Common Core Math: A Glimpse in the Classroom
The fourth grade students sit on a carpet, wriggling, shaking their hands, looking in all directions as a teacher uses the most basic of tools — a red sharpie and a big white pad — to deliver her lesson.
The day’s agenda: teaching the Common Core standard of finding “whole number quotients.” She writes an equation on the board, and the answer works out to be 100. But she’s not done.
“How do you know it was 100?” the teacher asks in a video shown at the Education Writers Association’s National Seminar this spring in Boston. The video, presented by Rhode Island math specialist Audra McPhillips, was meant to demonstrate exemplary teaching to the common math standards.
The fidgety mini-mathematicians in the video start reasoning out the problem in their own words, miles away from the dry language of the standards. One student raises his hand.
“I know that, well, three times one hundred equals three hundred,” he says.
In another problem, the fourth graders are asked to divide 420 by 3. The teacher tells the students to find the answer among themselves, and then explain “why it is that way.”
Then the camera shifts, and it’s the teacher talking to a filmmaker.
“What I’m looking at is if she can articulate where these two parts are in the whole of the problem,” she says.
Back to class. “Can you explain why it’s 140?” she asks.
A student in a ponytail and a pink shirt raises her hand: “You have to add the first two numbers, and you can just add the first two answers,” she said. “So because I added the two dividends, I could get the answer right here?”
This is the Common Core as it should be taught, according to McPhillips, who helped develop the math standards, as well as the common PARCC exam in that subject.
Though the Common Core has been taught for several years now, teachers across the country are still struggling with its implementation. So professional development is crucial.
What works about the math lesson in the video, McPhillips said, is that students are empowered to work out the math on their own. They’re being collaborative, the teacher doesn’t make students feel dumb, and despite the students’ squirmy activity, she holds their attention. And another thing: The teacher lets wrong answers fly while resisting a natural urge to correct them, “which, from a teacher perspective,” McPhillips said, “is hard to do.”
The strategy of allowing students to discuss answers in small groups before they are presented to the class as a whole is supported by research, McPhillips said. That strategy particularly helps students with disabilities who might need more time to feel confident in their solutions.
The goal in this lesson is to try to get students to start thinking about division and its components. They need to understand dividends. That’s why, she said, the teacher in the video felt comfortable working things out aloud, and letting students suggest incorrect answers without correcting them.
Under the Common Core, fourth grade is about getting used to division, she said — but not necessarily getting the answers right just yet. In fifth grade, students have to execute these operations with more fluency.
The teacher in question, though, she said, could have been better at paying attention to students’ math vocabulary.
A Complicated Relationship
McPhillips herself has a complicated relationship with the common math standards, adopted by more than 40 states. She was part of a group of teachers that provided feedback to Jason Zimba, one of the lead authors of the standards. The first of five drafts, she said, was “horrendous.” The final product is imperfect, but much better than the standards Rhode Island had before, she said. Still, she’d like to see a revision. Separate from the standards, McPhillips chooses to opt her children out of tests, because of what she’s observed as schools’ incessant focus on test preparation.
Following each video of a model lesson, McPhillips herself modeled good teacher behavior, asking the reporters to discuss their observations in groups. She circled around the classroom, asking questions, and then had groups to present their findings.
And ever the good Common Core practitioner, not once did she say, explicitly, that the assembled journalists got something wrong.