Most of the CC methods aren't even new lol. Many are based on very old methods.
Again I'm not pro or anti CC. I just hate the argument that memorization is better or that new ways are automatically bad.
Last year at one of our admin PD meetings they were doing a whole thing on number lines as a math model. They showed how to use it to teach subtracting negative numbers. Holy crap I wish I had used that model when I taught grade 8 math, it made so much more sense.
Kind of funny, because I'm as old-school as they come, but this is kind of how I do math in my head. I've just never thought to draw it out or analyze it. Believe me, if I'm adding or subtracting (in my head, not on paper), I'm certainly not visualizing carrying the one or borrowing a ten - I'm essentially doing what is shown here!
Me too.
I always struggled with rote math learning, and this is essentially how I taught myself to do it in my head - so this kind of approach might have actually helped me as a kid who had little natural aptitude for math. But I can see how it would be weird for others, if it's not an approach you're used to.
Ok, so I see the big jumps are 100, but why are the small jumps 1s when they are labeled 10s?
So I see 100 200 300 310 320 330 340 350 360. I think that's why I'm so confused. Or is that part of the solution, that the number line is labeled incorrectly?
That threw me too. I think the parent/student wrote that part in and it wasn't in the original worksheet.
Ok. I can see it now. We have to look at the typed numbers, not the written ones. Thank you! I appreciate your time.
I really want to believe in common core, honestly. The theory sounds great, it's the technical stuff I'm lacking. I can appreciate wanting to teach understanding the relationships between numbers. I feel like so many people are bad at math, and something needs to be changed. I just need to learn the new methods as DD goes. Luckily she is 4 so I can grow with her.
Kind of funny, because I'm as old-school as they come, but this is kind of how I do math in my head. I've just never thought to draw it out or analyze it. Believe me, if I'm adding or subtracting (in my head, not on paper), I'm certainly not visualizing carrying the one or borrowing a ten - I'm essentially doing what is shown here!
We want kids to eventually do mental math and be able to explain how they arrived at an answer.