Teaching teachers

How do you get students fired up about fractions? Reinvent math class.

PHOTO: Alex Zimmerman
Math Lab co-founder Peter Cipparone walks teachers through the morning's lesson before students arrive.

Earlier this week, Peter Cipparone was ending a meticulously planned lesson when the student he’d called to the board suddenly slipped. Kris, a rising fifth grader, was, Cipparone later said, a “plant” — selected because Cipparone felt confident he could clearly explain the fractions problem at hand to the rest of the class.

But when Kris got to the board, his understanding seemed to vanish. He was supposed to be placing the fraction five-thirds on a number line, but instead he marked off five and one-third, almost four points too far.

With just a few minutes left in class, held at the High School for Fashion Industries in Manhattan, Cipparone had to make a split-second decision: Should he offer the correct answer, or let students leave for the day without a clear resolution?

It was a tough call, but Cipparone knew he had backup. Unlike a traditional lesson, where educators teach in isolation, in this case, Cipparone was surrounded by 21 other teachers who would pore over every element of his teaching once the class ended.

The lesson is part of a New York City program, now in its second year, that is tasked with teaching two groups of people simultaneously: A group of rising fifth-graders like Kris, who spend two hours each day learning about fractions — and a group of educators from across the city who have signed up to improve their own teaching.

The program, known as the New York City Math Lab, gives educators an opportunity to perform the surprisingly rare work of watching each other teach. It also lets them hone an approach encouraged by the Common Core learning standards that many of the participating teachers said they have struggled to perfect: Getting students to learn math not just by practicing problems, but also by having conversations.

“With rules-based teaching, if you don’t understand why you’re doing what you’re doing, then that rule only applies to that very specific type of problem,” explains Kim Van Duzer, a teacher at Brooklyn’s P.S. 29 who co-founded the lab program along with Cipparone and Kate Abell, who have both taught in New York City schools. “If you have an underlying understanding of operations and the number system, you can build on that to answer other sorts of questions — that’s what reasoning is.”

***

For a week during the summer, Van Duzer, Cipparone and Abell host roughly 25 educators with a range of teaching experience who watch the trio perform a sequence of lessons on fractions, sitting on the sidelines of a large classroom as the class works. Then, when the students leave, returning to a summer program offered by the Hudson Guild, the teachers talk about what they saw.

The Math Lab’s emphasis on learning math by talking and thinking about it is clear almost as soon as the students enter the room. A list of the class’ “math community agreements,” posted on a board, reminds students to “add onto each other’s thinking” and “analyze and observe each other’s work.”

Teachers observed students taking in Tuesday's lesson.
PHOTO: Elizabeth Green
Teachers observe students taking in Tuesday’s lesson.

To help students internalize that philosophy, Van Duzer led an activity called “convincing a skeptic,” where students were asked to fold pieces of green paper into squares one quarter the size of the original and then convince their partner that the new shape was, in fact, one-fourth of the original.

Some students struggled to articulate why the squares they folded were one-fourth of the whole piece of paper. “Sometimes my partner asked questions I didn’t understand,” one student admitted. But encouraging students to challenge each other’s ideas paid off later that morning.

After introducing the idea of representing fractions on a number line, Cipparone asked students to begin thinking about whether eight-sixths is greater than one. Nine and 10-year-old skeptical voices quickly emerged.

One student declared that eight-sixths is less than one, only to be told by someone sitting nearby that he had the numerator and denominator confused. The ensuing debate ended when the first student admitted his mistake and leapt at the chance to offer a correct answer in his own words.

Many of the teacher observers said the lab was the first time they were able to watch another educator teach consecutive lessons. Watching others teach, they said, helped them become more confident in their own ability to guide students through conversations about fractions.

“You can read a [lesson] plan, but they do so much more that’s not in the plan — how to elicit students’ thinking, or how to get them to respond to each other,” said Julie Heller, a teacher at Brooklyn’s P.S. 29, where Van Duzer also teaches.

Laura Burns, a 20-year veteran teacher from P.S. 73 who also attended last year’s lab, said the experience gave her ideas about how to tweak her instruction, including posting a schedule outlining the elements of the day’s lesson so students have a sense of where they are headed.

“I can just watch and see everything – the language, the materials, the way they’ve laid stuff out. They’ve agonized over every decision,” she said.

***

As teachers reflected on Tuesday’s lesson, a debate of their own emerged. They began wondering about how Cipparone handled what the group would begin calling “Kris’ problem” — the moment that morning when Kris misplaced five-thirds on the number line and Cipparone had to make a split-second decision about whether to correct him before the students left for the day.

Deirdre Flood, a teacher at Brooklyn’s P.S. 11, said it could make sense to end the lesson ambiguously if “every single [student] made a decision before they left, so they were thinking about it on their way out.”

Another teacher wondered whether withholding the correct answer might leave Kris feeling tricked when he inevitably discovered his answer had been wrong all along. Meanwhile, Abell, one of the Math Lab’s facilitators, suggested a different approach altogether.

“It feels like a terrible thing to not let him finish his idea,” she said. “The question for the community is, ‘What is Kris thinking?’ Because he’s thinking something that makes sense.” Instead of debating whether to correct him or not, she argued, teachers should encourage other students to explain why he came to equate five-thirds for five and a third — because he mistakenly considered five as the whole, rather than the number of parts.

For his part, Cipparone never pointed out Kris’ error that morning. He threw the question back to the class for a quick debate. And even though some students argued their classmate was wrong, Cipparone stood back and facilitated.

“Sometimes you have questions and you don’t get the answers all at once,” he said, just moments before students filed out. “If you’re not convinced, that’s OK!”

ready for prime time

Four ways Amazon’s arrival in New York City could impact public schools

PHOTO: Reema Amin/Chalkbeat
John Schoettler, Amazon's vice president of global real estate and facilities, (left) sits with Gov. Andrew Cuomo and Mayor Bill de Blasio at a press conference about Amazon's announcement to open part of its new headquarters in Long Island City.

After months of speculation, Amazon announced Tuesday that it picked Long Island City for one of its two new headquarters.

Details about the new Queens hub are still emerging, and some of the particulars are already raising eyebrows — including billions in incentives Amazon was offered to locate here. The deal, which officials claim will create as many as 40,000 jobs over 10 to 15 years, will undoubtedly affect New York City’s public school system.

The formal agreement between Amazon and New York City lays out several direct ways that the deal could impact city schools. The company agreed to house a 600-seat intermediate school on or near its Long Island City campus, replacing a school that had already been planned in a residential building nearby. Amazon also plans to offer “career exploration activities” and internship opportunities to high school students. And there is a proposal to relocate some Department of Education offices in Long Island City to make way for the tech giant.

If Amazon’s impact on Seattle, its primary headquarters, is any guide, there could be reverberations felt in New York City classrooms, especially those districts in or adjacent to Long Island City. Still, given New York City’s size and economy, Amazon’s arrival may not create the same sweeping changes — and officials are already trying to reassure New Yorkers.

“The city and state are working closely together to make sure Amazon’s expansion is planned smartly, and to ensure this fast growing neighborhood has the transportation, schools, and infrastructure it needs,” de Blasio said in an Amazon blog post announcing the move.

Here are four potential issues to look out for.

Overcrowded schools

Amazon has pledged to donate space for a new middle school — space that parents say is desperately needed. De Blasio said Tuesday that the school will replace another that had been proposed for the area. “There is no loss of school seats,” he said.

But Meghan Cirrito, a member of the Gantry Parent Association, an education advocacy group in Long Island City, is skeptical that the school will ease the crunch for classrooms. Queens parents have long fought for more school space in the borough. In the Long Island City neighborhood, schools that serve grades K-8 are already at 102 percent capacity.

“It will absolutely not relieve the overcrowding. They will keep up with their own development,” she said. “We’re already behind school seats.”

Deborah Alexander, the co-president of Community Education Council 30, which includes Long Island City, echoed that the school plan feels like “a pittance.”

“We’re still playing catch up for the city’s lack of infrastructure in Long Island City,” she said.

The need for more classrooms could also have consequences for de Blasio’s push to make pre-K available to all the city’s 3-year-olds, an effort the city is rolling out slowly in part because of existing space constraints.

But even if thousands of students arrive with new Amazon employees, they will still represent only a drop in the bucket of the city’s 1.1 million public school students. De Blasio cautioned at Tuesday’s press conference that while some employees will live in the neighborhood, not all will move to Long Island City and some may commute from other areas. Still, the neighborhoods around Queens are some of the most crowded school districts in the city.

Concerns about the city’s record student homelessness

Seattle has struggled to address a surge in homelessness as home prices have soared more rapidly in the city than anywhere else in the country — an increase that many have attributed to its booming tech sector.

As the number of high-earners there has shot up, so has student homelessness, which has increased threefold between 2011 and 2017. But when the city tried to pass a new tax dedicated to boosting services for the homeless, Amazon led a campaign against the measure, which eventually died.

Amazon is promising to pay an average salary of $150,000 in New York City. In the school district that will host the tech giant’s new hub, about 72 percent of students come from low-income families.

In New York City, the number of homeless students is already at an all-time high. More than 114,000 students here lack permanent housing, which poses challenges for schools that may struggle to meet the needs of children who often lag behind their peers on academic measures.

Schools Chancellor Richard Carranza recently announced the education department would hire 100 new employees to help schools with high concentrations of homeless students.  

De Blasio said the arrival of large companies such as Amazon could exacerbate homelessness in other cities that “don’t have substantial affordable housing, are not building a lot of new affordable housing,” specifically calling out San Francisco.

But, he said, the impact of tax revenue from Amazon’s move will be “central” for supporting existing affordable housing in New York City.

Other changes in student demographics

School leaders in Seattle say the number of students who are learning English as a new language has jumped with Amazon’s growth, opening the need for teachers and curriculum to serve those students.

New York City has rapidly expanded its language programs under de Blasio, which are often seen as a tool to help spur more diverse schools. But the education department has also historically struggled to serve English language learners well.

Amazon’s move could have other effects on school diversity at a time when advocates have put increasing pressure on the the city to step up integration efforts. New York City schools are among the most segregated in the country, an issue that Carranza has pledged to tackle.

But with more higher-income families potentially lured to Queens by Amazon jobs, Cirrito worries about gentrification in a borough and neighborhood known for its diversity, and the effect that could have on classrooms.

“How can we say we welcome new Americans here if they can’t afford to live in Long Island City and they can’t afford to live in neighborhoods where their kids have good schools?” she asked. “At the time we have a chancellor in place calling for the desegregation of schools, this seems to be a move that will completely undermine his efforts.”

Even if low-income families live side-by-side with Amazon’s workers, it’s not at all clear their children will learn together. Long Island City is home to the New York’s largest housing project, and whether high-earners would opt into schools where many students are poor is an open question.

A philanthropic boost?

New York’s agreement with Amazon doesn’t offer many details about how the company will interact with or the nation’s largest school system, but it does include a promise to create internships and “work-based learning opportunities” — including activities such as career days and mock interviews.

What that will look like, and whether a bigger stream of philanthropic support could follow, is unclear. Amazon has offered some support for public education in Seattle, including supplies for needy students. And its founder, Jeff Bezos, recently announced a $2 billion investment to launch a network of preschools in low-income communities.

Kathryn Wylde, the president and CEO of the nonprofit Partnership for New York City, which serves as the business community’s lobbying group, said she hopes Amazon’s presence helps fuel career and technical programs in city schools.

“The frustration has been a lack of employer engagement in opportunity for [career and technical education] and workplace opportunities,” Wylde said. “Obviously this is a bonanza in providing those opportunities.” She added that Amazon could support schools similar to Brooklyn’s P-Tech, a high school that partners with IBM to offer students opportunities in the tech sector. (Wylde said there were no concrete plans in place yet for Amazon to participate in such a partnership.)

Others were less optimistic.

Alexander, the co-president of Community Education Council 30, said she hopes the city would partner “as much as possible” to harness any investments Amazon is willing to make in public schools.

Still, she added, “It sticks a little in my craw —  the richest person in the world getting billions of dollars in money from New York State when New York State owes schools so much money.”

“It’s hard to see what internship or guest speakers or whatever could make that balance.”

Chalkbeat live

Education for all? Let’s talk about that, Chicago.

Since Chalkbeat Chicago launched in June, we’ve convened small gatherings of parents, educators, school council members, and community leaders to talk about city schools.

On December 12, we’re hosting our biggest public forum to date — with pie! — on the topic of Chicago’s next mayor and the future of schools in the city.

  • Which items should top the next mayor’s schools agenda?
  • How do we build on successes like the district’s record-high graduation rates?
  • And how do we grapple with persistent challenges such as declining enrollment and equity gaps in performance and resources?

We are inviting educators, students, advocates, policy makers, and more to join us for this critical conversation. Taking part in the centerpiece panel will be Chicagoans with experience in and around schools including:

  • Jesus “Chuy” Garcia, founder of the Little Village Community Development Corporation and newly elected congressman from the 4th District
  • Elizabeth Swanson, vice president of strategy and programs at the Joyce Foundation and the former deputy chief of staff for education for outgoing Mayor Rahm Emanuel
  • Daniel Anello, CEO of Kids First, which produced a new report that examines school access and capacity on the city’s South and West sides
  • Jitu Brown, national director of the Journey for Justice Alliance

Guests will be encouraged to record a message to the city’s next mayor in our storybooth and to network with other people who care about public education and Chicago youth. The evening also will feature student performances and a coffee-and-pie reception with treats from Justice of the Pies and Dark Matter Coffee.

The event is free and open to all ages, but space is limited and registration is required. RSVP here.