Common-Core Subtraction: Teaching Many Methods
"For some, common core is creating common confusion," said education correspondent Rehema Ellis on a recent NBC News segment.
The crux of the news piece was that parents are struggling to help their children with math homework under the Common Core State Standards because the teaching is so differenta claim we've heard in our reporting here as well. (The Washington Post has picked up on this strand, too.)
Ellis showed a subtraction problem, performed both using the traditional regrouping, or borrow-and-carry, algorithm and using an example from the common core. Here's a screenshot of the two methods. (The common-core technique is on the right.):
The new method uses "three times as many steps to get to the same answer," Ellis said.
The explanation is, well, utterly confusing. I had to watch it several times to understand what was being done. (See the video below.) Essentially, the method requires skip-counting upfirst by ones, then by 10s, and then by ones againfrom 9 to 34. The idea is that it's easier to add 1 + 20 + 4 than it is to count down or carry and borrow.
And while it's not the way most traditional textbooks teach subtraction, it's also not exactly new. I both used this with some of my elementary students when I was teaching (we called it "jumping to the tens"), and saw other teachers use it, too. And when I asked Diane Briars, the president of the National Council of Teachers of Mathematics, about it, she chuckled. "That's been around forever," she said.
What's in the Standards
(CORRECTION) Ellis is right to point out that the regrouping method is not part of the early math standards--students do learn this, however, in 4th grade, long after they have the basics of subtraction.
As far as I can tell, the common-core approach she describes comes mainly out of a 1st grade standard (CCSS.MATH.CONTENT.1.OA.C.6). It states students should be able to:
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a 10 (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
In the NBC example, students decompose the difference between 34 and 9 into numbers that are easier to work with. And they add on the number line in order to subtract, demonstrating that they understand the relationships between the operations.
So yes, this method can be seen as a common-core approach. It's one that a teacher might choose to teach, or a textbook publisher might choose to publish, under the common-core standards.
Moving Toward Mental Math
But as Briars explained to me in an interview, there are many more ways to do this problem under the same standard. One way "is to show that 34-9 is the same problem as 35-10" by shifting up the number line. Another way would be to have students break 9 into 4+5. Then they can count backward from 34, first taking away 4 to get to 30, then taking away the remaining 5.
The specific methods differ, but they all come from the same standard.
A teacher in the NBC video makes this point as well. "There are lots of ways to show 34-9. And who's to say what is the best way for any particular kid," she said. "It's my job to show them different ways to do it."
All of these methods are ultimately leading toward having students do more mental math, said Briars. The 2nd grade standards require students to "fluently add and subtract within 20 using mental strategies" (CCSS.MATH.CONTENT.2.OA.B.2). So while the strategies may take longer at firsteven three times longer, as Ellis saideventually under the common-core students should be able to do these kinds of problems in an instant.
A previous version of this post incorrectly characterized the way the standards teach subtraction. Students learn regrouping and the standard algorithm in 4th grade.