I don't directly teach math but I support it as a special education teacher. I was horrible at math when I was younger because I could not memorize the steps. Also, it took me until college to figure out that multiplication was repeated addition. Now that is one of the strategies for learning multiplication. The way it is taught now allows the student to see the big picture of math. In the example you can visualize that both addition or subtraction can be used to solve the problem. Also, as a previous poster has said it leads to being able to use mental math and not need a pencil or paper.
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.
i'm willing to consider the conclusion that maybe it is a better way to learn. i think i am good at math bc it comes naturally, but for most, there is nothing natural about it. maybe this new method will ensure chart more kids develop an aptitude for math-like subjects? idk.
Hmm. Maybe?
I've read everything in this thread. It makes sense in theory.
But my mental math is just fine, if not excellent, not having gone through this process.
i'm willing to consider the conclusion that maybe it is a better way to learn. i think i am good at math bc it comes naturally, but for most, there is nothing natural about it. maybe this new method will ensure chart more kids develop an aptitude for math-like subjects? idk.
Hmm. Maybe?
I've read everything in this thread. It makes sense in theory.
But my mental math is just fine, if not excellent, not having gone through this process.
Absolutely possible, however, not true for everybody. For many years, too many, math has either been a subject that people loved (usually because it came easily) or hated (usually because only one way was right). That time has come to an end. One way of teaching and learning math does not, and cannot, reach all learners. And math shouldn't be something that only some people can access. There are totally people who were successful using the old models and strategies, but not everyone and typically those who who struggle, struggle very badly and come to believe that math is completely inaccessible to them and that they are simply 'not a math person'.
The benefit to teaching math using different strategies and models is that it allows more students to learn and it encourages all students to learn in new ways.
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)
I've never learned this method but I think it is pretty intuitive. And what my little 5 years of teaching has taught me, is that everyone's brains works differently and different methods work for different people. By teaching our kids new ways of doing math, we help them develop their own understanding of numbers. FYI the curriculum has been changed to competency based here about 10ish years ago too, because research shows that it works. Just because we learned it differently doesn't mean it is wrong.
There's a sharp learning curve right now for parents, but eventually there will be no "old way" vs "new way"...everyone will just know multiple ways. I took a class in college that required us to break down problems like kids do now, in effort to teach us how to help kids who struggle with math. (This was before schools were using the "new" way across the board. It was "saved" for helping teach kids who struggled.) It was the hardest class I took in college, simply because I had to re-wire my math thinking. I was always a math person. One more than one occasion, I wanted to stand up in class and yell "TWO PLUS TWO EQUALS FOUR BECAUSE IT JUST DOES!!! ALWAYS HAS, ALWAYS WILL! (In elementary math). I SHOULDN'T HAVE TO WRITE A FOUR PAGE PAPER PROVING IT!!!"
I think a lot of "math people" have naturally figured out many of these strategies & use them without realizing it. I know my H does! I'm always amazed at his mental math skills & then he explains how he figured it out so quickly. I look forward to my kids doing it eventually.
Someone explained it once like counting change. Ask someone to make change from $1 for any amount & they'll likely get the answer much quicker than if you asked the same question as "100-x". We naturally think in units of pennies, nickels, dimes, and quarters & are taught to make change by counting up. Same concept, different application.
This article is very long, but a very good explanation of why this transition is being made in classrooms. I found it worth the read and it gave me more reassurance about how the math curriculum is changing.
I've read everything in this thread. It makes sense in theory.
But my mental math is just fine, if not excellent, not having gone through this process.
Absolutely possible, however, not true for everybody. For many years, too many, math has either been a subject that people loved (usually because it came easily) or hated (usually because only one way was right). That time has come to an end. One way of teaching and learning math does not, and cannot, reach all learners. And math shouldn't be something that only some people can access. There are totally people who were successful using the old models and strategies, but not everyone and typically those who who struggle, struggle very badly and come to believe that math is completely inaccessible to them and that they are simply 'not a math person'.
The benefit to teaching math using different strategies and models is that it allows more students to learn and it encourages all students to learn in new ways.
I guess I remain skeptical that this method will reach "non-math" people.
Some people are good at math. Some people are bad at it. Some people are good at sports. Some people are bad at them.
It doesn't matter how much or how hard I practice kicking a soccer ball or dribbling a basketball. It doesn't matter if somebody teaches me or coaches me in a different manner. If I have no such innate ability, I'm simply not going to excel at those things.
I guess I remain skeptical that this method will reach "non-math" people.
Some people are good at math. Some people are bad at it. Some people are good at sports. Some people are bad at them.
It doesn't matter how much or how hard I practice kicking a soccer ball or dribbling a basketball. It doesn't matter if somebody teaches me or coaches me in a different manner. If I have no such innate ability, I'm simply not going to excel at those things.
I see your point. I don't necessarily think it's going to turn "non-math" people into top notch engineers or mathematicians. I do think it'll make a difference in people's attitudes towards math. It also may open new opportunities for non-math people. (My sister, a successful college graduate professional, was once denied a job at a movie rental store because she didn't pass the math portion of their test! She saw math & freaked out.)
More lessons in sports may never turn you into a professional athlete, but you would gain an appreciation for it & would be able to talk about it & follow when watching a game. They would keep you from completely throwing your hands up & saying, "I just don't GET soccer! I don't have a clue what's going on!" then walking away.
I guess I remain skeptical that this method will reach "non-math" people.
Some people are good at math. Some people are bad at it. Some people are good at sports. Some people are bad at them.
It doesn't matter how much or how hard I practice kicking a soccer ball or dribbling a basketball. It doesn't matter if somebody teaches me or coaches me in a different manner. If I have no such innate ability, I'm simply not going to excel at those things.
I see your point. I don't necessarily think it's going to turn "non-math" people into top notch engineers or mathematicians. I do think it'll make a difference in people's attitudes towards math. It also may open new opportunities for non-math people. (My sister, a successful college graduate professional, was once denied a job at a movie rental store because she didn't pass the math portion of their test! She saw math & freaked out.)
More lessons in sports may never turn you into a professional athlete, but you would gain an appreciation for it & would be able to talk about it & follow when watching a game. They would keep you from completely throwing your hands up & saying, "I just don't GET soccer! I don't have a clue what's going on!" then walking away.
But, for argument's sake, I don't have to "get" soccer. I can be good at other things. I don't need to waste my time trying to "get" soccer. I don't have to like soccer, and I don't have to be good at soccer.
But, for argument's sake, I don't have to "get" soccer. I can be good at other things. I don't need to waste my time trying to "get" soccer. I don't have to like soccer, and I don't have to be good at soccer.
Same for math for other people.
Perhaps this is too extreme a view. LOL.
Haha. Not too extreme. You can absolutely ignore soccer for the rest of your life & be fine. You can't do that with math. You can choose a different career, but most people have to do some sort of math on a regular basis (tips, passing of time/time remaining, etc). It's not always as easy as pulling out your phone & using the calculator. You have to pass math classes to get any college degree and take entrance exams. You can avoid making a living using math, but you can't completely ignore it.
The "new" way won't make a difference for people like you & me who "get" it using the old way. I hope it'll help people like my sister, though. Generally smart, but didn't get math. Not only did it significantly impact her GPA, but it made her feel stupid and affected her self-confidence. No one should have to feel that way if it can be helped. Educators are finding new ways to help.
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.
Well it IS an inefficient way to get the answer. I don't think you can argue that it's generally more efficient at a grade school level. My 2nd grader can do the math in her head or in a traditional way much faster.
However, I absolutely see value in it. There are so many adults who are all "ooh, word problems are scary" that there are internet memes about it, but because my 2nd grader's math has ALWAYS been word problems, this is just normal. And in the real world, being able to figure out your real-life word problem is what makes math useful to most of us.
I feel like, if I were bad at math, the "new" math would be even more frustrating.
But, transitioning to new curriculum assumes that students have not already learned one method. It's not like saying "You were bad with this version, let's try another one."
I have my BS in Math and work in an analytical field - I think there's a lot of value in teaching a different method.
People that say "It's easier just to subtract 316 from 427" (like the OP image) assume that a child inherently knows to line up numbers and subtract starting from the ones column. But they don't - that's taught, too. The number line allows children to see a visual and understand the "why" of what they're doing - and I see a lot of value in that.
Right. I am not saying that a kid who is bad at math the "traditional" way who then switches to this new way is going to get more frustrated. I am speculating (with zero basis, LOL) that a kid who would have otherwise encountered difficulties the old way would still have difficulties with common core.
Are there any studies showing that this is a more effective way to teach? Or a more effective way to learn?
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.
My whole life I thought I was horrible at math. And I probably still am. But my son is in first grade and I help him with his homework every night. Knowing what I know now about algebra, if I had learned math like he's learning now, I am certain it would not have been nearly as difficult for me when I got older.
Absolutely possible, however, not true for everybody. For many years, too many, math has either been a subject that people loved (usually because it came easily) or hated (usually because only one way was right). That time has come to an end. One way of teaching and learning math does not, and cannot, reach all learners. And math shouldn't be something that only some people can access. There are totally people who were successful using the old models and strategies, but not everyone and typically those who who struggle, struggle very badly and come to believe that math is completely inaccessible to them and that they are simply 'not a math person'.
The benefit to teaching math using different strategies and models is that it allows more students to learn and it encourages all students to learn in new ways.
I guess I remain skeptical that this method will reach "non-math" people.
I can see how it might. I like math, but I've always been a shape person, not a number person. Like PP said, the original image is close to how I solve math problems in my head. I visualize numbers more as "chunks" of space moving toward the number I'm trying to reach. I actually have a hard time understanding how people solve math in their heads without visualizing it physically. It's not a "work-around" because I have a hard time with numbers. It's just how my brain figures things out. If a kid has a difficult time with numbers as symbols, I can see how showing them numbers spatially can make them look at math in a way that makes a lot more sense for them.
People have always developed ways of thinking about numbers that made personal sense to them, despite the methods they were being taught. This is no different, it's just using a different kind of math intelligence as the "standard." Now it's the pure numbers kids who have to figure out the way that makes sense for them.
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
I'm only 1.4 years into school but I have never had a problem helping my son with his homework. Directions are your friend.
PLUS homework is supposed to be practice/reinforcement. They really should know what they're doing by the time they bring work home.
I feel like, if I were bad at math, the "new" math would be even more frustrating.
As a bad math person I can assure you it's not. I think it makes a lot more sense and again, bc of my experience with my son I can see it setting the building blocks for algebra later. (as an example)
And I don't like the soccer analogy. You never need to play soccer for a second in life. You need math. It's very important.
Reading this thread made me think, have you EVER heard someone say, "I'm not an English person. Never got it. Never will."
Why do you think that is? And even if that were true and there were a segment of people who said that, would you seriously be ok with it like you're ok with some people being dumb at math? I consider them both to be life skills and both to be extremely important. I'm decidedly NOT ok with settling for only teaching something one way b/c who cares if some people can't get it?
I feel like, if I were bad at math, the "new" math would be even more frustrating.
As a bad math person I can assure you it's not. I think it makes a lot more sense and again, bc of my experience with my son I can see it setting the building blocks for algebra later. (as an example)
And I don't like the soccer analogy. You never need to play soccer for a second in life. You need math. It's very important.
Reading this thread made me think, have you EVER heard someone say, "I'm not an English person. Never got it. Never will."
Why do you think that is? And even if that were true and there were a segment of people who said that, would you seriously be ok with it like you're ok with some people being dumb at math? I consider them both to be life skills and both to be extremely important. I'm decidedly NOT ok with settling for only teaching something one way b/c who cares if some people can't get it?
Sure, lots of people aren't good at language. Lots of people can't spell. Lots of people have poor reading comprehension. Lots of people can't write well.
Am I "seriously ok with [this]"?
Yeah, I am.
People can't be good at everything, and sometimes people aren't good at "life skills."
It doesn't mean that they can't lead fruitful lives.
The world is filled with dumb people, smart people, and everything in between.
I'm not advocating education "one way." I'm simply questioning why this new method has been selected to replace the old.
And, because it has been selected to replace the old, this new way is the new "one way," so I'd like to know why it is superior.
Inevitably, there will be people who do better the old way. I'd like some documentation or proof that this new way helps more people than the old way.
Otherwise, it's just a change for the sake of change without potential mass improvement of math proficiency.
miso I didn't ask if some people are bad at language or spelling. I asked if you've ever heard anyone say "I'm bad at English." Or "I'm a 'bad English' person." I realize some are better than others, but you never hear anyone say that. And I genuinely wonder why that is. It's not about ability. It's about attitude and perception. And if someone thinks they're bad at something before they've even tried it due to the methods of a previous instructor, I would say those methods should be scrutinized.
And I would argue that the world isn't filled with dumb people and smart people. Except for disabilities and often in spite of disabilities, most people have strengths and weaknesses but that doesn't mean they can't learn. However, I realize this is likely the ever optimistic educator in me speaking so I'll just say this: educators don't have the luxury to say some people are smart and some people are dumb so we won't worry about the dumb ones. We are held to a higher standard now. So we have to figure out how to reach all those "dumb" people. It's not about making them whizzes at the subject. It's about making them as successful in the subject as possible.
Now, whether these new ways of teaching mathematical concepts is a better way is another matter. It's not my content area and I haven't been in the profession for all that long. However, I am most familiar with Singapore and yes, it is my understanding that the excellence of Singaporean math scores in comparison to ours is why their method was studied and copied. A quick Google search brought up a few studies that support this. Whether it's been studied enough? EH. Probably not. I'll give you that. But I think we can agree that due to our past math performance a change was in order and copying the most successful math program in the world isn't exactly a bad idea.
And again, my understanding is that math is not being taught one way. It's being taught multiple ways (which other, more credible people, have said in this thread.)
Absolutely possible, however, not true for everybody. For many years, too many, math has either been a subject that people loved (usually because it came easily) or hated (usually because only one way was right). That time has come to an end. One way of teaching and learning math does not, and cannot, reach all learners. And math shouldn't be something that only some people can access. There are totally people who were successful using the old models and strategies, but not everyone and typically those who who struggle, struggle very badly and come to believe that math is completely inaccessible to them and that they are simply 'not a math person'.
The benefit to teaching math using different strategies and models is that it allows more students to learn and it encourages all students to learn in new ways.
I guess I remain skeptical that this method will reach "non-math" people.
Some people are good at math. Some people are bad at it. Some people are good at sports. Some people are bad at them.
It doesn't matter how much or how hard I practice kicking a soccer ball or dribbling a basketball. It doesn't matter if somebody teaches me or coaches me in a different manner. If I have no such innate ability, I'm simply not going to excel at those things.
So basically what I do every day as a math teacher is pointless? Kids are either going to get it or not?
Innate ability , while important, is not everything.
It is not okay for children to believe that they can't learn and it is definitely no longer ok for teachers to be telling students that they 'aren't math people' (them, the math teachers I mean). Students need to believe that they can learn, that they have the capacity to be mathematicians. If you have come to believe, by the age of 9 or 10, that you can't learn math, why would you try?
Jo Boaler out of Stanford speaks to the power and importance of Growth Mindset in math instruction. It speaks to the belief that all students can learn and excel in math when challenged in an appropriate way.
There is research to support reform math vs traditional math, I will have to link later because I am on my phone, but just like anything else, research can be used to both defend and criticize.
That being said, the era of the attitude that some people are 'just bad at math' needs to come to an end.
Edit: correction, Jo Boaler out of Stanford speaks to the new math instruction strategies. Carol Dweck, also of Stanford, speaks to Growth Mindset in math instruction.
I guess I remain skeptical that this method will reach "non-math" people.
Some people are good at math. Some people are bad at it. Some people are good at sports. Some people are bad at them.
It doesn't matter how much or how hard I practice kicking a soccer ball or dribbling a basketball. It doesn't matter if somebody teaches me or coaches me in a different manner. If I have no such innate ability, I'm simply not going to excel at those things.
So basically what I do every day as a math teacher is pointless? Kids are either going to get it or not?
No, not at all. Where did I say that?
Some kids will get it. Some kids won't. Is that so hard to accept?
It doesn't mean "what [you] do every day as a math teacher is pointless."
Or are you the type of person who truly believes the nonsense that people tell kids, "You can be anything you want to be as long as you work hard for it"?
I'm a realist.
Because, truly, we can't all be anything we want to be.
Post by pantsparty on Oct 20, 2014 12:14:55 GMT -5
As someone who is not good at math, I hate this system. While struggling through math, I at least took comfort in the fact if you knew the steps and followed them correctly, you would arrive at the correct answer. Adding a layer of complication, I think, would not have helped me to understand it better. It would have confused me more, because now you're taking the equation and moving it into separate parts and OMG I JUST CAN'T.
Absolutely possible, however, not true for everybody. For many years, too many, math has either been a subject that people loved (usually because it came easily) or hated (usually because only one way was right). That time has come to an end. One way of teaching and learning math does not, and cannot, reach all learners. And math shouldn't be something that only some people can access. There are totally people who were successful using the old models and strategies, but not everyone and typically those who who struggle, struggle very badly and come to believe that math is completely inaccessible to them and that they are simply 'not a math person'.
The benefit to teaching math using different strategies and models is that it allows more students to learn and it encourages all students to learn in new ways.
I guess I remain skeptical that this method will reach "non-math" people.
Some people are good at math. Some people are bad at it. Some people are good at sports. Some people are bad at them.
It doesn't matter how much or how hard I practice kicking a soccer ball or dribbling a basketball. It doesn't matter if somebody teaches me or coaches me in a different manner. If I have no such innate ability, I'm simply not going to excel at those things.
Yup. I have always been pretty competent when it comes to grammar. Spelling and sentence structure came naturally to me. I hated diagramming sentences, though. I could pick out what sounded correct, but I couldn't tell you why.