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!”

Future of Schools

IPS students have made their high school choices. Here’s where they want to go.

PHOTO: Dylan Peers McCoy

High schoolers across Indianapolis Public Schools have made their choices for next year, and some schools are proving far more popular than others.

With all but four high schools set to close, the district is already in the midst of an upheaval. Students’ choices this year could have far-reaching implications for the configuration of the district for years to come.

Shortridge High School had the greatest increase in demand, with more than triple the 400 students enrolled there now listing it as their first choice for next year. George Washington High School, which also enrolls more than 400 students now, is not likely to grow too much. And while Arsenal Technical and Crispus Attucks high schools are both likely to grow by hundreds of students, neither saw interest grow as exponentially as Shortridge.

The final enrollment at each school will determine such critical issues as how many teachers are hired, what courses are available to students, and how much it costs to operate the buildings. Ultimately, students’ choices are likely to shape course offerings over the next several years, district officials said.

The enrollment figures are the result of a district mandate requiring students from across the district to select high schools and magnet programs this fall. More than 90 percent of 8th to 11th grade students have made selections so far. All students will be placed in their top choice program, according to the IPS spokeswoman Carrie Cline Black.

Fewer than 500 IPS students have chosen programs at George Washington so far, according to district data obtained exclusively by Chalkbeat. In contrast, more than 1,300 students have selected Shortridge, which will house the arts magnet program currently at Broad Ripple and the International Baccalaureate Programme. More than 2,300 students have chosen programs at Arsenal Tech (currently the district’s largest high school with 1,826 students) and 1,050 have selected Crispus Attucks (which currently enrolls 695).

The uneven distribution of students did not take  Superintendent Lewis Ferebee’s administration by complete surprise.

At an Indiana State Board of Education meeting on Oct. 4, state Superintendent Jennifer McCormick asked, “What happens if you don’t have a nice, somewhat-even distribution? … What if it’s very out of whack?”

Ferebee said that the district will have room to accommodate students if a school proves especially popular. In the long term, he added, IPS may have to adjust, by replicating  popular programs and discontinuing unpopular ones.

But Ferebee also said the district was hoping to persuade students to take another look at some of the programs that might not be popular at first.

For instance, he said, “We do know it’s going to take some time to educate families on construction and engineering. So we knew out of the gate, not many students may be interested, so it will take some time to build a program.”

Here is a full breakdown of the schools and programs that students chose:

In total 5,142 IPS students chose their preferred programs as part of a broad reconfiguration plan that includes closing nearly half of the seven high school campuses because of low enrollment. The district has not provided projections of how many students would enroll in each high school. But if enrollment doesn’t shift in the coming months, some campuses will be far closer to capacity then others. While the initial deadline for choosing schools and programs has passed, enrollment remains open to any students who have not yet made their selection.

If no other students enrolled in IPS high schools, Shortridge would be nearly 89 percent full. Arsenal Tech and Crispus Attucks would each be over 76 percent full. And George Washington would be about 25 percent full.

At the four remaining high school campuses, the district is aiming to “reinvent” high school by vastly expanding specialized programs in subjects such as business, engineering, and the arts, which students will study alongside their core classwork.

Next year, every student will be enrolled in specialized programs within high schools. District leaders hope that students will choose schools based on their interests, rather than their neighborhood.

Principal Stan Law will take over George Washington next year. In an interview about the school last week, before IPS released student selections numbers, Law said that it was important for students and families to get accurate information so they would select schools based on student career interests rather than neighborhood.

“Everyone has their ideas about things, but only certain people have the accurate information,” he said.

The most popular programs are the health sciences academy at Crispus Attucks and the Career Technology Center at Arsenal Tech, where students can study subjects such as culinary arts, welding and fire rescue. Each attracted more than 900 students. The least popular are the teaching program at Crispus Attucks, chosen by  104 students, and the information technology program at George Washington, chosen by 80.

Despite its apparent unpopularity with IPS students, the information technology program fits in with a state push to prepare students for careers in computer science and related fields. Gov. Eric Holcomb’s legislative agenda calls for requiring high schools to offer computer sciences classes, and the Indiana Chamber of Commerce wants computer science to be a high school graduation requirement.

breaking

Breaking: Indiana didn’t set aside enough money for schools. Senate leader says a fix is ‘top priority.’

PHOTO: Photo by Shaina Cavazos/Chalkbeat
Students at Global Prep Academy, a charter school, learn about comparing shapes. All schools could see less funding if lawmakers do not fix the funding shortfall.

State education officials are expecting a shortfall in school funding this year that could be as high as $9 million because state and local officials underestimated Indiana’s student enrollment.

If the legislature does not act to increase funding, districts, charter schools and private schools that receive state vouchers could all get less money than they were promised this year.

Senate President David Long said new legislation to appropriate more money to schools would be proposed, though other lawmakers involved in budget-making were less certain on what a solution would look like this early.

“It’s our top priority, education is, so it’ll have our full focus when we come back in January,” Long said.

But on the upside, he said, public school enrollment increased since last year.

“It’s not a bad problem,” Long said. “We have more kids going into public schools than we did last year, but it’s a challenge for us only in a sense that we need to adjust our numbers.”

A memo from the Indiana Department of Education said the legislature’s budget appropriation was short by less than one-half of 1 percent. When the amount the legislature allocated for school funding does not line up with its funding formula, “the law requires the Department to proportionately reduce the total amount to be distributed to recipients,” the memo said.

It’s not clear how the miscalculation in enrollment numbers occurred, said Rep Tim Brown, a key budget-writer and chairman of the House Ways and Means Committee. The budget dollars are estimated based on projected school enrollment counts from districts themselves, the education department and the legislative services agency, which helps provide information and data to lawmakers.

Brown urged people to keep the number in perspective, especially since the budget is crafted based on estimates. Brown said this was the first year since he became involved with budget writing in 2013 that projected budget allocations ended up being less than school enrollment, which was calculated based on counts from September Count Day.

“We’re looking at what our options are, but let us keep in mind it is $1.50 out of every $10,000 a school gets,” Brown said, adding that he wasn’t sure this early on how lawmakers would act to make up the shortfall.

But J.T. Coopman, executive director for the Indiana Association of Public School Superintendents, said even small amounts of money make a difference for cash-strapped schools. Districts have already started making contracts and have obligations to pay for teacher salaries and services at this point. It’s pretty late in the game for this kind of news, he said.

“I did see that it’s less than a half a percent, but for schools that’s a lot of money,” Coopman said. “Can we get this fixed before it becomes a real problem for school districts?”

Indianapolis Public Schools Superintendent Lewis Ferebee, who leads a district that is already in deficit, was optimistic. In a statement, he said, “we’re encouraged by the commitment and urgency demonstrated by our legislative leaders.”

Neither Brown nor Long knew how much public school enrollment had increased. The $32 billion two-year budget passed in April increased total dollars for schools by about 3.3 percent from 2017 to 2019, for a total of about $14 billion. Included within that was a 2.5 percent average increase for per-student funding to $6,709 in 2019, up from $6,540 last year.

The news of a funding shortfall comes as the state continues to see declining revenue. The Northwest Indiana Times reports that state revenue is down $136.5 million (2.8 percent) from what lawmakers estimated this past spring for the next two-year budget.

During the annual ceremonial start to the 2018 legislative session today, leaders discussed a need to provide more resources to schools and the state board of education. So far, many of the priorities involving education this year look to address workforce needs and encourage schools to offer more computer science courses.

But House Speaker Brian Bosma also shouted out “innovative” steps made by Indianapolis Public Schools and Fort Wayne Public Schools.

“People are trying something different and they are having great results with it,” Bosma said. “We need to give them more tools, we need to give them more opportunities.”