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McGraw Hill Math: Intended to Confuse Parents and Students?

September 20, 2015

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


Addendum 09-21-15: In this post, I question the quality of McGraw Hill’s math products. A parent came to me with the worksheet featured in this post. She said she and other adults could not figure out what the worksheet expected her son to do. The worksheet lacks adequate explanation and illustration, which is particularly important given that the term “regroup” is foreign to those who learned to “borrow.” This distinction might seem trivial, but terminology shapes paradigms. As a publisher, McGraw Hill should recognize this by including a stand-alone explanation/illustration on what is intended to be a worksheet of explanation. 

In my post, I wonder whether McGraw Hill is trying to meld traditional math with CC math standards. I have had readers react strongly to this idea, stating that the varied ways of teaching math preceded (and are not unique to ) CC. However, CC was a virtually nationwide shift in math instruction forced upon teachers, students, and parents. This jolt has the public jumpy, which is all the more reason for math info purchased by districts and sent home as a homework help to be clear to parents. 


This is a post about a fourth-grade assignment for a Louisiana student, and given that Louisiana is under Common Core for 2015-16, it is logical to conclude that the assignment below is McGraw Hill’s effort at a Common Core math assignment for fourth grade. (I write “effort” since the worksheet appears to try to offer traditional math and satisfy Common Core at the same time.)

The assignment is about carrying in subtraction. However, the explanation of how carrying works when one cannot borrow from the next column and must “borrow in order to borrow” is a lesson in frustration.

Note that at the top of the worksheet page (posted below), McGraw Hill offers help via ConnectED, a login service offered by by McGraw Hill for its math products.

Interestingly, in July 2015, McGraw Hill decided to sell its summative (“high stakes”) testing division to Data Recognition Corp (DRC) and concentrate on classroom materials– like the math worksheet and online help featured in this post:

McGraw-Hill officials say leaving the summative and shelf testing markets will allow them to focus on products and services that more directly serve teachers and students in the classroom.

David Levin, McGraw-Hill Education’s president and CEO, said in an interview that the company’s major emphasis will be on “instructional materials, and the tools and software to make the most” of resources for students and teachers.

If we go back in time, to 2004, McGraw Hill intended to become “the leader in assessment reporting” as it acquired Common Core “architect” David Coleman’s assessment company, Grow Network, and kept Coleman on as CEO until 2007.

The best-laid assessment plans. Pity.

Let us now turn our attention to an example of the McGraw Hill math product: that fourth-grade worksheet in subtraction by carrying.

In characteristic Common Core math fashion, the explanation on the worksheet is confusing; it lacks detailed directions/illustration and therefore appears to require many parents to log in online for “homework help” (click on image to enlarge):

common core math carrying

(The above reads like some effort to cross Common Core and traditional math. Here are the Common Core math standards for grade 4, “Number and Operations in Base Ten,” for those who wish to view and compare to McGraw Hill’s worksheet.)

But let us now leave McGraw Hill, for the explanation of the same concept, for example, on under “How to Borrow when Subtracting” is much clearer:

In some cases, the column directly to the left may not have anything to lend. Suppose, for instance, you want to subtract 1,002 – 398. Beginning in the ones column, you find that you need to subtract 2 – 8. Because 2 is smaller than 8, you need to borrow from the next column to the left. But the digit in the tens column is a 0, so you can’t borrow from there because the cupboard is bare, so to speak: 


When borrowing from the next column isn’t an option, you need to borrow from the nearest non-zero column to the left.

In this example, the column you need to borrow from is the thousands column. First, cross out the 1 and replace it with a 0. Then place a 1 in front of the 0 in the hundreds column:


Now, cross out the 10 and replace it with a 9. Place a 1 in front of the 0 in the tens column:


Finally, cross out the 10 in the tens column and replace it with a 9. Then place a 1 in front of the 2:


At last, you can begin subtracting in the ones column: 12 – 8 = 4:


Then subtract in the tens column: 9 – 9 = 0:


Then subtract in the hundreds column: 9 – 3 = 6:


Because nothing is left in the thousands column, you don’t need to subtract anything else. Therefore, 1,002 – 398 = 604.

In the spirit of promoting practical solutions necessary for efficiently navigating life, perhaps Louisiana school districts should ditch the expense of McGraw Hill and its Common Core confusion and invest in straightforward explanations.

Common Core Sense.

question clipart


Schneider is a southern Louisiana native, career teacher, trained researcher, and author of the ed reform whistle blower, A Chronicle of Echoes: Who’s Who In the Implosion of American Public Education.

She also has a second book, Common Core Dilemma: Who Owns Our Schools?, published on June 12, 2015.

both books

  1. Or in both cases add a bit to the top number and the bottom number to make for a simpler sum
    is the same as
    and keep it up until you get a better looking sum

    Or use a calculator. Teaching kids some things is wasting their time.

    • Eric Brandon permalink

      One problem with always relying on a calculator is that students make mistakes punching in the numbers sometimes. But if you can’t do this sort of thing in your head, then you can’t catch your mistakes. That is a huge problem. I’m all for teaching kids to do math with paper and pencil and in their heads.

  2. 2old2tch permalink

    And get out the Cuisenaire rods (sp?), so they can see concretely how it works and is not just an algorithm to memorize. They could then write the numbers in expanded form (300+90+8) to help explain what they were doing with the rods. If they don’t understand what they are doing, it leads to difficulties as they have more and more algorithms to memorize. One mistake and they’re lost. No calculators until they know what they are doing or as a check for work they have already done. That problem was ridiculous as no understanding was required or expected. Sorry for going off on a tangent. My special ed students were pushed along for years on “magic math.”

  3. Worth a viewing…especially noting what the speaker says at the 9:44 mark. This was, for me, a nice explanation of different teaching methods especially if you’re interested in one individual’s explanation of math learning strategies based on place value. It illustrates the many, many challenges parents face with their children when actual classroom teachers, researchers and parents are not involved in some way providing feedback on standards creation and curriculum. I am not a mathemetician nor a teacher nor a researcher, but I am a parent of K-12 students. I think the comments below the video are very helpful. Everyone has a view, some seem more informative than others. Over and over again we see when you leave parents and a broad swath of actual teachers out of conversations you get these problems since we were taught math with a focus on algorithms. And what happens when entire classrooms of students struggle to master learning strategies based on place value that their parents don’t know and can’t help them with at home? What happens when the high-stakes test is in a few months and a teacher’s professional evaluation is 50% based on test scores? What happens to the student who just can’t seem to master their place value strategies in one academic year? After all, the next academic year is pushing on, pushing on to new concepts with higher bars. What happens when that they still can’t understand and the frustration, tears and feelings of defeat seem very high? Schools create things like a “Math Lab”. Sure. As I understand it from another parent, math lab in our public school district K-12 is: kid, computer screen, drilling, in lieu of recess and PE. Perhaps it’s more than that but there’s no real content information at the district’s web site.

  4. Further to my first comment I tried out the “UK standard algorithm”. No problems, no going forward and then back. This is the “borrow 1, pay it back” algorithm. Icannot believe that anybody actually earned a living using the “American standard algorithm” in historical times.
    The problem with the “borrow 1, pay it back” algorithm is its description. This disguises the simplicity of the logic behind the algorithm, and makes it appear magical!

  5. Since the children are no longer being taught place-value this explanation is meaningless! Borrowing is the wrong terminology and has been replaced with regrouping. This is such a clear example of Common Core and dumbing down of America.

    • I note the paradigm shift in an addendum.

    • WA Teacher permalink

      Some of us still teach place value, regardless of what some crappy core or confusing curriculum says we need to do.
      Sadly, the McGraw-Hill is less confusing that the Pearson Envisions “math”.

    • “Place value” appears all over the place in the CCSSM document.

    • sallyo57 permalink

      I don’t understand what you are referring to. Students are still being taught place value. If anything it has more emphasis now. And regrouping has been the standard terminology for at least 20 years. I have many disagreements with Common Core but the math does not “dumb down” anything.

      • sallyo57 permalink

        FYI My comment above is directed to mrscullen2015.

      • When does Common Core get to Algebra 2? (Trig?)

  6. Strange that the purveyors of Common Core insist that it does not dictate pedagogy, yet there has been a “shift” in instructional methods that are nowhere called for in the CC standards themselves. This could be because CC standards contain code words (Tom Loveless calls them ‘dog whistles’) that people in the reform math movement respond to, and thus lend the CC standards to be interpreted to comply with the reform math agenda: student-centered, inquiry-based classrooms, and an insistence on “understanding” where such term is generally manifested by having students ascribe meaning to every step of a procedure, lest they fall in the habit of automaticity, which is erroneously viewed as “rote”.

    • 2old2tch permalink

      Automaticity and rote are not necessarily the same thing. The fluent use of algorithms eventually requires some understanding, otherwise the individual has no idea of when to use a particular process (those dreaded word problems!). Figuring out how many square feet of wall space for which we need paint requires understanding how the heck multiplying 12×8 is a useful piece of information. Given time and practice most children develop the requisite understanding. I taught those children who didn’t. They tried to memorize an endlessly growing list of algorithms with no idea how to use them. Since even the ability to memorize through rote practice the basic operations tables, you can imagine that understanding was essential to even use a calculator meaningfully.

      • Agree, but automaticity is viewed as “not understanding” by the fuzzies. Rote (i.e., non-understanding) learning is pretty hard to accomplish with elementary math because the very learning of procedures is, itself, informative of meaning, and the repetitious use of them conveys understanding to the user. Also, I and people who think like me, do not advocate teaching that leaves the onus on the student to impose their own understanding through procedure, without guidance. As my examples from old textbooks in my various articles show, not even the texts from the age so denegrated by the fuzzies structured learning that way. Meaning was almost always integral to any widely accepted system of instruction.

    • Barry, I believe the Common Core Standards for Math Practice ( do dictate instructional practices. All the “integrated” math programs refer to the practice standards.

      • Right, yet the purveyors of CC insist that the standards do not dictate pedagogy.

  7. Ken Watanabe permalink

    Quickest & Easiest explanation on subtraction.

    * Borrow number 1 from an upper digit to make 10 when a number to be subtracted is smaller than subtracting number in a lower digit.

    * Complete number 10-subtraction in a lower digit.

    * Subtract 1 from a given number on the target digit borrowed for number 10-subtraction. If a target digit is 0, move to the upper digit(s) that is at least 1 or larger for borrowing.

    Describe these sentences into a dummy book formula.

  8. It’s easier to “borrow” 1 from top,next col, to make 10 without subtracting it. Then “pay it back” in the same col in the bottom number. This is a “proper” algorithm, and does have a simple, logical explanation. See earlier comment.

  9. J.Adkins permalink

    Isn’t it interesting that we can invent new technology, new medicines, new construction materials, new fashions, new ways of delivering media…but when we try to implement a new way of teaching and learning, everyone loses their minds.

    • New ways are good when they improve the old ways. When the old ways are the best ways……..then the reason for change needs to be investigated. And believe me what is going on in education reform is not to better the education process for our children. If you do not know that then you are either in favor of Communist education system of training and indoctrination or you are very uninformed. Or perhaps both?

  10. BATS are just that BATS. Sorry but they are way to progressive for my taste. I believe there are more infiltrators than actual activists against CC.

  11. Part of the problem with the CC algorithm—and almost all other algorithm—is the insistence that we work AGAINST the left to right orientation that we have already taught children through reading. Why not work left to right in these problems instead of right to left? Also, children want to deal with the big chunks first, not the small chunks. So left to right is doubly logical.

    My fourth and fifth graders do the following (though vertically, not horizontally): 1002-398 = 1000-300=700. 2-98= -96. 700-96 = 604. Fourth grade is a great time to learn about negative numbers! They love it because, until now, it has been implied that they don’t exist, that they are irrational.

    OR, rounding to “friendly numbers”:

    1000-400 = 600, add the “2” you took off 1002 and the “2” you added to 398, and you have 604.

    Work with what they know and make math logical!

  12. At a seminar for teaching math through Common Core, a colleague was told that Smarter Balanced tests feature almost no geometry because supposedly few professions require it. Never mind carpenters, astronomers, engineers … Perhaps this rationale was to justify the lack of CC instruction on pi.

    Have any of you observed a lack of geometry in either testing or Common Core? Were you given a rationale?

    • Former Teacher permalink

      Amazing. Most of my job as an integration automotive engineer requires geometry. We even use terminology like coplanar, collinear… not to mention many discussions of angles, symmetry, reflection, etc. Every automotive designer needs to have a deep understanding of geometry, too. A lot goes into designing parts! To say most professions don’t use geometry is ignorant.

      Also, if common core’s goal is to “deepen understanding of math”, this problem is a sad attempt.

  13. Long before common core, another way I taught elementary math subtraction was by ‘counting up’ on number lines, which I can often do in my head for problems like this. If nothing else, as a crosscheck to the nightmare of all that crossing out that so confuses students no matter if you call it regrouping or borrowing. Students tend to whap numbers on top of the zeros without understanding why, then crossing them off, again not understanding why.

    One way to picture this number line:



    Count up starting at 4795. Go 5 more to get to 4800. Then 200 more to get to 5000. 5000 more to get to 10,000. And 200 more to get to 10,200. Add up the hops: 5+200+5000+200 = 5402.

    I’m not advocating getting rid of stacking numbers for traditional algorithms, but when there’s easier ways to figure it out, I’m all for using them.

    • Former Teacher permalink

      Exactly! And it’s about exposing students to various methods because there are many ways to do basic mathematical operations, and as you said, some are easier than others in some contexts.

  14. On NYS assessments often a student must explain how to do a problem. This explanation is wrong. It mixes up the order needed to solve and the “graphic” is wrong. As a teacher I often ignore the textbook explanation and just do what has worked for the past 50+ years I have been doing math. I often tell my students and their parents that there is the right way to solve amd the CC way. I take the right way

  15. Joe permalink

    Let’s all keep clear here that this has absolutely nothing to do with mathematics. Arithmetic algorithms are to mathematics what punctuation is to poetry. The unacknowledged problem in discussions about mathematics education is that all the mathematics has been bled out of the curriculum. Students can go from pre-Algebra to AP Calculus and do almost no real mathematics. It is utterly pathetic that almost no-one in the ed-biz recognizes this…

  16. Dr. Rich Swier permalink

    Great. Posted:


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  1. Mercedes Schneider: A McGraw-Hill Common Core Question: Can You Solve It? | Diane Ravitch's blog

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