Mercedes Schneider came across a fourth grade question in a McGraw Hill textbook. She shows how confusing the question is. She knows that the text is trying to form a Common Core question. She thinks it was designed to confuse everyone–students and parents alike. There is an easy way to solve it, and a hard way. The McGraw Hill text picks the hard way.

Categories Education Reform

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Susan Lee Schwartz says:

September 26, 2015 at 11:13 am

Incredible.

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kaveriamma says:

September 26, 2015 at 11:33 am

This is what it says at the link

“PLEASE DO NOT REPOST THIS ON THE BATS FB PAGE. It will be removed. Commentary became ugly; math is a touchy subject. Thank you.”

Is this proper to post here?

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- dianeravitch says:
  
  September 26, 2015 at 3:42 pm
  
  Kaver:
  
  I don’t post copyrighted material. I try to stick to the fair use dictrine, using excerpts.
  
  Everything else is ok unless it offends my sensibilities.
  
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- TC says:
  
  September 26, 2015 at 4:06 pm
  
  I can see how it got ugly. The term ‘borrow’ assumes it will be returned. Over the course of history, how many times has a decimal column had 10 ‘borrowed’ from it never to be returned?
  
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  - Michael Paul Goldenberg says:
    
    September 26, 2015 at 5:08 pm
    
    @TC: that’s likely part of the debate. Virtually every mathematics education researcher/professor I know after 25 years in the field agrees that “borrowing” is an unfortunate term. It’s not part of official mathematics, but an artifact of American primary educational tradition. The movement to change the terminology to “regrouping,” which comes much close to what is going on, is hardly new and has NOTHING to do with the Common Core other than that the writers of the CC Math Content Standards went along with what the majority of mathematics educators have been teaching for several decades. Mercedes is a traditionalist and despises K-5 curricular materials that emerged from various National Science Foundation projects in the late 1980s through the mid-1990s. Specifically, she abhors the University of Chicago’s EVERYDAY MATH. A similar program I’m sure she’d also loathe is TERC’s INVESTIGATIONS IN NUMBERS, DATA & SPACE. My son had that program in K-4 and we liked it a lot. No one will ever convince Mercedes that these programs have any value, and she has zero interest in discussing or arguing over her beliefs on the subject. Her standard retort is that kids, teachers and parents should have a choice as to what to use/learn from.
    
    Now, there’s no little irony in the fact that she is a shining light in the fight against the educational deform/GERM juggernaut; to me that requires recognizing the phony arguments for “choice” that are at the heart of the corporate push for vouchers and charter schools. So why is that sort of “choice” wrong, but this other sort of “choice” that Mercedes feels is vital for teachers (mostly) perfectly reasonable? I think there is a fundamental contradiction there, but then, I don’t consider her to be truly politically progressive, even if her analysis of the money and machinations behind Common Core is spot on and invaluable. When it comes to actual issues of curriculum, she would NOT be my go-to person.
    
    I could add a detailed analysis of the worksheet here, but I’ve done that sort of thing many times in the last couple of years. What I find is that some folks are open to learning a different way of mathematical thinking/reasoning/learning, and some simply are not. Mercedes is not and she does not want to be “forced” by anyone, well before the existence of the Common Core, to have to do so. Like some other critics, she lumps things that I consider progressive and student-centered into the same bucket as everything to do with “Common Core” and finds it to be evil and deserving of banishment from the face of the earth. In my opinion, her analysis of this work sheet is highly biased and unreasonable. Kids getting this material are not being handed it cold with no classroom instruction. The instruction may not be on the worksheet itself, but learning has already been initiated in the classroom before the assignment is given. I would argue, frankly, against giving homework to K-3 students, and I would strongly advise that any teacher who expects to teach successfully any sort of program in math that isn’t just like the 1950s better be communicating often with parents about what is going on and how to help their children. Publishers provide materials for this, but often either teachers fail to share that with parents, parents never receive the materials from their children, or parents never bother to read those materials.
    
    The result is resentment, confusion, and the undermining of what the teacher is trying to accomplish in class. This happened in the 1960s and early 1970s with the “New Math” movement. It happened in the 1990s with NCTM’s Standards and curricular programs like those I mentioned above. And it’s happening again with so-called Common Core programs.
    
    I am NOT saying that there is zero basis for criticism, but I do feel there is not a solid basis for the sort of stubborn rejection of all books and ideas that happen to have the words “Common Core” appended to them. Some of these ideas predate the Common Core by several decades and on my view are sound. Any given book may have bad problems, but that doesn’t mean the whole shooting match is garbage. The next mathematics book I read that is error free, at ANY level of math you care to investigate, will be the first. The next math text I read that is always reader-friendly and perfectly clear will be the first. Schneider and many like-minded critics want to throw the baby out with the bathwater. Indeed, they don’t want some particular babies to ever be allowed to enter the classroom. I think such rigid thinking is unfortunate. And ultimately it harms a lot of children who would benefit from the work mathematics educators have been doing for the last 30 years or so.
    
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  - TC says:
    
    September 26, 2015 at 6:32 pm
    
    Yes, you’ve convinced me, very few math differences of opinion blamed on the common core are specific to the common core.
    
    Reading through the comments in the link, one person said English reads left to right, so do math that way. What if the ones place was on the left? Would that have been a better convention? That would be tough to get used to, even if it were.
    
    I always thought that from a line to a sloped line to a quadratic maybe made more sense to be y=Cx^2+Bx+A as a convention, or maybe y=A+Bx+Cx^2 in a left justified universe
    
    Also I would have picked base 12. Also I would have picked .785 as the circle constant instead of pi. So I guess I would have built math differently if it was up to me.
    
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  - bethree5 says:
    
    September 27, 2015 at 9:08 am
    
    Michael Paul Goldenberg – yes to all you say here, & especially on the importance of teachers communicating post-1950’s methods to parents. My kids had Everyday Math in the ’90’s (elementary sch). The CCSS-math-hw/ worksheet parental complaints circulated in the press tells me methods haven’t changed much, there’s just more attention being paid.
    
    Math did not come easily to my artsy-musical kids (nor does it to me), and the concept-heavy approach was cumbersome. However, ’50’s rote methods were no better: I was a whiz at memorization, but that was of little help past 6th grade.
    
    The transition to algabraic concepts was the stumbling-block in both methods. Except for my eldest, who apparently inherited some of his engr-dad’s math brain. However, he had a processing LD which made writing out the lengthy number-decomposing etc an impossibility. (In 8th gr, he could explain to me how quadratic equations worked in a couple of sentences, but could not write out all the steps).
    
    Excellent math teachers can overcome the obstacles in old or new methods with their pedagogy. But I cannot help wondering whether using abacus from PreK on, & perhaps slide rule in hs, would circumvent the need for such lengthy written math expressions & explanations in early grades– when writing itself is still laborious.
    
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  - 2old2teach says:
    
    September 27, 2015 at 1:02 pm
    
    As you suggest, bethree5, I believe there are brains tuned to abstract mathematical concepts. The people so blessed can manipulate these ideas in their heads. The sticking point comes when some of them have to translate that understanding into words. I need a neurologist to really speak to this point, but I have a suspicion that verbalizing is not a step that certain individuals use in understanding abstract mathematical concepts nor is it necessary for them to be able to do so.
    
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- Michael Paul Goldenberg says:
  
  September 26, 2015 at 4:42 pm
  
  Mercedes Schneider doesn’t abide disagreement, at least on issues of elementary mathematics education. I haven’t seen the “ugly” commentary but based on my attempts to discuss math with her, I have to speculate that “ugly” = people not going along 100% with her viewpoint.
  
  That said, she’s entitled to ask that something not be posted in specific places. She only stipulated one particular place. Diane’s blog isn’t that place. And the issue is not copyrighted material.
  
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Peggie says:

September 26, 2015 at 11:39 am

Instead of “borrowing” call it regrouping, but of course the second explanation is much more straightforward and makes more logical sense.

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TC says:

September 26, 2015 at 11:47 am

Shouldn’t the five steps relate to the five decimal positions, with subtracting being the final action in each step? How do you get 11 or 9 out of 10? If doing a detailed step by step process, why skip steps?

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Jeff adkins says:

September 26, 2015 at 12:31 pm

It’s not that complicated. Just borrowing by writing a 10 in the next lower column instead of adding one to the next higher. Just a different algorithm.

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roxanne says:

September 26, 2015 at 12:38 pm

When I describe the test to people I compare it to trickery. I think this is a suitable word for it. I encourage others to use it too.

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SomeDAM Poet says:

September 26, 2015 at 1:22 pm

“Core Truths”

The problem with the Common Core
Is “Tried and true is bad”
“Why use doorknobs on the door
If zipper’s to be had?”

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- SomeDAM Poet says:
  
  September 26, 2015 at 1:23 pm
  
  make that
  
  “Core Truths”
  
  The motto of the Common Core
  Is “Tried and true is bad”
  “Why use doorknobs on the door
  If zipper’s to be had?”
  
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J. Adkins says:

September 26, 2015 at 1:41 pm

I tried to explain it, but my post was moderated. It is simply borrowing to the right, not borrowing to the left as is traditional. Every column gets borrowed.

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- Elaine says:
  
  September 27, 2015 at 7:30 am
  
  “Borrowing” implies giving back, which does not happen. We are essentially “regrouping” as noted by McGraw Hill. While I am NOT. A fan of the My Math series, the argument should be against Common Core. My students have much stronger number sense than cohorts before.
  
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  - Elaine says:
    
    September 27, 2015 at 7:31 am
    
    Should NOT be against Common Core…
    
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NYC public school parent says:

September 26, 2015 at 1:47 pm

Interesting. I remember when kids were taught: Add 2 to 398 to get 400. At 600 to get 1,000. Add 2 to get 1,002. 2+600+2 = 604. They could practically do it in their head.

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rbeckley58 says:

September 26, 2015 at 2:05 pm

Smarter Balanced features almost no geometry. Do any of you find this true for Common Core in general? A colleague was told at a Common Core math seminar that this was because “so few professions require it?”

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- Duane Swacker says:
  
  September 26, 2015 at 6:15 pm
  
  hmmm, a straight line is a geometric concept, degrees in an angle, the angle itself, squares, cubes, cylinders, two dimensions, three dimensions. . .
  
  noooo, few professions require geometry concepts-damn near everything I am looking at right now is related to geometry in one fashion or another.
  
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- SomeDAM Poet says:
  
  September 26, 2015 at 7:04 pm
  
  The irony is that more professions require geometry — or at least geometric thinking — than algebra (which is part of Common Core).
  
  Pretty much anything related to the building trades (architecture, engineering, carpentry, plumbing, even electrical work) requires geometry.
  
  The people who make claims like “few professions require geometry” are completely (and hopelessly) clueless.
  
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- NY Teacher says:
  
  September 27, 2015 at 8:19 am
  
  In NYS, Common Core geometry is taught (and tested) in 10th grade. When I asked our geometry teacher about the new CC Regents test, he said it was way too difficult for the average 15 or 16 year old.
  
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- bethree5 says:
  
  September 27, 2015 at 8:25 am
  
  I don’t know about the SBAC. But I looked for info on how CCSS-Math covers geometry– I was curious, as an artsie whose only area of hs math prowess was geometry. I found this great link, “Teaching Geometry According to the Common Core Standards” by math prof-emeritus H Wu of Berkeley, covering grades 4-8 plus hs geometry.
  
  Click to access Progressions_Geometry.pdf
  
  Looks like there’s plenty of geometry in CCSS.
  
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2old2teach says:

September 26, 2015 at 9:21 pm

I got lost with the “new math” in the late 60s. There was nothing inherently wrong with it. The problem was a new kid coming into a program that was foreign just being expected to pick it up. My teacher was a scary PhD who had no patience with kids who were not as quick to grasp the concepts as she expected. Years later I saw her in operation in a classroom where I was subbing. She became visibly upset by a student who didn’t get her great math game. I took over helping that child. She was quite a dynamic speaker but as a teacher she was intimidating to anyone who could not keep up with her. I think parents, kids, and their teachers are feeling intimidated by a way of presenting ideas that is new or different than what they are familiar with. Textbook publishers need to be extra supportive in their explanations if the sensible part of the math standards are going to be accepted.

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NY Teacher says:

September 27, 2015 at 8:11 am

There is no reason to teach any method for this type of subtraction problem. Electronic calculators are faster and more accurate. Teaching the concept of re-grouping does nothing to help kids gain number sense.

We live in an age when you can simply ask Alexa (or Siri), “What is ten thousand two hundred minus seven thousand four hundred twenty five?” When our current third graders are 18 (2025) asking someone to work a subtraction problem like this one will seem laughable.

However, kids should work at memorizing basic subtractions as well. I find that the mental math skills are non-existent in the vast majority of kids I teach.

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- Elaine says:
  
  September 27, 2015 at 8:19 am
  
  Mental math is only possible when students have number sense. Memorization does not equate to understanding. Fluency is our goal but that also is not about memorizing. I have first graders, who in December, can tell you 24+25 = 49. They don’t yet understand regrouping but know about decomposing numbers and doubles plus/minus one. So 24+24 = 48 (because 20+20=40 and 4+4= 8) and 48 and one more is 49.
  
  Being able to manipulate numbers is a necessary skill similar to bring able to decode words. Along the lines of your argument, why couldn’t students just ask Siri 8×9 or read aloud the Declaration of Independence?
  
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  - NY Teacher says:
    
    September 27, 2015 at 8:31 am
    
    I agree. However teaching regrouping will never help kids with number sense because it becomes a rote exercise. Knowing the answer to “8×9” is pure memorization and I would never advocate against memorizing times tables, squares and some cubes.
    Number sense comes from application in the real world. I teach science and I can assure you that mathematics education does nothing to invoke number sense. Nothing.
    When “getting” the right number is the end, instead of a means, you stand no chance of making numbers meaningful to most kids. In science, getting the right number is only half right. We are constantly asking kids, “Seven point five what?”.
    
    As far as asking Siri, that ship has sailed.
    
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  - Elaine says:
    
    September 27, 2015 at 8:35 am
    
    Respectfully noted. If you have opportunity to visit K and first grade classrooms that are genuinely using the CCSS you will witness growing number sense. The older students might not be the best testament to effectiveness of CCSS because they have not had it since the beginning. My major issue which CCSS is not necessary the standards themselves, rather the implementation. Should have been a gradual rollout like some states.
    
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  - NY Teacher says:
    
    September 27, 2015 at 8:34 am
    
    “Understanding” math concepts and operations is way over-rated. Until you can figure out how to make math meaningful, most students will forever dislike it. And for good reason.
    
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  - NY Teacher says:
    
    September 27, 2015 at 8:46 am
    
    “My major issue which CCSS is not necessary the standards themselves, rather the implementation. Should have been a gradual rollout like some states.”
    
    The CC standards were not developed to improve teaching and learning. That was never David Coleman’s/Bill Gates’/Arne Duncan’s goal. The standards, companion tests, VAM evaluations, data mining, and charter caps were a package deal in the RTTT extortion scam and NCLB waiver scam. Implementation wasn’t even a thought.
    When 2014 arrived, we all turned into pumpkins.
    
    CC math will never instill number sense. Over complicating simple ideas is never good pedagogy.
    
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  - 2old2teach says:
    
    September 27, 2015 at 12:55 pm
    
    Geez, NY Teacher! Give Elaine a break. You are commenting on issues that the two of you see through different lenses. I understand your point about meaningful application to make math “real.” I had no trouble with mathematical manipulations in science or in statistics. The application aided my mathematical understanding although in the case of the sciences, it did not eliminate my need to “understand” what I was doing. I can’t say the same for the statistical formulas. I had to memorize what they were intended to do, so I knew where to use them. Naturally, without a sound understanding of the concepts, I have forgotten how to use them and most of what they are supposed to show me. My special ed students showed me time and time again why understanding the math was critical. They were very handy with their calculators but did not/could not identify errors. Problem solving was frequently beyond them because they had no idea how to apply math toward finding a solution and if by chance they chose the correct algorithm(s), they didn’t know if their answers made sense or not. Do you remember that wonderful visual of the Pythagorean Theorem where the actual geometrical figures (squares) are drawn out from each side of the triangle? It was that visual that turned the light on upstairs for me and gave me an understanding that made application to real situations possible. Understanding opens up a world of possibilities. Wise elementary teachers are using lots of concrete examples. High school math teachers, I hope, more than they did in my day. There are kids who manipulate abstract mathematical concepts without having to rely on concrete examples. I’m guessing that more of us need that support; I think, you have suggested as much.
    
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  - SomeDAM Poet says:
    
    September 27, 2015 at 11:13 am
    
    Aligned tests, curriculum and teaching for the purpose of creating markets — that’s what Common Core is all about.
    
    Has been from the getgo.
    
    Take it from the horses’ mouths.
    
    Common Core creator David Coleman (in 2011)
    
    “the great rule that I think is a statement of reality, though not a pretty one, which is teachers will teach towards the test. There is no force strong enough on this earth to prevent that. There is no amount of hand-waving, there‟s no amount of saying, “They teach to the standards, not the test; we don‟t do that here.” Whatever. The truth is – and if I misrepresent you, you are welcome to take the mic back. But the truth is teachers do. Tests exert an enormous effect on instructional practice, direct and indirect, and it‟s hence our obligation to make tests that are worthy of that kind of attention.’
    
    Common Core funder Bill Gates in 2009
    
    “When the tests are aligned to the common standards, the curriculum will line up as well—and that will unleash powerful market forces in the service of better teaching”
    
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  - dianeravitch says:
    
    September 27, 2015 at 11:34 am
    
    Some DAMpoet,
    
    Agreed that tests “drive” curriculum and instruction, as David Coleman said.
    
    That is why Arne Duncan broke the law when he funded two assessments. Federal law clearly prohibits any federal official from attempting to influence, control, or direct curriculum and instruction. Arne broke that law.
    
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