Deborah Loewenberg Ball, an expert in elementary school math instruction and professor of education at the University of Michigan, still teaches in the classroom, in part for research purposes. She recently counted the frequent judgment calls a teacher is asked to make during the course of the day. Some are about instruction. Many more concern student behavior.
In a one-minute 28-second period that was filmed in her classroom, Loewenberg Ball counted 20 separate micro moments when she had to decide how to react. She calls them “discretionary spaces,” and in a lecture at the American Educational Research Association annual meeting in April 2018, Loewenberg Ball put a scientist’s microscope on discretionary space #19 to give us all a lesson in how racism and sexism unintentionally creep into the classroom.
“Teaching can have very powerful amazing effects,” said Loewenberg Ball. “It can also do incredible damage. Even in a moment.”
Moment #19 begins with one of her students standing where a teacher usually does, at the front of the classroom with a dry-erase marker at the board. Aniyah, round-faced and earnest, perhaps diffident, starts to explain how she solved a problem about fractions. “I put one-seventh -.”
Click on the video to see the short classroom scene, which begins at 1:23:05.
Her classmate Toni interrupts, “Did she say one-seventh?” Toni’s voice climbs upwards as if to emphasize her disbelief. Someone off camera whispers, “Shhh.” Toni appears muscular, tall, lean and confident. Both girls are black, as are 22 of the class’s 30 students.
Aniyah addresses Toni with a calm “yeah,” and turns back to the board to finish her explanation. “Because there’s seven equal parts like one, two, three, four, five, six and then seven,” she said, positioning her thumb and forefinger like pincers as she counts up the number line from zero past two. It’s a magnificent, clear explanation. Only the answer is wrong.
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The students haven’t been told yet that the correct answer is 1/3. Loewenberg Ball can see from their worksheets that 23 of the students, like Aniyah, haven’t solved it right.
Toni’s hand shoots up and the teacher calls upon her. Toni smiles and plays with her hair. “Why did…,” Toni hesitates.
“Go ahead, it’s your turn,” Loewenberg Ball says.
Toni repeats, “Why did you pick one-seventh?” To my white, middle-aged ears, the pitch of Toni’s voice sounds like she’s taunting Aniyah. “You did not,” says another student across the room. Toni starts laughing, plays with her hair more, and joyfully points at the off-camera student as if they’re in on some joke together. More laughter and hair fiddling ensue.
What would you do in that moment?
Three options teachers commonly choose in the classroom are these, according to Loewenberg Ball:
1. “Toni, when you’re ready to participate appropriately by not playing with your hair and laughing and have a question to ask, I will come back to you.”
2. “You need to be a better listener, Toni. Aniyah already explained why she picked one-seventh. Who else has a real question for Aniyah?”
3. Or the ubiquitous, “What do others think?”
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Loewenberg Ball maps out the consequences to each of these options like a chess game. The first accuses Toni of being off-task. The second accuses Toni of not listening and asking a bad question. All three exclude Toni from the discussion.
“She is seen as being a distraction, maybe mocking Aniyah and playing with her hair,” said Loewenberg Ball.
Loewenberg Ball draws a connection between teacher judgments in small moments like this and why black girls are disproportionately suspended. One of six students in public schools is black, but they account for more than half of girls who are suspended multiple times.
“It is not hard to imagine how Toni could easily be asked to be sent away from the group, or not talk, or be sent out in the hall. And if she’s out in the hall, she’s not learning,” said Loewenberg Ball.
Toni was actually one of the few students in the class to arrive at the right answer of 1/3 on her worksheet.
Loewenberg Ball points out that Toni’s question — why 1/7? — is the key question to ask because it gets to the heart of the lesson, learning how to count the intervals on a number line between whole numbers and not every tick mark on the line. But it can take a veteran math educator who is familiar with students’ common misunderstandings to interpret Toni’s mathematical question. “Toni’s actually listening very closely to a classmate’s presentation,” said Loewenberg Ball. “There is no other question that would have been a better question to ask at that moment.”
The actual classroom played out like a fairy tale. Loewenberg Ball publicly acknowledged the importance of Toni’s question. Aniyah explained her faulty reasoning a second time and it prompted a group discussion that clarified the interval confusion for most students. Toni was one of two students who went back up to the board to model how to locate a fraction on the number line and explain it. On the students’ exit tickets at the end of class, 25 out of 30 were able to answer correctly and explain their reasoning.
Aniyah reflected in her notebook: “I did well on my goal today because my goal was to share my ideas with the class and I did. I went up to the board and shared my idea with the class on fractions.”
I was worried that Toni was teasing Aniyah and I wanted to defend the classroom’s underdog but it seems like the experience of going up to the board and sharing her mistake actually make Aniyah feel more self-confident.
Classmates benefited in two ways from Lowenberg Ball’s praise of Toni. They got the opportunity to see black girls as brilliant. Given the sexist and racist society we live in, those opportunities are rare. And the class had a great math discussion that they might not have otherwise had.
Loewenberg Ball makes the argument that teacher training ought to address these constant judgment calls directly. “We need to scrutinize habits that we’ve come to assume are just neutral practices that aren’t neutral at all,” she said.
Even more, she said, it’s not enough to see when teachers’ implicit biases are creeping into the classroom. She called upon education researchers to develop a “repertoire” of teaching practices that could help counter racist habits.
“The challenge for us,” she told the researchers, “is not to leave to chance that teachers will exercise good discretion.”
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