A few weeks ago, a self-described “frustrated father” posted a page from his son’s supposed common-core math assignment on Facebook, claiming that despite his own degree in engineering, he could not solve the problem.
As you can see in the photo, the problem asks students to figure out where fictional student “Jack” went wrong in calculating 427 minus 316. It shows that Jack drew a number line and skip-counted backward to solve the equation. It then asks students to “write a letter to Jack telling him what he did right, and what he should do to fix his mistake.”
The father, Jeff Severt, wrote that the problem “is solved in under 5 seconds” when using the traditional process for subtraction. The approach on the assignment “is ridiculous,” he wrote.
The post went viral. Conservative pundit Glenn Beck, who interviewed the father on his show, said, “I can’t figure the damn math problem out. ... This doesn’t make any
sense to a normal human being.” He argued that the assignment takes a simple subtraction problem and makes it “overtly complex.”
The Hechinger Report asked two lead writers of the Common Core State Standards why the problem was so difficult. It’s not strictly a common-core problem, said Bill McCallum and Jason Zimba, and is the product of a poorly written curriculum. While the common core requires students to explain their thinking, this problem combines standards on the number line and place value, which can be confusing, they said.
Stephen Colbert, in his portrayal of a conservative pundit, also chimed in (with characteristic sarcasm). “Folks, that word problem couldn’t be easier to solve. All you have to do is check the semicircles on the same-side arrow, put the two numbers up in it, and bing-bang math!” (He also said it “teaches two important workplace skills: math and passive-aggressive note writing.” That gave me a chuckle.)
Recently, a father of a 5-year-old wrote to me, asking that I explain the viral word problem, which he believes has been unfairly demonized. “I personally am not giving in to all this outrage,” he wrote in an email. "[M]y understanding is that this ‘mental math’ is supposed to encourage students to think more about the theories behind math to form a better foundation of knowledge instead of using ‘tricks.’”
While I report on math (and even taught it for a while), I by no means call myself a math expert, so I’ll decline to offer my own explanation. But on Vox today, reporter Libby Nelson wrote in reference to this problem that “the idea behind using a number line for subtraction is that students get a visual representation of what subtraction is: figuring out the ‘distance’ between two numbers.” It’s a fairly common pedagogical technique—one also used with multiplication, she said. Under the common core, “students are still expected to learn the standard approach, which is indisputably faster. But the emphasis is switching from speed to understanding.”
I also checked in with W. Gary Martin, a professor of secondary math education at Auburn University. He said the goal of the problem is to have students “critique the reasoning of others,” one of the common core’s Standards for Mathematical Practice. "[T]he intent of the task is valid, although the task itself is problematic. That is, helping students see the underlying place value meanings inherent in multidigit operations is certainly a good thing, although the number line would not be my choice for addressing this standard since it does not represent place value very effectively,” he wrote. “I think the task might have been saved by asking, ‘What other drawings or models might you use to help Jack better understand this problem?’ That is, give the students a chance to not only analyze the flaws in Jack’s thinking but to think about appropriate tools.”
Overall, I think there are really two discussions going on here: One is about this particular task. Is it mathematically sound? Does it convolute skills or encourage skill transfer? The other is a much larger one about the standards. Should students be asked to explain their thinking on what could be a very simple problem? Is it useful to push conceptual thinking when equations will get you to the same answer much faster? Which process will students use as adults? (That second debate—math concepts vs. tricks—is one I’ve covered quite a bit recently.)
Interestingly, since all of the hubbub over the problem began, Jeff Severt, the father who launched the debate with his Facebook post, has weighed in again to provide more clarity and context—and even a defense of the problem. In a lengthy Facebook post, he wrote that his son, who has autism spectrum disorder, “knew the math answer immediately in his head. But this problem required a narrative answer utilizing a number line. While he knew the math, he balked at the answer being a writing assignment—his greatest anxiety. ... [The letter] was just reflective of our frustration with and experience of a creatively valid yet ridiculously complicated, age-inappropriate method.”
As always, please do add your own two cents on this below.
A version of this news article first appeared in the Curriculum Matters blog.