The core problem

Why is this Common Core math problem so hard? asks Hechinger’s Sarah Garland.

A frustrated father posted a subtraction problem from his second-grade son’s math quiz on Facebook.  Students are supposed to write a letter to “Jack” telling him what he did right and wrong in using a number line to subtract 316 from 427.
Common core math problem
The father, Jeff Severt, who has a bachelor’s in engineering, told “Jack” he was stumped by the problem himself. “In the real world, simplification is valued over complication,” Severt wrote.

Severt’s son is on the autism spectrum and has problems with attention and language, so this kind of problem is especially difficult, the father said.

Jason Zimba and William McCallum, lead writers of Common Core math standards, blamed a poorly written curriculum for the problem, writes Garland. Common Core requires fluency in the simple skills of adding and subtracting, just what the critics want, said McCallum.

The question appears to be aiming for several Common Core math standards for second grade, writes Garland.

Students are supposed to understand place value and to add and subtract using “models or drawings and strategies based on place value … and relate the strategy to a written method.” They must “explain why addition and subtraction strategies work, using place value and the properties of operations.” The standards call for using number lines.

“Being able to explain how you arrived at an answer – not just memorizing a formula – is also one of the standards’ key goals for students,” she writes.

In the math problem encountered by Severt’s son, “What the kid did is kept subtracting 10. So they didn’t go down to the smaller unit. And whoever is looking at the problem is supposed to see that the student was confused about place value,” said McCallum. “A discussion in the classroom is supposed to talk about how 10 is 10 times bigger than one, and 100 is 10 times bigger than 10.”

But mashing together the different standards for place value and the number line is potentially confusing. “The number line is not an appropriate model for place value,” Zimba said.

The writing component is also problematic. “The standards don’t require essay writing in mathematics,” Zimba said.

The Common Core isn’t a curriculum, said Zimba. “The curriculum authors are going to interpret the standards in different ways.” Some of them will do it badly.

There’s going to be lots of bad implementation. It’s inevitable. Test scores will drop. That’s inevitable too, if only because the tests will be new and unfamiliar. Parents and teachers can share their frustrations on social media. Politicians are getting cold feet. Arne Duncan is out of bribe money. I think Common Core is in trouble.

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  1. Barry Garelick says:

    The Common Core standards lend themselves to poor interpretations by virtue of the requirements (in the content standards) that students “explain” this and “understand” that. Such language plugs into the 20+ years of math reform ideology that has plagued schools. Reform math is now been given a huge shot of steroids thanks to Common Core. The type of problem the father highlighted has been around for some time. The publicity given to Common Core has now made such problems much more noticeable. Jason Zimba and Bill McCallum, quoted in Garland’s article are doing spin control.

    The Standards for Mathematical Practice (SMPs) which also are in the Common Core are also a driving force in such interpretations. They are taken from NCTM’s process standards in part and are being interpreted as requiring students to develop certain mathematical “habits of mind”. Such habits should come as a natural part of the topic being discussed–but as they are being implemented, students are required to develop “algebraic thinking” habits well outside of an actual algebra course.

    See Ze’ev Wurman’s article on this here:

  2. SC Math Teacher says:

    If they really wanted to break up the traditional algorithm into parts, why not just line up “400 + 20 + 7” on top of “300 + 10 + 6”? That would illustrate place value and simultaneously lead into the simplicity (rightly) desired by the engineer father. Borrowing could follow later.

    Understand that in the second grade and you’re in pretty good shape.

    • What? The kid might gain comprehension and be able to function in the world with your idea.

      But most importantly, the author of the exercise wouldn’t get those sweet curriculum royalty checks.

      Everyone involved in publishing this exercise should be fired. That is not a number line, it isn’t logarithmic. It in fact requires the child to completely abandon number lines which would be equidistant for equal values. Instead on that line, to go from 127 to 111, the increments must be 2.6666. Even if second graders were taught irrational numbers, it is a stupid way to increment an axis when trying to solve a whole number problem.

  3. Sharon R. says:

    Oh gosh, this almost made me cry. I’ve also got an autism-spectrum kid who is perfectly good at math but has a very hard time converting his thoughts into writing. We try to work through the “Explain how you did this” and “Explain what he did wrong” problems because explaining your work can be an important skill. But I am so sick of “math strategies”!!!! This isn’t really a Common Core failing – I’ve seen the same crap for years in California Math homework. Now they use the same worksheets as last year but call them “Common Core”. Kids spend *months* learning “math strategies” that for the most part make the problems harder and more complicated. Last week my younger son had a math test on division – but instead of just using long division to solve the problems (which took him about five minutes to learn how to do) there are diagrams of rows of blocks you are supposed to count up and then divide into groups to solve the problems. Sure, that might help a kid who *doesn’t understand division* but why do we have pages and pages of it? One of the multiple choice problems was just badly written and didn’t even include the right answer (84/4 is not 22). Isn’t the point of math strategies to help the kids who don’t get the standard method of, you know, solving the problem? Everyone is going to blame Common Core, but this has been going on for at least 5 years and probably a lot longer. We see the same thing in English, where the kids spend years learning “strategies” for reading and writing instead of actual reading and writing. It’s *better* this year with the Common Core push, in that I see a lot more emphasis on actual writing of factual paragraphs (“support your argument”) and less “tell how you feel about it” silliness. My Aspy kid still has a hard time doing the writing, but at least for the most part they are no longer asking him to write (which is hard enough) and also talk about his private feelings (which is intrusive as well as nearly impossible)!

  4. You don’t LEARN math by writing about it, you learn math by actually DOING it (unknown author).

    It annoys the h*ll out of me when I see stuff like this being passed off as math. What happens when this kid gets to perhaps calculus (I can guarantee you won’t see any of that stuff in calculus)?

    • Mark Roulo says:

      “What happens when this kid gets to perhaps calculus … ?”
      A lawyer would say that you are assuming facts not in evidence 🙂

  5. The mistake doesn’t make any sense at all. It’s not a typo sort of mistake. Jack used the units digit to subtract tens. Some extra words of explanation by Jack might explain his misunderstanding, but maybe not. How could a student explain to Jack how to fix the mistake other than to repeat the process of subtracting by different units. And what, exactly, would that explanation be; the same explanation the teacher gave that didn’t help Jack in the first place? This is cargo cult education.

    What if the question was to subtract 146 from 127? When you get to the point where you have to subtract 10 from 17, you get 7, but what do you get when you have to subtract another 10 from 7? Do you get -7? Who says that these so-called “understanding” techniques are not subject to the same issues of rote application of rules? Someone could make the same size tens “hop” but label it with -7.

    The number line is supposed to help, but what if students don’t count and only see it applied to problems with positive solutions? No amount of words will help if your understandings haven’t been tested by all variations of problems. That’s what proper textbook problem sets do. You don’t need words on a few problems. You need math on a lot of variations. You need practice that proves understandings. Words don’t do that.

    There is so much interpretation slop in the CC standard that K-8 educators will implement it using whatever matches their pedagogical beliefs. Besides, it’s not STEM preparation by definition. On purpose. In black and white. Unless kids in K-6 get extra help and higher expectations at home, it’s all over by 7th grade. CC proponents can talk about compacting in high school for cover, but that’s too late and it won’t work. They don’t want to set higher expectations or track in K-6, so parents do it at home. Educators can then ignore it and get really excited when little urban Suzie gets to go to the community college because she is “college ready”. Never mind whether she could have gotten to Harvard.


    • See the post just previous to this one for the problem with “extra help and higher expectations”. The kids are conditioned to please the teacher. They are conditioned to do what is required regardless of its educational value. Very shortly after starting school, they don’t listen to parents and others who might want them to actually learn or develop comprehension because that is not what the “educators” expect of them. A common refrain is “We don’t have to know that.”

      School helplessness conditioning is very hard to overcome. You’ll have an easier time getting the kid off heroin.

      • Michael E. Lopez says:

        I nominate this for the best comment of the year so far.

      • Roger Sweeny says:

        “We don’t have to know that” arises for two reasons.

        1) Kids are pragmatic. They understand that they have to do certain things to pass and get credit and go on to the next grade (which means staying with friends and acquaintances). That is what they “have to” do.

        2) To the student–and to most adults!–schools and teachers define what it means to be educated. Even if a student honestly doesn’t want to be a grade grubber and wants to be “educated,” the school is telling him what that means. If he doesn’t need to know something to succeed in the school, it is very easy to think he doesn’t need to know it in order to be educated.