Teacher, Teach Thyself: In Pursuit of a Better Classroom

When Deborah Loewenberg Ball arrived at the Spartan Village school in East Lansing, Michigan, in the fall of 1975, it did not take long for the other teachers to size her up. “A natural-born teacher,” said Mindy Emerson, the teacher across the hall.

Other new teachers went through a predictable litany of challenges. They couldn’t get the students to listen, they tried too hard to be the students’ friends, they doubted whether all the children could really learn, they struggled to feel comfortable in the new role. But if Deborah felt any of the typical jitters, she did not show it. She had a calm, gentle way with the children, connecting even with the ones who came unable to speak English. Her discipline struck that rare balance, leaving the children both happy and well behaved.

Even the new principal, a young woman named Jessie Fry, had to admit that there was something extraordinary about Deborah. She scrutinized every teacher under her watch, but after observing Deborah, all she could say was, “Great!” and “Thank you!” Within two years, Deborah was petitioning her to create an unheard-of first-, second- and third-grade combination class with another teacher. And, call Jessie naïve, but she heard herself saying yes. She even let Deborah drag in a working refrigerator and stove off of the street and into her classroom — for cooking lessons.

Some of the older teachers, already annoyed with Jessie, began to grumble. Why didn’t every classroom have a stove? But as the years passed, the grumblers became acolytes. They rearranged schedules so that their students could use Deborah’s stove. They requested subs so that they could leave their own classrooms and watch Deborah teach. And sometimes, they invited her to join them in theirs.

By 1980, only one person in all of Spartan Village doubted Deborah’s gift. That was Deborah.

***

Mindy, Jessie and the others had one thing right: teaching had become Deborah’s passion. But she did not find it easy. To the contrary, her favorite part about teaching was how hard it was.

Take the puzzle of how to teach children to read—a mystery for any literate adult, but especially so for Deborah, who had learned to read at age four and could not remember a time when words weren’t synonymous with sounds and meanings. The job of a teacher was to explain to others what you already knew by heart. Adults know intuitively all the different ways that “ea” can be pronounced, depending on the context. But teachers needed to be able to explain that break, beak, read (present tense) and read (past tense) all make different sounds.

The greatest teaching problem Deborah encountered arose in 1980, when, teaching fifth grade, she discovered that her students were struggling with math. And not just a few of them. All of them. One day, 25 notebooks would fill with perfect little number houses as she walked them through the steps of long division. The next day, left to reconstruct the steps alone, the children would flounder. It did not escape Deborah’s notice that a sizable number of these clueless students came from the very same first-, second- and third-grade math classes she had taught with apparent success a few years before. What had she been doing when she thought she was teaching? What had they been doing when she assumed they were learning?

Stumped, she took her problem to a professor back at Michigan State’s College of Education, where she’d gotten her degree. The professor suggested that she try out a new experimental curriculum for elementary school math.

“Experimental” put it mildly. For first grade alone (Deborah had moved again after teaching fifth), the teacher’s guide filled more than 700 pages. The curriculum was strange, suggesting that lessons move forward according to scripted discussions about, in one case, an elephant named Eli.

Deborah had held discussions in reading, where students could talk about stories—discussing the characters and what the students thought might happen next—and in science, where they could guess the results of an experiment. But she had never led a discussion about math, and despite the assurances in the teacher’s guide, she wondered whether her students would really have much to say. 2 + 2 always equaled 4. What was there really to discuss?

Yet when she tried it, the curriculum began to show its wisdom. Eli the elephant, for example, turned out to love peanuts—and his peanuts took two forms: regular peanuts and “magical” ones, which were like negative numbers. When a regular peanut and a “magical” one met, it was like adding 1 and –1: both disappeared. Following the story, Deborah’s first-graders quickly picked up the idea of negative numbers—a concept that often befuddled much older students.

In discussions, meanwhile, the challenge wasn’t in getting the students to talk, but in making sense of all they had to say. The deeper into the math the students got, the more questions they presented to their teacher. For instance, are there “afinidy” possible ways to use a 24-story building’s elevator to get to the second floor—or are there 25? What exactly did it mean to add a negative number? What about to subtract one (for example, 3 minus −5)? Even rudimentary ideas now raised complicated questions that Deborah felt unprepared to answer. Talking about math was surprisingly interesting, but for the talking to lead to learning, it seemed the teacher needed to know something more.

Once again, Deborah turned to Michigan State, this time not to the College of Education, but to the Department of Mathematics. As an undergrad, she had tested out of math completely. Now she started from the beginning, venturing through elementary algebra, geometry, and calculus while her students studied addition, subtraction, and fractions. The courses produced some exciting aha! moments, as when the details of limits and integrals helped her steer students through a problem about area.

The most important revelation arrived in her final course: Number Theory. Taught by the chair of the math department, a professor named Joseph Adney, the class addressed a mathematical subject Deborah hadn’t studied before (one deeply relevant to an elementary school teacher). And, even more important, Adney taught it in a new way. Instead of marching methodically through a list of concepts, he invited his students to discover the ideas for themselves. He’d write something on the board and then ask, with a straight face, “Is that always true?”

Discussions in Adney’s class were not just fun ways to pass the time. They were vital to the work of doing math. By talking about math—puzzling over problems, making conjectures—they practiced it. In the process, Deborah—the classic humanities type, who never took a single left-brained class in college—fell in love with the subject. The math she’d learned in school was dull, rote, blah—“uninspiring at best, mentally and emotionally crushing at worst,” she wrote not long after taking the class. Adney presented a different subject altogether. In his class, math was powerful, rich, even awe-inspiring. For days, a problem boggled. But then someone would offer another way of looking at it, and suddenly it would make sense.

***

What would it look like to teach elementary school children math in the way she was learning it? One summer, Deborah decided to experiment. She had agreed to run a summer course for eight- and nine-year-olds that was also supposed to be a professional development opportunity for other teachers. Together, she and the teachers could try out a new way to teach math. Technically, only Deborah taught the children. But really she was the group’s surrogate—a kind of “pedagogical daredevil,” she decided, trying out ideas on everyone’s behalf. Every day, before the children arrived, the teachers walked through the lesson Deborah had drafted, trying out problems, imagining how students might react, and discussing what Deborah might say in response. When the lesson began, the other teachers served as extra eyes and ears, studying each child and noting what they did and did not understand. At the end of each day, Deborah had the students leave their notebooks behind so the teachers could study those too. Then they all sat together and talked about what had just happened. What did everyone think about what this or that student had said? What ideas did the class still not seem to grasp? What should Deborah do tomorrow?

Deborah came to call the experience a teaching lab, and over the course of many labs, the most productive methods and problems made themselves clear. One good approach was to have students with different ideas present them to the class. When one student got confused about, say, fractions, some of them undoubtedly shared the misunderstanding, in one form or another. Listening to their peers could help the confused students sort out their ideas.

The lab group also studied turns—which students Deborah called on, in what order, and what she asked each of them to do. Her decisions came to hold more significance over time, as she learned the many different types of turns, each with varying dimensions of both academic difficulty (offering a math fact versus offering an interpretation) and social risk (giving an answer even though you hadn’t raised your hand was moderately risky; coming up to the board and offering a detailed description of your incorrect answer, much more so).

Other considerations mattered too. To make sure everyone participated, it was advisable to call on the three students who had not spoken yet, but this might not be a good strategy if all three had the same answer. Over time, more conventions emerged. It was crucial, for instance, to make sure that students did not talk just to Deborah, but to the entire class. Everyone had to learn everyone else’s name. Then, instead of saying “that weird idea about one-half and one beside it,” they could simply say “Shamar’s idea” or, if Shamar posited an argument, “Shamar’s conjecture.”

Deborah came to see these named conjectures as “fence posts” for a productive conversation. The students could peer backward over the landscape of their evolving understanding and name the key turning points. And when another part-whole misunderstanding inevitably arose, they could undo it more quickly by thinking back to Shamar’s idea and the reasons it didn’t hold up.

***

Deborah, now dean of the University of Michigan School of Education, still holds her summer labs to this day. They have changed in size, rather than form. Instead of a small group of local teachers gathering informally around the side of a classroom, the lab class is now held in an auditorium at the University of Michigan, and observers now sit in stadium-style bleachers. But the point of the lab still stands: the children learn a lot of math, and Deborah and the teachers learn a lot about teaching. The structure has created teaching that truly seems to work. Children leave able to solve problems, and teachers leave with a better understanding of the kinds of problems, questions, and approaches that will work.

The evidence first emerged back at Spartan Village, where Deborah continued teaching elementary school for more than 15 years. Now that the students conjectured, reasoned, argued and proved, they were building one idea on top of another. They sometimes forgot what they’d learned, like all students do. But now, when they stumbled, they could pick themselves up. Deborah saw it happen one day a few weeks into the fractions unit, when two third-graders were puzzling over a problem about cookies that involved the number 4⁄2.

“How can we have this?” Betsy asked Jeannie, pointing to the confusing fraction.

“I don’t know,” Jeannie said.

“Four twoths?” Betsy asked.

“We take something and divide it into two parts . . . and take four of those parts?” Jeannie asked.

“I’m confused,” Betsy said.

“Me too,” Jeannie said.

Just then, Sheena walked up. “Four halves, isn’t it?”

“Yeah!” Betsy exclaimed. “Four halves! Halves are two parts. So . . .”

“So we need two cookies and cut them each in half, then we have four halves,” Jeannie said. “One, two, three, four. Twoths. I mean halves.”

They were really learning. And so had Deborah. Teaching, she realized, was not a talent naturally born in anyone. To truly help their students learn, teachers had to learn, too.

Excerpted from Building a Better Teacher: How Teaching Works (and How to Teach It to Everyone) by Elizabeth Green. Copyright © 2014 by Elizabeth Green. With permission of the publisher, W. W. Norton & Company, Inc. All rights reserved.