Fabulous Parental Response!
Most ridiculous #ccss nonsense. Created more confusion and explosion with Math Calculation Errors. Too convoluted, too many steps, yielding errors. My biggest dear is a generation of Math Illiterate children & adults. Who in H—- came up with this CRAPOLA?
More parents need 2 expose this instead of attending parental tutorials in their kids’ schools. Making sense out of nonsense is nonsense!
Yeah! Speak up for our kids. One chance 2 learn it.

I suspect that this is meant to be a mental math activity, one that teaches kids to carry out an algorithm for doing such subtraction in his or her head.

Or the authors might have had in mind the Common Core principle of teaching kids various algorithms for each operation in the hopes that they will generalize a deeper understanding of the algorithm (which, of course, very young kids will NOT do, so the CC$$ premise, there, is stupid; it will work for some alternative algorithms and not for others).

If what they had in mind, however, was teaching kids this procedure for the purpose of doing mental math, the algorithm being employed is worth teaching, but only for that purpose.

That said, I agree that this particular activity is terrible. If the purpose is to teach an algorithm for doing subtraction in one’s head, then the kid should not be doing it on paper. And, if the kid is learning how to do carry out this algorithm for mental math purposes, then modeling an error in the already difficult (for a kid) algorithm just for the sake of an exercise is quite confusing. The algorithm being taught (not the standard algorithm, as this parent rightly says) is confusing enough already to the kid trying to learn it, and modeling the error runs the risk of adding to the child’s confusion about what the correct alternative algorithm might be.

my take is that this “problem” is NOT about learning how to subtract, it is about problem solving/critical thinking… uhhh, therein lies the source of jack’s problem… he didnt jump in the “ones” enough times: he only jumped 5 times beyond the 10’s jump, so needed to jump once more in the one’s jump… that gets you to 111!! so, the goal here is the puzzle/problem to solve, NOT the learning of subtraction; i would agree tho, IF the goal is to learn subtraction, then this OBVIOUSLY is not the way to do that!

correction: Or the authors might have had in mind the Common Core principle of teaching kids various algorithms for each operation in the hopes that they will generalize a deeper understanding of the OPERATION

This teaches kids nothing. Do any of us use a number line in our heads to do subtraction, or a number line on paper? I line up the numbers in my head, just like this father did on paper and do the math. I find much of what I see on the CCSS worksheets to be over complicating very simple procedures. I didn’t do well it math as it was as a kid, I’d have gone home in tears every day over what the kids in my school have to do now. I wonder what grade this paper is from, I’d have to guess about 3rd from the looks of it, though knowing CCSS it’s 1st!

As near as I can tell, the Common Core approach is to take examples of what mentally flexible people have done in the past, to solve a problem in mathematics or the reading of complex texts. Then the teacher is supposed to teach the strategies, instead of allowing students to find their own, which would have encouraged them to develop mental flexibility of their own. I have done this kind of number line problems with Second Graders. It confuses the hell out of them, and since I’m always on a deadline to get the lesson done, I usually end up simplifying the hell out of it. Common Core? Bah. As the old New Yorker cartoon put it, I say it’s spinach, and I say to hell with it.

Thank you for “simplifying” it — my fifth grader brings home her CC “bs” worksheets and I figure them out, teach her, and she goes back to school the next day and shows the teacher. Invariably, it is “trying to make something simple seem complicated”. I have been fighting my whole math-teacher life to make math MORE TRANSPARENT, not less so!

Let me disagree. If you can get a kid to do a problem like this, it is because they like you. That will only go so far and last so long. If you have some time to spend with this (in this case imaginary) kid, it would be better to spend that time helping them understand place value (the understanding behind the regular algorithm). The (literally unlimited) number of algorithms one could develop to solve such problems using drawn out number lines do not do anything to advance a cause of understanding math, and there is no reason for anyone to spend their time in this way, and it would be an unlikely person that would want to. Advance the understandings of place value and estimations — beyond that, it’s a time-waster. Technology is here to stay, and life is too short to spend just goofing around with arithmetic.

That’s all fine. You explained how teaching children a number line task – number line subtraction technique – might be done. And asking them to show proficiency at number line subtraction could be reasonable. But here is the implicit argument that people who are freaking out to a greater or lesser degree over these examples are making — that children should learn the basic technique of subtraction, and these alternate methods can be an as-needed add-on. They shouldn’t be the preferred or required method.

Good teaching involves having several tools and techniques in your pocket. Many children can quickly learn the basic techniques of subtraction and apply the tool to multiple situations. Others will need ‘mental tricks’ or visual strategies like number lines, or manipulatives, to ‘get it”. Some will need a lot of work – every tool in the box, plus some unique ones. That’s Good Teaching!

What these approaches that are getting passed around on Facebook, etc., seem to many to do – is force all children to learn a rather idiosyncratic approach, when 427-316=111 will work for many. Is it forcing a child to use a tool they don’t need and may confuse them? I’m not saying throw out the number line method — just use it as needed.

The idea of trying to figure out where someone else got something wrong isn’t the worst idea in the world. However, what Jack was allegedly doing would need to be done in the head, because this method is so unweildy if written out — as many people have pointed out. Also, if that was a carefully printed out number line, then I hope the problem is entirely imaginary, because unless we are teaching about logarithmic plots, then mathematicians take care to make sure that scales are linear (meaning that the distance from 100 to 200 equals the distance from 0 to 100, which are each exactly ten times the distance from 90 to 80 or from 57 to 67.)

As a mental exercise, number lines like this are not an entirely useless method.

Nobody seems to have pointed out that Jack made two math errors, not just one.

Since this problem asks 427-316, if you are doing this in your head, you could either count backwards from 4 by 3 units, or ask yourself how far it is from 3 to 4 — obviously 1. Writing the number line out is a lot of work, but saying silently to yourself, “427, 327, 127” isn’t much work. So far so good.

But it’s not only in the mathematics that the imaginary Jack made an error:

I’m not sure, but it seems like the problem writer wanted Jack to confuse 16 and 60. This is not hard to do when HEARING the number, but more difficult if you are SEEING it written out. So this makes the problem a bit more, well, problematic, because nowhere in the problem is there any hint that Jack tends to hear poorly.

So this imaginary Jack misakenly counts backwards in the tens place by tens by going 127, 107, 97, 87, 77, 67, 57 — which appears to be his final answer. Maybe. I can’t quite tell on this sheet.

So that means that “Jack” made another error in leaving out the decade 117.

Since it looks like this problem was written by some low-paid contract worker (think of “call centers” in Malaysia or India) with little scrutiny afterwards, we don’t know if the intention of the problem writer was for the student to realize that Jack is both hard of hearing and mis-counted by skipping the 117?

Sounds like an error on the part of the error-writer, but I could be wrong.

The most interesting part of this write up, is that you interpreted it incorrectly, yet you tried to blame it on the parent. Even you and your math colleagues couldn’t get it correct the first time. So how can you attempt to say it’s ok for middle school aged children, when you are having problems with it?

You are just wrong here — this is EXACTLY the sort of thing Common Core requires elementary school students to do — I would say “suffer through”. We’re creating a generation of kids who hate math even more . . . . read the standards — they are VERY prescriptive — tell you exactly what kids have to be able to do, and this example is very much “common core”. Now, with that said, someone not in common core could choose to use it too, I guess, but I (as a person with advanced degrees in math and over 30 years of math teaching experience) have certainly seen huge numbers of successful math students and none of them, including myself, were taught this way — lucky us! If you have Common Core in your school, this is the kind of crazy bs you must use with your students.

Regarding Michael Goldberg’s comment to the effect that I am “closed minded” to the new math and that I refuse to “engage” in discussion about the issue:

I have tried to tell him that I consider this “new math” to be “the long way home,” and that if teachers want to choose it, that’s fine, but that I don’t like the idea of teachers’ being required to use it– the rigid, no-options signature route that is CCSS.

If Goldberg likes his math this way, fine. However, teachers (and parents) across the US are being forced to ditch traditional calculation in favor of this alternative way. It’s the “forcing” that I find to be the overriding problem.

Goldberg wants to talk me into his position. It isn’t going to happen.

Some believe that requiring young children to “explain
and illustrate” math concepts is fine. I think it is developmentally inappropriate.

Then there is the coup of having companies sell “CCSS-aligned”
curriculum that requires students to complete assignments like
the one in the example in Guy’s post.

If there were no CCSS, we would not have these same frustrating
math examples popping up across the US right now.

Yes. Michael, students, parents, and teachers are frustrated with being forced to complete math the way one is required to complete it in the example above.

“Forced” is the word: The corporate reformers’ goal is to align (and mandate) all: CCSS, curriculum, and tests.

And NGA/CCSSO are now debating how they might “approve”
the CCSS curriculum since they are the CCSS copyright holders. Stay tuned for more on that front.

I don’t know about you, but I was most certainly forced to answer math questions in one way growing up. I never learned the lattice method of multiplication until well into my teaching career. I was never shown the geometric properties of the pythagorean theorem, again, until much later in life. Fraction multiplication was “do this and then this and then you get the right answer”…I was a great rule follower….until I hit Math analysis and calculus and suddenly those proofs actually were supposed to mean something, and I was lost (I had done really well in geometry class, I memorized every proof there was). Why do so many adults still readily admit to having been bad at math, to still being bad at math, to having made college and career choices based on how much (or how little) math was required? CCSS and NCLB did not change that. Don’t get me wrong, I am an adamant anti-CC person, but see these kinds of arguments about how to teach math as being out of place.The “math wars” are still alive and kicking, and once CCSS are dead and buried, I would love to get into this more. We can argue that the rushed implementation of CCSS has led to a whole host of problems on worksheets, but to talk math pedagogy as CCSS or not, doesn’t make sense to me. Again, the “math wars” were around before NCLB or CCSS and will be around long after.

Fabulous Parental Response!

Most ridiculous #ccss nonsense. Created more confusion and explosion with Math Calculation Errors. Too convoluted, too many steps, yielding errors. My biggest dear is a generation of Math Illiterate children & adults. Who in H—- came up with this CRAPOLA?

More parents need 2 expose this instead of attending parental tutorials in their kids’ schools. Making sense out of nonsense is nonsense!

Yeah! Speak up for our kids. One chance 2 learn it.

I suspect that this is meant to be a mental math activity, one that teaches kids to carry out an algorithm for doing such subtraction in his or her head.

Or the authors might have had in mind the Common Core principle of teaching kids various algorithms for each operation in the hopes that they will generalize a deeper understanding of the algorithm (which, of course, very young kids will NOT do, so the CC$$ premise, there, is stupid; it will work for some alternative algorithms and not for others).

If what they had in mind, however, was teaching kids this procedure for the purpose of doing mental math, the algorithm being employed is worth teaching, but only for that purpose.

That said, I agree that this particular activity is terrible. If the purpose is to teach an algorithm for doing subtraction in one’s head, then the kid should not be doing it on paper. And, if the kid is learning how to do carry out this algorithm for mental math purposes, then modeling an error in the already difficult (for a kid) algorithm just for the sake of an exercise is quite confusing. The algorithm being taught (not the standard algorithm, as this parent rightly says) is confusing enough already to the kid trying to learn it, and modeling the error runs the risk of adding to the child’s confusion about what the correct alternative algorithm might be.

my take is that this “problem” is NOT about learning how to subtract, it is about problem solving/critical thinking… uhhh, therein lies the source of jack’s problem… he didnt jump in the “ones” enough times: he only jumped 5 times beyond the 10’s jump, so needed to jump once more in the one’s jump… that gets you to 111!! so, the goal here is the puzzle/problem to solve, NOT the learning of subtraction; i would agree tho, IF the goal is to learn subtraction, then this OBVIOUSLY is not the way to do that!

correction: Or the authors might have had in mind the Common Core principle of teaching kids various algorithms for each operation in the hopes that they will generalize a deeper understanding of the OPERATION

This teaches kids nothing. Do any of us use a number line in our heads to do subtraction, or a number line on paper? I line up the numbers in my head, just like this father did on paper and do the math. I find much of what I see on the CCSS worksheets to be over complicating very simple procedures. I didn’t do well it math as it was as a kid, I’d have gone home in tears every day over what the kids in my school have to do now. I wonder what grade this paper is from, I’d have to guess about 3rd from the looks of it, though knowing CCSS it’s 1st!

As near as I can tell, the Common Core approach is to take examples of what mentally flexible people have done in the past, to solve a problem in mathematics or the reading of complex texts. Then the teacher is supposed to teach the strategies, instead of allowing students to find their own, which would have encouraged them to develop mental flexibility of their own. I have done this kind of number line problems with Second Graders. It confuses the hell out of them, and since I’m always on a deadline to get the lesson done, I usually end up simplifying the hell out of it. Common Core? Bah. As the old New Yorker cartoon put it, I say it’s spinach, and I say to hell with it.

Thank you for “simplifying” it — my fifth grader brings home her CC “bs” worksheets and I figure them out, teach her, and she goes back to school the next day and shows the teacher. Invariably, it is “trying to make something simple seem complicated”. I have been fighting my whole math-teacher life to make math MORE TRANSPARENT, not less so!

Please read my reply to this image at relearningtoteach.blogspot.com

It’s actually a good task and a good way of helping kids understand the math behind the algorithms. See here for an excellent explanation of the process: http://storify.com/mylifeasprose/common-core-math-this-is-how-it-works.

Let me disagree. If you can get a kid to do a problem like this, it is because they like you. That will only go so far and last so long. If you have some time to spend with this (in this case imaginary) kid, it would be better to spend that time helping them understand place value (the understanding behind the regular algorithm). The (literally unlimited) number of algorithms one could develop to solve such problems using drawn out number lines do not do anything to advance a cause of understanding math, and there is no reason for anyone to spend their time in this way, and it would be an unlikely person that would want to. Advance the understandings of place value and estimations — beyond that, it’s a time-waster. Technology is here to stay, and life is too short to spend just goofing around with arithmetic.

That’s all fine. You explained how teaching children a number line task – number line subtraction technique – might be done. And asking them to show proficiency at number line subtraction could be reasonable. But here is the implicit argument that people who are freaking out to a greater or lesser degree over these examples are making — that children should learn the basic technique of subtraction, and these alternate methods can be an as-needed add-on. They shouldn’t be the preferred or required method.

Good teaching involves having several tools and techniques in your pocket. Many children can quickly learn the basic techniques of subtraction and apply the tool to multiple situations. Others will need ‘mental tricks’ or visual strategies like number lines, or manipulatives, to ‘get it”. Some will need a lot of work – every tool in the box, plus some unique ones. That’s Good Teaching!

What these approaches that are getting passed around on Facebook, etc., seem to many to do – is force all children to learn a rather idiosyncratic approach, when 427-316=111 will work for many. Is it forcing a child to use a tool they don’t need and may confuse them? I’m not saying throw out the number line method — just use it as needed.

The idea of trying to figure out where someone else got something wrong isn’t the worst idea in the world. However, what Jack was allegedly doing would need to be done in the head, because this method is so unweildy if written out — as many people have pointed out. Also, if that was a carefully printed out number line, then I hope the problem is entirely imaginary, because unless we are teaching about logarithmic plots, then mathematicians take care to make sure that scales are linear (meaning that the distance from 100 to 200 equals the distance from 0 to 100, which are each exactly ten times the distance from 90 to 80 or from 57 to 67.)

As a mental exercise, number lines like this are not an entirely useless method.

Nobody seems to have pointed out that Jack made two math errors, not just one.

Since this problem asks 427-316, if you are doing this in your head, you could either count backwards from 4 by 3 units, or ask yourself how far it is from 3 to 4 — obviously 1. Writing the number line out is a lot of work, but saying silently to yourself, “427, 327, 127” isn’t much work. So far so good.

But it’s not only in the mathematics that the imaginary Jack made an error:

I’m not sure, but it seems like the problem writer wanted Jack to confuse 16 and 60. This is not hard to do when HEARING the number, but more difficult if you are SEEING it written out. So this makes the problem a bit more, well, problematic, because nowhere in the problem is there any hint that Jack tends to hear poorly.

So this imaginary Jack misakenly counts backwards in the tens place by tens by going 127, 107, 97, 87, 77, 67, 57 — which appears to be his final answer. Maybe. I can’t quite tell on this sheet.

So that means that “Jack” made another error in leaving out the decade 117.

Since it looks like this problem was written by some low-paid contract worker (think of “call centers” in Malaysia or India) with little scrutiny afterwards, we don’t know if the intention of the problem writer was for the student to realize that Jack is both hard of hearing and mis-counted by skipping the 117?

Sounds like an error on the part of the error-writer, but I could be wrong.

The most interesting part of this write up, is that you interpreted it incorrectly, yet you tried to blame it on the parent. Even you and your math colleagues couldn’t get it correct the first time. So how can you attempt to say it’s ok for middle school aged children, when you are having problems with it?

You are just wrong here — this is EXACTLY the sort of thing Common Core requires elementary school students to do — I would say “suffer through”. We’re creating a generation of kids who hate math even more . . . . read the standards — they are VERY prescriptive — tell you exactly what kids have to be able to do, and this example is very much “common core”. Now, with that said, someone not in common core could choose to use it too, I guess, but I (as a person with advanced degrees in math and over 30 years of math teaching experience) have certainly seen huge numbers of successful math students and none of them, including myself, were taught this way — lucky us! If you have Common Core in your school, this is the kind of crazy bs you must use with your students.

My response below is part of the comments section on Guy Brandenburg’s post of the “Jack” math problem:

http://gfbrandenburg.wordpress.com/2014/03/23/jacks-famous-427-316-common-core-math-problem/

On March 23, 2014 at 6:39 pm deutsch29 said:

Regarding Michael Goldberg’s comment to the effect that I am “closed minded” to the new math and that I refuse to “engage” in discussion about the issue:

I have tried to tell him that I consider this “new math” to be “the long way home,” and that if teachers want to choose it, that’s fine, but that I don’t like the idea of teachers’ being required to use it– the rigid, no-options signature route that is CCSS.

If Goldberg likes his math this way, fine. However, teachers (and parents) across the US are being forced to ditch traditional calculation in favor of this alternative way. It’s the “forcing” that I find to be the overriding problem.

Goldberg wants to talk me into his position. It isn’t going to happen.

Some believe that requiring young children to “explain

and illustrate” math concepts is fine. I think it is developmentally inappropriate.

Then there is the coup of having companies sell “CCSS-aligned”

curriculum that requires students to complete assignments like

the one in the example in Guy’s post.

If there were no CCSS, we would not have these same frustrating

math examples popping up across the US right now.

Yes. Michael, students, parents, and teachers are frustrated with being forced to complete math the way one is required to complete it in the example above.

“Forced” is the word: The corporate reformers’ goal is to align (and mandate) all: CCSS, curriculum, and tests.

And NGA/CCSSO are now debating how they might “approve”

the CCSS curriculum since they are the CCSS copyright holders. Stay tuned for more on that front.

I don’t know about you, but I was most certainly forced to answer math questions in one way growing up. I never learned the lattice method of multiplication until well into my teaching career. I was never shown the geometric properties of the pythagorean theorem, again, until much later in life. Fraction multiplication was “do this and then this and then you get the right answer”…I was a great rule follower….until I hit Math analysis and calculus and suddenly those proofs actually were supposed to mean something, and I was lost (I had done really well in geometry class, I memorized every proof there was). Why do so many adults still readily admit to having been bad at math, to still being bad at math, to having made college and career choices based on how much (or how little) math was required? CCSS and NCLB did not change that. Don’t get me wrong, I am an adamant anti-CC person, but see these kinds of arguments about how to teach math as being out of place.The “math wars” are still alive and kicking, and once CCSS are dead and buried, I would love to get into this more. We can argue that the rushed implementation of CCSS has led to a whole host of problems on worksheets, but to talk math pedagogy as CCSS or not, doesn’t make sense to me. Again, the “math wars” were around before NCLB or CCSS and will be around long after.

I agree that the “math wars” go beyond CCSS; however, the rigid, top-down nature of CCSS is now entangled with “math wars.”