6 ms·

This Is What Common Core Looks Like

14 points by loupereira 12y ago

sp332 12y ago
Common core is not a curriculum. It is not a textbook. It is not a method of subtraction. There are badly-written textbooks both in and outside of Common Core. Edit: Here we go, Common Core math standards. Grade 2 starts on page 17. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf http://www.corestandards.org/wp-content/uploads/Math_Standar... Have a look, it's only 4 pages long. To be specific, this is a third-grade textbook. Students learn subtraction in previous grades, so this is just a quick review before moving on to third-grade topics like multiplication. Notice the problems at the bottom don't require students to use this particular method. If your third-grader can't subtract, they were already behind before you switched to Common Core. Also, is the method given really that hard to understand? It's probably not my favorite way to subtract, but it's kinda cool.
- seanflyon 12y ago
  Just to be clear "But standardized tests, the SAT, and the ACT are all moving over to Common Core. So our child has to learn this insanity." which implies that standardized tests test for this particular "counting up" subtraction method. If I understand your statement you are saying that this is not the case. Right?
  - sp332 12y ago
    Common Core standards do not include the counting-up method. So a test that only measures Common-Core compliance would not test for that.
  - AnimalMuppet 12y ago
    It's really hard for a standardized test to measure how you subtracted. (Yes, I am aware that it could be done.) But what it really measures is, can you subtract? Do you get the right answers? Personally, I don't like this approach, because to do one subtraction, you have to do four additions. That's kind of inefficient, in my view. But as sp332 pointed out, the kids should already know how to subtract numbers by this point. If a kid didn't get it before, this curriculum throws a new method at them, hoping that this one will make sense to them. I'm not sure that I have a problem with the approach (though it wouldn't hurt tweak it so as to not confuse the kids who already know how to subtract).
    - sp332 12y ago
      I doubt the count-up method was intended to be a new method. I think the new curriculum had it in the second-grade book, and assumed that former second-graders had seen it there. It's not the textbook makers' fault that the school changed between years.
blkhp19 12y ago
While I agree that one example is not enough to grasp the concept for most people, I think that the "counting up" method is actually better because it shows kids what is going on in subtraction. The borrowing method that I learned growing up doesn't make much sense. You just follow the rules with no real reason. I'm in my third year of college and only just learned why the borrowing method works - and I only learned it because I had to start subtracting numbers in different bases for my MIPS assembly class.
- seanflyon 12y ago
  Perhaps the counting up method makes it easier for most kids to grasp the underlying concepts. The borrowing method can also teach kids the underlying concepts and follows nicely from addition as it is the inverse of "carrying the 1". > You just follow the rules with no real reason. This is the real problem here. We should not teach our kids to memorize a set of rules but to understand the concepts. When I was in school I had a rule that I would not memorize rules that I did not understand or formulas that I could not derive. I would probably be faster at arithmetic if I had memorized my multiplication table like I was supposed to, but I think that rule served me well.
  - adamtj 12y ago
    When you're in 2nd or 3rd grade, it's more important to learn the mechanics of subtraction than to understand why it works. Kids at that age need to fill their brains with facts so that they have the raw materials for developing understanding when the are more mature and more able to understand. In this case, borrowing is more compact and efficient. That makes it faster and easier, both on paper and in your head. If you write out the borrowing method as verbosely as this counting-up method, it's almost as easy to understand. However, that's not important in elementary school and shouldn't be done. The counting-up method has the disadvantage that you can't write it more compactly. Students who learn the counting-up method will be hobbled in algebra: they'll be wasting their limited brainpower on the mechanics of subtracting the hard way when they could be using an easier method and devoting more brainpower to learning the concepts of algebra. Of course it's important to understand how subtraction works, but by the time you get to algebra, that should be easy. Anybody who is uncomfortable in their ignorance can either just think about it, or ask a teacher. It's not hard. Just note that 325 = 300 + 20 + 5. Then line everything up and go. That understanding isn't worth a lifetime of pain.
PaulHoule 12y ago
As a homeschooler I think Common Core is a good thing in that it tells you what you need to cover, and it means that I can choose from a lot of different curricula which include it. If you work through Kahn Academy math, you will certainly run through some of these areas where kids are pushed to do some kind of math problem in a highly stylized way that (i) they struggle with and (ii) don't see the relevance of. Elementary school teachers have told me the same thing, but it is not the end of the world. There is "no one true way" to do arithmetic. When I was in the fourth grade I had the worst time with 3-by-3 digit multiplication. That didn't stop me from getting a B.S. in Physics and Math, with an A average in my majors, and also getting a PhD in theoretical physics. Recently I read that a lot of other people who were "good at math" struggled with the curriculum when I was a kid so nothing is going to be perfect.
jeff303 12y ago
This is what one implementation of Common Core looks like
mturmon 12y ago
This seems like generated outrage. The OP should take a minute to think about how the method of subtraction works, and then explain it to his kid. I associate this panic reaction (OP: "this new method makes no freaking sense") with people who are math-phobic. The solution is to just settle down and think about it. (Common core, third grade objectives, number 1: "Make sense of problems and persevere in solving them.") And, one thing I've learned about elementary educators is that they don't want to fight with parents. (Unsurprising!) So if you say (like OP did), "This common core math sucks," they are going to say, "yes, we don't like it either." If you said it was an interesting way to do subtraction, they'd agree with that too.
cafard 12y ago
Back in the days before computerized cash registers, this was typically how cashiers made change. Hand one $5 for a $1.34 purchase, and the cashier counts it back out as (penny) $1.35 (nickel) $1.50 (quarters) $1.75, $2 (dollar bills) $3, $4, $5 Some still do it that way. In Teacher in America, chapter "Let x Equal ...", Jacques Barzun mentioned as an example of widespread innumeracy the half-trained cashiers who did not know this technique. That was written in the early 1940s.
- mturmon 12y ago
  This is a nice observation. I remember being given change-making assignments in school, and being unable to complete them because I was not sure that the greedy algorithm (http://en.wikipedia.org/wiki/Change-making_problem#Greedy_method http://en.wikipedia.org/wiki/Change-making_problem#Greedy_me...) would always give the optimal result. I was not able to articulate the reason for my uneasiness until years after I had failed to complete the work.
- wahern 12y ago
  It's actually a very useful method for quickly finding the difference between two numbers. And I would think that any computer programmer would appreciate the algorithm. The algorithm is a classic divide-and-conquer technique that is perfect for quickly performing arithmetic in ones head. And it would also be a good entre into teaching things like associativity and commutativity. I use something similar to avoid getting too much change at a cashier, and to use up loose change (pennies, nickels, etc), except I usually count down and add in the difference. So, for example, if some bubble gum cost $1.28, I might give the cashier $2.03. Then, assuming the bewildered cashier doesn't try to give me the pennies back, I get three quarters for laundry, instead of two quarters, two dimes, and two pennies. If I don't need laundry change, I'll count up or down searching for the amount that will maximally reduce the number of coins in my pocket (without avoiding bills, which would just be annoying to everybody). With practice you can do this in a split second, and it really blows the mind of some cashiers. Isaac Asimov said something to the effect that smart people will tend to figure out these algorithms on their own. So it's kind of ironic that now somebody is complaining that it's being taught to kids. I suppose the only real legitimate criticism here is that, according to the link, there's only one example of this method, and then it's never mentioned again. If anything, it should be expounded upon.
holychiz 12y ago
I'll echo the comment that Common Core is not a textbook nor a particular way to add/subtract. It's a standard to establish baseline knowledge US kids must master. That blog post is raging about a new way to do subtract which seems to be out of reach for his comprehension, can't teach an old dog kindda thing, so he blames it on Common Core. He also mentioned that there are 4 new ways to do subtraction. This should be good news. Kids/people learns to do things differently. 4 different ways means kids have more arsenals to tackle their problems. I wish I had that learning opportunity! Specifically about that subtraction, did you noticed that it'd make it easier to do the math in your head? maybe there is a reason for the madness after all.
DanBC 12y ago
> They cannot help their children. The math makes no sense and seems to offer no practical purpose other than it is new. First of all parents were not able to help their children with old methods either. Give someone a pen and paper and ask them how to add 17% to 58. You don't want an answer - just a working method. A lot of people can't do this on paper, but that's okay because we have computers to do that stuff. Lots of people can't add 17% to 58 using a computer. I find that a bit scary. Going on to the example: I'm pretty stupid; I've often said that I am hopeless at math. I found that single example really easy to understand. I've not had any exposure to similar examples. I don't believe the author is actually baffled by the example. Perhaps a book might help? http://www.robeastaway.com/books/maths-for-mums-and-dads http://www.robeastaway.com/books/maths-for-mums-and-dads > What on earth are number bonds? What are partitioning and chunking? And why does my child look blank - or have a tantrum - when I demonstrate long multiplication? This book is for mums, dads and grandparents who want to help their primary school children or grandchildren with maths. To do so, many parents find they need to overcome their own rustiness and also to learn the strange new methods and terminology. Throughout the book are games, puzzles and examples of amusing ways in which kids ingeniously 'get it wrong'.
deleted 12y ago
[deleted]
jdanner 12y ago
Common Core is just fine as a set of standards and has a good shot at being adopted around the world, so we need to get over it. Common Core is going to lead to a lot more innovative solutions, because the market of students on it will be large. It's very nice from a computer science standpoint as well. Check out the game we built at Zeal. While it's a nice simple game on the surface, behind the scenes we are maintaining a complete map of everything every child has mastered in Common Core Math and Literacy K-8, which lets us figure out an ordering of skills to learn and what to do if a child is struggling on a given skill. This is the kind of thing that has been solved in every other industry, but Common Core enables in education.
daltonlp 12y ago
The first two paragraphs illustrate a huge problem with US math education, which pre-dates common core, but is reinforced by it. That problem is the false belief that numeracy is improved by learning different ways of looking at number operations. (i.e. four ways to subtract). Our child's second-grade teacher (a very good teacher) has a poster illustrating 7 ways to subtract. Seven ways, no exaggeration. This poster is older than common core. Students learn math just like they learn to kick a ball. By practicing. Learn one way to subtract, and practice it really really well. Or learn two ways, and practice each way really, really well. Learn more ways if you want, but practice each way really really well. Most math curriculums assume that learning multiple ways is equivalent to (or better than) practicing one way. They don't require the repetitive practice. As comments have pointed out, the common core standards don't explicitly require this multi-way approach. But the CC standards compound the problem by requiring students to explain concepts in order to demonstrate mastery. Completing lots of subtraction problems with a low rate of error doesn't count. You must explain, in order to understand. And if you really understand, shouldn't you be able to explain different approaches? I would say no. Or at least, not yet. I don't want a third-grader explaining how to subtract unless they can also finish 50 subtraction problems in a row without pausing to struggle. And if they get the problems right? Good job, you get an A. Wonderful, let's skip grading the explanation because that is subjective as hell. TL/DR: The article rightly points out a crap way to teach math. Common core is not totally to blame, but it makes a bad problem worse.
- DanBC 12y ago
  Children learn by getting things wrong. A child doing the sum and getting the wrong answer may be learning as much as a child doing the sum and getting the right answer. http://www.bbc.co.uk/programmes/b04dwbkt http://www.bbc.co.uk/programmes/b04dwbkt Most relevant is probably this one: http://www.bbc.co.uk/programmes/b04gw6rh http://www.bbc.co.uk/programmes/b04gw6rh
  - daltonlp 12y ago
    Yes exactly. That's the reason so much practice is necessary. When you learn subtraction, you need to see lots and lots of number combinations, many of which you'll initially get wrong, but soon learn to do correctly, then recognize instantly, and finally use as building blocks.
warmfuzzykitten 12y ago
Perhaps more disturbing than the author's inability to understand a simple procedure in a third-grade math text is his attempt to cast Common Core as part of an overarching conspiracy of corporations and (of course) government to turn our little ones into docile robots. This is what a nut case looks like.
hyperair 12y ago
I wouldn't fault Common Core. I'd fault the textbook. That little page on counting-up subtraction didn't make sense to me either, so I went to Wikipedia, read this shorter snippet[1], and understood it immediately. That textbook's just crappy. [1] https://en.wikipedia.org/wiki/Subtraction#Counting_up https://en.wikipedia.org/wiki/Subtraction#Counting_up

14 points by loupereira 12y ago

sp332 12y ago

Common core is not a curriculum. It is not a textbook. It is not a method of subtraction. There are badly-written textbooks both in and outside of Common Core. Edit: Here we go, Common Core math standards. Grade 2 starts on page 17. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf http://www.corestandards.org/wp-content/uploads/Math_Standar... Have a look, it's only 4 pages long. To be specific, this is a third-grade textbook. Students learn subtraction in previous grades, so this is just a quick review before moving on to third-grade topics like multiplication. Notice the problems at the bottom don't require students to use this particular method. If your third-grader can't subtract, they were already behind before you switched to Common Core. Also, is the method given really that hard to understand? It's probably not my favorite way to subtract, but it's kinda cool.

seanflyon 12y ago
Just to be clear "But standardized tests, the SAT, and the ACT are all moving over to Common Core. So our child has to learn this insanity." which implies that standardized tests test for this particular "counting up" subtraction method. If I understand your statement you are saying that this is not the case. Right?
- sp332 12y ago
  Common Core standards do not include the counting-up method. So a test that only measures Common-Core compliance would not test for that.
- AnimalMuppet 12y ago
  It's really hard for a standardized test to measure how you subtracted. (Yes, I am aware that it could be done.) But what it really measures is, can you subtract? Do you get the right answers? Personally, I don't like this approach, because to do one subtraction, you have to do four additions. That's kind of inefficient, in my view. But as sp332 pointed out, the kids should already know how to subtract numbers by this point. If a kid didn't get it before, this curriculum throws a new method at them, hoping that this one will make sense to them. I'm not sure that I have a problem with the approach (though it wouldn't hurt tweak it so as to not confuse the kids who already know how to subtract).
  - sp332 12y ago
    I doubt the count-up method was intended to be a new method. I think the new curriculum had it in the second-grade book, and assumed that former second-graders had seen it there. It's not the textbook makers' fault that the school changed between years.

blkhp19 12y ago

While I agree that one example is not enough to grasp the concept for most people, I think that the "counting up" method is actually better because it shows kids what is going on in subtraction. The borrowing method that I learned growing up doesn't make much sense. You just follow the rules with no real reason. I'm in my third year of college and only just learned why the borrowing method works - and I only learned it because I had to start subtracting numbers in different bases for my MIPS assembly class.

seanflyon 12y ago
Perhaps the counting up method makes it easier for most kids to grasp the underlying concepts. The borrowing method can also teach kids the underlying concepts and follows nicely from addition as it is the inverse of "carrying the 1". > You just follow the rules with no real reason. This is the real problem here. We should not teach our kids to memorize a set of rules but to understand the concepts. When I was in school I had a rule that I would not memorize rules that I did not understand or formulas that I could not derive. I would probably be faster at arithmetic if I had memorized my multiplication table like I was supposed to, but I think that rule served me well.
- adamtj 12y ago
  When you're in 2nd or 3rd grade, it's more important to learn the mechanics of subtraction than to understand why it works. Kids at that age need to fill their brains with facts so that they have the raw materials for developing understanding when the are more mature and more able to understand. In this case, borrowing is more compact and efficient. That makes it faster and easier, both on paper and in your head. If you write out the borrowing method as verbosely as this counting-up method, it's almost as easy to understand. However, that's not important in elementary school and shouldn't be done. The counting-up method has the disadvantage that you can't write it more compactly. Students who learn the counting-up method will be hobbled in algebra: they'll be wasting their limited brainpower on the mechanics of subtracting the hard way when they could be using an easier method and devoting more brainpower to learning the concepts of algebra. Of course it's important to understand how subtraction works, but by the time you get to algebra, that should be easy. Anybody who is uncomfortable in their ignorance can either just think about it, or ask a teacher. It's not hard. Just note that 325 = 300 + 20 + 5. Then line everything up and go. That understanding isn't worth a lifetime of pain.

PaulHoule 12y ago

As a homeschooler I think Common Core is a good thing in that it tells you what you need to cover, and it means that I can choose from a lot of different curricula which include it. If you work through Kahn Academy math, you will certainly run through some of these areas where kids are pushed to do some kind of math problem in a highly stylized way that (i) they struggle with and (ii) don't see the relevance of. Elementary school teachers have told me the same thing, but it is not the end of the world. There is "no one true way" to do arithmetic. When I was in the fourth grade I had the worst time with 3-by-3 digit multiplication. That didn't stop me from getting a B.S. in Physics and Math, with an A average in my majors, and also getting a PhD in theoretical physics. Recently I read that a lot of other people who were "good at math" struggled with the curriculum when I was a kid so nothing is going to be perfect.

jeff303 12y ago

This is what one implementation of Common Core looks like

mturmon 12y ago

This seems like generated outrage. The OP should take a minute to think about how the method of subtraction works, and then explain it to his kid. I associate this panic reaction (OP: "this new method makes no freaking sense") with people who are math-phobic. The solution is to just settle down and think about it. (Common core, third grade objectives, number 1: "Make sense of problems and persevere in solving them.") And, one thing I've learned about elementary educators is that they don't want to fight with parents. (Unsurprising!) So if you say (like OP did), "This common core math sucks," they are going to say, "yes, we don't like it either." If you said it was an interesting way to do subtraction, they'd agree with that too.

cafard 12y ago

Back in the days before computerized cash registers, this was typically how cashiers made change. Hand one $5 for a $1.34 purchase, and the cashier counts it back out as (penny) $1.35 (nickel) $1.50 (quarters) $1.75, $2 (dollar bills) $3, $4, $5 Some still do it that way. In Teacher in America, chapter "Let x Equal ...", Jacques Barzun mentioned as an example of widespread innumeracy the half-trained cashiers who did not know this technique. That was written in the early 1940s.

mturmon 12y ago
This is a nice observation. I remember being given change-making assignments in school, and being unable to complete them because I was not sure that the greedy algorithm (http://en.wikipedia.org/wiki/Change-making_problem#Greedy_method http://en.wikipedia.org/wiki/Change-making_problem#Greedy_me...) would always give the optimal result. I was not able to articulate the reason for my uneasiness until years after I had failed to complete the work.
wahern 12y ago
It's actually a very useful method for quickly finding the difference between two numbers. And I would think that any computer programmer would appreciate the algorithm. The algorithm is a classic divide-and-conquer technique that is perfect for quickly performing arithmetic in ones head. And it would also be a good entre into teaching things like associativity and commutativity. I use something similar to avoid getting too much change at a cashier, and to use up loose change (pennies, nickels, etc), except I usually count down and add in the difference. So, for example, if some bubble gum cost $1.28, I might give the cashier $2.03. Then, assuming the bewildered cashier doesn't try to give me the pennies back, I get three quarters for laundry, instead of two quarters, two dimes, and two pennies. If I don't need laundry change, I'll count up or down searching for the amount that will maximally reduce the number of coins in my pocket (without avoiding bills, which would just be annoying to everybody). With practice you can do this in a split second, and it really blows the mind of some cashiers. Isaac Asimov said something to the effect that smart people will tend to figure out these algorithms on their own. So it's kind of ironic that now somebody is complaining that it's being taught to kids. I suppose the only real legitimate criticism here is that, according to the link, there's only one example of this method, and then it's never mentioned again. If anything, it should be expounded upon.

holychiz 12y ago

I'll echo the comment that Common Core is not a textbook nor a particular way to add/subtract. It's a standard to establish baseline knowledge US kids must master. That blog post is raging about a new way to do subtract which seems to be out of reach for his comprehension, can't teach an old dog kindda thing, so he blames it on Common Core. He also mentioned that there are 4 new ways to do subtraction. This should be good news. Kids/people learns to do things differently. 4 different ways means kids have more arsenals to tackle their problems. I wish I had that learning opportunity! Specifically about that subtraction, did you noticed that it'd make it easier to do the math in your head? maybe there is a reason for the madness after all.

DanBC 12y ago

> They cannot help their children. The math makes no sense and seems to offer no practical purpose other than it is new. First of all parents were not able to help their children with old methods either. Give someone a pen and paper and ask them how to add 17% to 58. You don't want an answer - just a working method. A lot of people can't do this on paper, but that's okay because we have computers to do that stuff. Lots of people can't add 17% to 58 using a computer. I find that a bit scary. Going on to the example: I'm pretty stupid; I've often said that I am hopeless at math. I found that single example really easy to understand. I've not had any exposure to similar examples. I don't believe the author is actually baffled by the example. Perhaps a book might help? http://www.robeastaway.com/books/maths-for-mums-and-dads http://www.robeastaway.com/books/maths-for-mums-and-dads > What on earth are number bonds? What are partitioning and chunking? And why does my child look blank - or have a tantrum - when I demonstrate long multiplication? This book is for mums, dads and grandparents who want to help their primary school children or grandchildren with maths. To do so, many parents find they need to overcome their own rustiness and also to learn the strange new methods and terminology. Throughout the book are games, puzzles and examples of amusing ways in which kids ingeniously 'get it wrong'.

deleted 12y ago

[deleted]

jdanner 12y ago

Common Core is just fine as a set of standards and has a good shot at being adopted around the world, so we need to get over it. Common Core is going to lead to a lot more innovative solutions, because the market of students on it will be large. It's very nice from a computer science standpoint as well. Check out the game we built at Zeal. While it's a nice simple game on the surface, behind the scenes we are maintaining a complete map of everything every child has mastered in Common Core Math and Literacy K-8, which lets us figure out an ordering of skills to learn and what to do if a child is struggling on a given skill. This is the kind of thing that has been solved in every other industry, but Common Core enables in education.

daltonlp 12y ago

The first two paragraphs illustrate a huge problem with US math education, which pre-dates common core, but is reinforced by it. That problem is the false belief that numeracy is improved by learning different ways of looking at number operations. (i.e. four ways to subtract). Our child's second-grade teacher (a very good teacher) has a poster illustrating 7 ways to subtract. Seven ways, no exaggeration. This poster is older than common core. Students learn math just like they learn to kick a ball. By practicing. Learn one way to subtract, and practice it really really well. Or learn two ways, and practice each way really, really well. Learn more ways if you want, but practice each way really really well. Most math curriculums assume that learning multiple ways is equivalent to (or better than) practicing one way. They don't require the repetitive practice. As comments have pointed out, the common core standards don't explicitly require this multi-way approach. But the CC standards compound the problem by requiring students to explain concepts in order to demonstrate mastery. Completing lots of subtraction problems with a low rate of error doesn't count. You must explain, in order to understand. And if you really understand, shouldn't you be able to explain different approaches? I would say no. Or at least, not yet. I don't want a third-grader explaining how to subtract unless they can also finish 50 subtraction problems in a row without pausing to struggle. And if they get the problems right? Good job, you get an A. Wonderful, let's skip grading the explanation because that is subjective as hell. TL/DR: The article rightly points out a crap way to teach math. Common core is not totally to blame, but it makes a bad problem worse.

DanBC 12y ago
Children learn by getting things wrong. A child doing the sum and getting the wrong answer may be learning as much as a child doing the sum and getting the right answer. http://www.bbc.co.uk/programmes/b04dwbkt http://www.bbc.co.uk/programmes/b04dwbkt Most relevant is probably this one: http://www.bbc.co.uk/programmes/b04gw6rh http://www.bbc.co.uk/programmes/b04gw6rh
- daltonlp 12y ago
  Yes exactly. That's the reason so much practice is necessary. When you learn subtraction, you need to see lots and lots of number combinations, many of which you'll initially get wrong, but soon learn to do correctly, then recognize instantly, and finally use as building blocks.

warmfuzzykitten 12y ago

Perhaps more disturbing than the author's inability to understand a simple procedure in a third-grade math text is his attempt to cast Common Core as part of an overarching conspiracy of corporations and (of course) government to turn our little ones into docile robots. This is what a nut case looks like.

hyperair 12y ago

I wouldn't fault Common Core. I'd fault the textbook. That little page on counting-up subtraction didn't make sense to me either, so I went to Wikipedia, read this shorter snippet[1], and understood it immediately. That textbook's just crappy. [1] https://en.wikipedia.org/wiki/Subtraction#Counting_up https://en.wikipedia.org/wiki/Subtraction#Counting_up