As regular readers of this blog know, I’ve been a long-time, energetic, enthusiastic defender of the Common Core standards. That’s because those of us at the Fordham Institute believe these academic standards to be much stronger, in a variety of ways, than what preceded them in most states. They aren’t perfect, but they represent an ambitious, good-faith effort to identify the knowledge and skills kids need in order to be on track—from kindergarten through high school—for college and/or a remunerative career. And when it comes to math, the standards in the early grades are particularly strong, focused as they are on basic arithmetic and “math facts.”
That said, certain elements of the standards have been driving parents crazy.
So it was probably only a matter of time until my karma caught up with me. And so it happened the other day: My third-grader came home from his (Common Core-teaching) public school and asked, with eight-year-old exasperation, “Why do I have to explain my answer in math class? I just know it.”
I decided to turn to the Google gods for an answer—a suggestion of a script I might use to help him understand why it’s important to be able to articulate how he got the right answer, and not just state the right answer itself. I didn’t find much online, though, so I turned to some teacher friends and Common Core experts.
Before we get to the script—actually, several possible scripts—that emerged, some background is necessary. Because, as it turns out, the admonition for students to “explain their answers” (or, relatedly, “show your work”) has been widely misunderstood, including by more than a few teachers. And the Common Core standards themselves don’t actually encourage schools to ask students to explain their answers when doing simple arithmetic (as was the case with my son, who was asked to explain why 8+5=13).
Here’s how Jason Zimba, one of the lead writers of the Common Core math standards, put it to me:
Eventually, students are to know the value of 8 + 5 from memory. However, until that point is reached, 8 + 5 isn’t a fact so much as a problem—an occasion to do some math.
When my kids were in this phase, the math that I taught them for problems like 8 + 5 was the method of making ten.
Once my kids knew the value of 8 + 5 from memory, I stopped asking them how they knew the answer. At that point, I also discontinued practice with making ten. The method had served its purpose.
For the particular case of single-digit sums and single-digit products, I have stressed in presentations that the eventual/target strategy is just knowing the answer, so once a student reaches that point, I would stop asking her how she knows.
P.S. In the [Common Core] standards about fluency and recall with single-digit sums and products, the verbs “explain,” “justify,” and “illustrate” do not appear.
So, if your child is complaining that he or she has to explain how they know simple math facts…they might be right, and you may need to have a gentle conversation with their teacher or principal. (Or you might tell them to suck it up, that this phase will pass.)
Beyond basic math facts, however, there are good reasons for kids to explain their answers, such as when solving word problems or doing multi-step addition or subtraction. Here we get to some possible “scripts,” starting with what Teach like a Champion author Doug Lemov suggests you say when your child complains:
Yes, but understanding how you did it will help you use it—maybe even a little differently—when you move on to harder problems. Plus it helps us make sure you can get similar problems right and maybe even that you know when and why to solve this way.
My colleague Dara Zeehandelaar, a former high school math teacher, suggests saying it this way, especially for somewhat older kids:
It's important to have math ‘instinct.’ A lot of people don't. But math gets more complicated the older you get, so the more you understand how your ‘instincts’ are actually grounded in fundamentals, the better you'll be able to apply those fundamentals to tougher problems that you haven't seen before when your instincts aren't enough.
And a good way to build that understanding, says my colleague Alyssa Schwenk, herself a former Kindergarten teacher, is to ask the child to explain how they got their answer to, say, his younger brother.
One last tongue-in-cheek thought, again from Doug Lemov, about what to do when these explanations don’t work:
I find “Because I said so, dammit” and “because your last name is Lemov” to be excellent.