A Two Hour Algebra Class in Brooklyn (Gotham Schools)

Ryan Hall teaches at Williamsburg Collegiate Charter Middle School. The New Teacher Project named Hall, who got his start as a teacher with Teach for America in 2007, as one of 20 teachers up for the Fishman Prize for Superlative Classroom Practice. Though Hall did not win the $25,000 prize, he was one of  two New York city teacher finalists. A “Gotham School” blogger observed the class and described the lesson on May 11, 2012.

 8 a.m. [A]fter first-period started, Hall’s 21 students were already sitting in silence, scribbling the answers to a set of six mathematical problems. As he does on most mornings, Hall started the class with two timed exercises: the “Cranium Cruncher” and the “Do Now,” which teachers across the city have used to kick off their classes since the Department of Education first mandated the “workshop model” in 2003.

Hall said it typically takes him 30-45 minutes to prepare for the class, which always takes place in the morning.

“The ‘Do Now’ is more like grade-level work, with five to six word problems, and we go over that,” Hall said. “Then there’s one to 12 problems on a ‘Cranium Crunch12.’ It’s a drill sheet — basic skills in isolation, like computation.”

 8:25 With four minutes left on the timer, Hall set up on a SmartBoard at the front of the room. He started to write out the problem the way he expected his students to in their notebooks.

8:29 A siren blared to signal the end of the activity. Hall instructed students to exchange papers with partners seated nearby, who acted as graders, then read off the correct answers in one breath. Each student read back his or her score, and Hall entered the information directly into a spreadsheet projected onto the board, showing data on everyone’s performance.

“Double snaps for these folks,” Hall said, pointing to the high-scorers while snapping his fingers in congratulations.

Why break up the math problems over multiple assignments, and time them? Hall said it’s part of a strategy to pace the class over its two-hour block.

“A big part of it is chunking it out. Otherwise it seems really long and can get really boring, if there aren’t what we call “brightened lines” between activities,” he said. “They need to feel like they’re moving fast to stay engaged. The timer keeps them moving.”

That timer also functions to create “a sense of urgency,” he said, which students carry with them to other classes. “Every second matters here,” he said. “We’re making sure that no one wastes time, and any time we see an opportunity to save instructional time we try to do it.”

8:32 The next exercise Hall prepared for students was called “Mental Math” — it consisted of computation problems for students to do in their heads, standing up so they would not be tempted to write in their notebooks. “Drumroll,” he said to signal the start of the drill, and everyone pounded on the desks a few times before leaping up.

“You can’t sit for two hours; you need to stand up at some point,” Hall said…. It’s also about being on your toes—you don’t have a pencil in your hand, you don’t have a notebook to use. And the kids like it because they get to get out of their seats.”

Like the timer, Hall uses the “drum roll” to mark boundaries between assignments.

“It’s just a mental cue to show that we’ve just done one thing, and now we’re doing something new,” he said. “We call it pacing. Pacing is how fast you move and how fast it feels like it’s moving to the kids. [We want] to create the illusion of speed so kids feel the pacing of the lesson is exciting and they know when they’re moving from one thing to the next.”

Ryan Hall works out a problem on the Smart Board while students take notes.

“Sometimes my mental math isn’t challenging enough for you,” Hall said to the group, as he wrote absolute value equations on the white board. “But I think today is going to be exciting. I know this is something you haven’t seen before.” The students called out the answers when they thought of them.

 8:49 Hall asked students to think about “real life” examples of the mathematical concepts of exponential growth and exponential decay. Several students quickly raised their hands with some ideas: bacterial growth, the slope of a launching rocket, a race car’s acceleration, and a roller coaster track. Hall wrote the examples on the board.

8:56 “Do you guys want to use our brains or our calculators for the next one?” Hall asked. The students seemed split between the two options, so Hall instructed them to find their graphing calculators, which they used to graph a couple more equations.

 9:08 Just over an hour into class, Hall said it was time for “independent practice” — essentially a worksheet with more equations to graph. The students entered data quietly into their calculators, interrupted only when Hall asked a couple of boys to lift their heads off their desks or arms and sit up straighter. They did so without complaining.

 9:13 Hall walked around the room slowly, glancing at students’ notebook papers, joined by Nigel Dean, another math teacher who would be teaching during the next period.

Hall’s classroom walls are decorated with dozens of posters, including a copy of the fight song of the University of Colorado (his alma mater), photos from an end-of-year student trip to Costa Rica he chaperoned last year, and “Top 10 List” of skills and students’ names.

“The Top 10 is a list of mastery data — each skill a student has mastered. It’s one of the ways we prepared for the eighth-grade state tests,” Hall said. “You have a chance to master the top 10 skills you need to know to get a 4 on the state exam. Every one that is colored in is a student who aced their mini-quizzes — five questions on an isolated skill. You have to get a perfect score.”

Another poster spells out the acronym SLANT — Sit up straight, Listen, Ask and Answer questions, Nod for understanding, Track the speaker — a common feature in schools that operated according to a “no-excuses” educational philosophy.

 9:38 Students partnered up to solve a worksheet with five more problems. In the back row, Gabrielle Ramos read the questions aloud while Julissa Palmero drew a graph. They were stuck on the second problem when Hall interrupted them.

Hall said he usually works on new material with the class as a whole group, and reserves individual work for assessments. But he also requires students to work in pairs on certain assignments that require multiple skills.

“I throw in partner work for two reasons: there’s actual value to teaching kids how to work in partners or teams. Learn how to help somebody, how to ask for help, behavioral things I want to teach them,” he said. “And some activities are better done in partners. You’re forced to verbalize what you’re learning. My partners are paired strategically also. Every low kid is paired with a higher kid to support them.”

 9:46 Hall asked the class to take a break to review one student named Sasha’s near-perfect answers on the white board. He told each pair to compare its results to hers, and then move on to problems four and five. “You should be moving much faster,” he cautioned.

“That graphing calculator activity is something that half of them could do well, and maybe half of them would have really struggled,” Hall said. “Each partnership is going to get them through that activity.”

 9:55 Another timer siren buzzed, and Hall instructed students to shift gears again. They started taking a quiz, called the “Exit Ticket,” which they needed to complete and submit before leaving class for the day.

The Exit Ticket, Hall explained, “is a daily quiz, which I grade and track every day to see who mastered what I taught today. And that data drives who I target the next day during the lesson, who I tutor, all kinds of purposes.”

After passing in their papers shortly after 10 a.m., Palmero and Ramos told me they weren’t exhausted at all by the two-hour-long marathon of mathematical problem solving.