Algebra for All

This Bronx elementary school is changing the way it teaches math — and it’s showing results

PHOTO: Christina Veiga
Fifth-grade student Darmairys Henriquez, center, presents her work to her classmates.

Fifth-grader Darmairys Henriquez used a green marker to write her answer to a math problem on a big poster board. Her classmates at P.S. 294 stopped by in small gaggles to take a look at her work.

The question: 3 + 6 – 2 x 4.

The students were learning how to use grouping and the order of operations to solve a math equation, but it would be at least 30 minutes before teacher Nicole Lent would stand in front of the class and reveal the answer.

This approach is part of a citywide effort to make sure all students pass algebra by the end of ninth grade — paving the way for college and high-demand careers.

In 67 elementary schools across the city, including P.S. 294, fifth-grade math instruction has been “departmentalized” just like in middle or high school. Instead of sticking with the same classroom teacher for every subject — reading, writing, math and science — students have a teacher responsible only for math instruction.

The idea behind the city’s Algebra for All initiative is to have the most dedicated and effective teachers focus on this critical subject area, an approach backed by research.

“There’s still a lot of anxiety among elementary teachers about teaching math, and they still cling to the textbook,” said Clara Hemphill, who coauthored a report about math anxiety for the New School’s Center for New York City Affairs. “One way to break through that is for an elementary school to pick a teacher who really loves math and [have him or her] teach all the students in fifth grade.”

With a solid foundation in elementary school, the city hopes students will be ready to tackle math in middle school — and higher-level courses such as calculus in high school.

“It is a building block for college readiness,” said Matt Larson, president of National Council of Teachers of Mathematics.

P.S. 294 in the Bronx has embraced the model, with specialized math teachers in not just fifth grade, but starting in third grade. One teacher serves as a coach for her fellow math instructors, allowing the strongest teachers to share what works and problem-solve when lessons go wrong.

Along with departmentalization, P.S. 294 launched a whole new way of teaching math, using a method that encourages students to engage in discussions the same way they might debate literary themes in a book club.

“In a lot of schools, literacy takes the forefront,” said Principal Daniel Russo. “What we do here is try to build the strongest, most inquisitive, abstract mathematicians we can.”

First, students try a problem on their own, and then debate it with their classmates, defending their answers or changing their minds entirely based on the input of their peers.

With her classmates gathered around, Darmairys began her defense: “So what I did was I added,” she said, describing her approach. She added parentheses around one part of the equation so it read 3 + (6-2) x 4.

“I got a total of 28,” she said. “I’m ready for questions and comments.”

That was the cue for her classmates to jump in. A boy who came to a different answer — 1 — was the first to speak up.

“You were supposed to just get 1, because you didn’t really need parentheses,” he said. “I thought it was just simple. You were just supposed to add.”

Lent had been floating around the room with a clipboard, but now she stopped by Darmairys’s group to listen in. She asked a few leading questions, like “Do I really need parentheses?” But Lent stopped short of providing any answers, even when her students came up with wrong responses. (The answer, by the way, was 1).

Instead, the students were left to explore the possible solutions and methods together. Eventually, one boy noticed his classmates came to different conclusions depending on where they placed their parentheses in the equation.

PHOTO: Christina Veiga
Students in Nicole Lent’s fifth-grade math class at P.S. 294 debate the correct way to solve a problem.

From the outside, Lent’s teaching seemed largely invisible. But everything was carefully curated, from the type of problem students were asked to solve to the students who were asked to present their particular approaches.

“It’s a lot of thinking on your feet,” she said. “You’re always looking for what is going to bring the most discussion.”

Class had started with a problem that was intentionally different from anything they had seen before. Lent looked over their shoulders as they worked, marking on her clipboard groups of students who used different strategies to come to different conclusions. Next she chose students to present their work, picking those who had some parts correct but demonstrated different misconceptions.

Lent said this kind of teaching “did not happen overnight.” But she “always felt more comfortable” teaching math, and passionate about sharing it with students.

PHOTO: Christina Veiga
Teacher Nicole Lent breaks down the different strategies students in her fifth grade class used to solve a math problem.

P.S. 294 was already using the model, along with “departmentalized” math teachers, when the city announced its Algebra for All initiative. The school joined the program to take advantage of extra training and resources. Teachers involved in Algebra for All receive at least 17 days of training, and P.S. 294 landed a city grant to pay for materials and professional development sessions tailored to the school’s needs after Lent noticed teachers needed help teaching fractions and algebra. Lent said the trainings were instrumental.

“It changed my way of thinking,” she said. “I always thought you had to teach the easiest way to just get an answer, and that is not the case. It really opened up my mind to thinking about the how and why.”

P.S. 294 overhauled its math instruction three years ago and “departmentalized” last year for the first time. Their first round of test results suggest the new approach is paying off.

In Lent’s class, 23 percent of students have a disability, 35 percent are current or former English Language Learners and 29 percent live in temporary housing. Another 19 percent have repeated a grade.

Yet the school’s students outperformed city and district averages on last year’s state math tests, with 53 percent of students passing, compared with 40 percent across the city. Students who are learning English — typically among the lowest-performing subgroup — improved their scores by 9 percentage points.

In the high-stakes environment that schools operate under, Russo hopes schools like his will encourage other principals to try new approaches to math. He understands the pressures well: P.S. 294 opened in the place of a school that was phased-out after struggling for more than a decade.

“If I don’t know for sure that this model is going to push my scores and my children, I’m afraid to try it, because I have so much to lose,” he said. “I think that when the Algebra for All schools come out with some data that’s trending a little bit stronger, that will pique the interest of more schools.”

Russo admits it takes the right teachers and leaders to make an approach like theirs work. The Department of Education has made departmentalization optional at elementary schools. So far, about 400 teachers across the city have gotten professional training to encourage the same kind of strategies that are in place at P.S. 294.

“We’re really focused on helping teachers understand the content and giving teachers … strategies to teach the content,” said Carol Mosesson-Teig, senior director of mathematics for the department. “We want to make sure that kids have a sense that they belong they belong in the math classroom.”

How I Teach

It’s not just about getting the right answer: How a fifth-grade teacher pushes her students in math class

PHOTO: Christina Veiga
Teacher Nicole Lent breaks down the different strategies students in her fifth-grade class used to solve a math problem.

At P.S. 294 in the Bronx, math is often a matter of debate.

In Nicole Lent’s fifth-grade class, groups of students take turns explaining how they solved the math problem of the day, respectfully disagreeing or enthusiastically lending support to their classmates’ arguments.

Lent floats around the room, asking probing questions but stopping short of revealing the right answer — opting to let students figure it out together instead.

“I always thought you had to teach the easiest way to just get an answer, and that is not the case,” she said. “I wasn’t giving them the opportunity to think critically about the problem and explore it in different ways.”

Lent is one of a team of teachers at P.S. 294, The Walton Avenue School, who focus only on math instruction. The city Department of Education has encouraged elementary schools across the city to take the same approach, called “departmentalization,” as part of its Algebra for All initiative. By placing the most capable teachers in charge of math instruction in fifth grade, the city hopes all students will be able to pass algebra by their first year of high school.

P.S. 294 has embraced the shift, starting departmentalized math instruction even earlier — in third grade. That’s in addition to its discussion-based approach. Lent has had a role of ushering both changes into the classroom.

She began using math debates and discussions after visiting another school that used the same model, and feeling struck by what she saw.

“I just remember going to those classrooms and thinking it was the coolest thing to see kids having a discussion,” about math. “I was just like, ‘How do I get my kids to do that?’”

The answer came through professional training offered by the city, along with picking and choosing the teaching resources that worked best for her needs. Soon, Lent’s new method spread throughout the school.

Now, half her time is spent in the classroom, and the rest of her day is spent working with her fellow math teachers as an instructional coach. She visits classrooms and regularly welcomes teachers into her own, all in an effort to provide constructive feedback, troubleshoot lessons and perfect new teaching strategies.

“It’s a different type of rewarding experience than working with children, but you see the same kind of growth,” she said. “We’re always working together to drive our instruction.”

This interview has been condensed and lightly edited.

Why did you become a teacher?

I never saw myself at a desk job where every day was the same. The great thing about teaching is that every day is different and truly rewarding, as you get to see your students grow and show progress over an extended period of time.

What does your classroom look like?

The students are the focal point of the room. You won’t find a teacher’s desk in my room. Around the perimeter are bookshelves containing student supplies … and “anchor charts” for students to reference … One example of an anchor chart would be to have the steps to adding fractions with unlike denominators, with the example of each step written out.

Students are permitted to get up at any time to access the supplies they need without asking for permission. We have set the expectation that they are in charge of their own learning and can self-assess when they need a resource to help them persevere through math tasks.

You had to learn a whole new way to teach math. What was the hardest thing about making that shift?

The hardest thing for me when making the shift from a teacher-led classroom to an approach that’s based on student inquiry and discussion was a shift in teacher mindset so as not to associate student conversation with off-task behavior.

What advice would you give to school leaders or teachers who might be considering departmentalizing math instruction?

I would advise them to start small and pilot departmentalizing on one grade first to see if it’s something they want to invest in doing at additional grade levels. We did this at P.S. 294, when I taught fourth grade last year, and it was very successful. We were able to work out any challenges and adjust what was necessary because we started small. At P.S. 294, we are now departmentalized on grades 3-5 for both [English Language Arts] and math. Teachers now receive the support they need and are focused on the content area they teach and have become true experts in their practices.

Fill in the blank. I couldn’t teach without my _____________.

I couldn’t teach without my computer because technology now plays a crucial role in education. Without my computer I wouldn’t be able to play instructional videos for my visual learners or have students come up to the Promethean board (an electronic whiteboard) and manipulate math content, which plays a pivotal role in assisting them in understanding math content.

What is one of your favorite lessons to teach? How did you come up with the idea?

One of my favorite lessons to teach this year was on division of fractions. I always thought we had to teach it using the strategy I learned as a child known as “keep, change, flip.” That’s a strategy used to solve an expression such as 1/4 divided by 3. You would keep the fraction, change the sign from division to multiplication, and flip the whole number from 3 to a fraction of 1/3. The quotient is 1/12.

I didn’t know exactly why this strategy works, I just knew it did.

After attending one of the Algebra for All professional developments last summer, I learned from a colleague at another school how to use visual models: We draw three “wholes” and divide each whole into fourths. The quotient is one piece out of the twelve total pieces you have from all three models (wholes you drew). We ask the students to think about the question: “How many fourths fit in three?” When it came time for me to teach them to my students this year, I knew exactly how to show them to divide fractions by whole numbers and by fractions in a purposeful and meaningful way.

How do you respond when a student doesn’t understand your lesson?

After a quick check for understanding that takes place after my mini-lesson, students who don’t understand my lesson meet in a small group with me on the carpet, while the rest of the students engage in differentiated math tasks on their level independently at their seats. During this time, I reteach students using a different method than the first time. This includes the use of manipulatives, instructional videos, and whiteboard work. Once I re-teach the concept using a different strategy, I conduct another quick check to see if they mastered the concept, and if so, they then go off independently to try some math tasks on their own.

How do you see your role as an instructional coach? What do you think is the most effective way to help other teachers improve their practice?

My role as an instructional coach is to build capacity across the school in the area of math instruction. Ultimately this means pushing practices down: taking the rigor and instructional approaches used at the 3-5 level and adjusting them to be used at the K-2 level according to the students’ individual needs.

The most effective way to help other teachers improve their practice is to hold debrief sessions following classroom visits, co-teaching sessions, or modeling lessons in their classroom, and providing actionable feedback that they can implement immediately.

What’s your go-to trick to re-engage a student who has lost focus?

Oftentimes, it takes some time to realize a student is lost and you don’t know exactly where they began to get lost. To avoid guessing and confusing them some more by repeating the last thing I said, I will restart and go step by step from the beginning while having that student assist me. Engaging the student along with the teacher has been the best strategy because you know they are listening and following along, because they are personally and directly involved with the teacher.

Your school has a common planning period. Has that helped change the way you teach?

Common planning periods bring teachers together to learn from one another and collaborate on projects.

During a recent common planning session, we had a consultant from Silicon Valley come and teach us about the difference between re-teaching vs. re-engagement lessons. Re-teaching lessons teach content again to a group of students who didn’t master it the first time. Re-engagement lessons allow students to work with a task to build mathematical ideas.

He showed us the data surrounding re-teaching vs. re-engagement lessons, which indicated that re-engagement lessons are what build students’ critical thinking skills. I realized that instead of having re-teach lessons built into my math block each day, that it would be much more beneficial to my students to participate in re-engagement tasks more often, as research had shown that that’s what truly pushes their levels.

Tell us about a memorable time — good or bad — when contact with a student’s family changed your perspective or approach.

A few years back, one of my students who had always been a Level 4 student [top-scoring on state, city and school assessments] started to act out in negative ways, not complete her homework, and be disruptive during lessons. After several warnings, I decided to call home to speak to the parent to notify the parent as to what was going on. As it turned out, this student’s father had recently moved out of state as the parents were getting divorced. Her mother said she was not taking it well and was acting the same way at home.

I asked the student to stay with me during her recess and spoke to her about what was going on at home. After some time, she finally opened up to me and let me know about her parent’s divorce.

We shared our own personal stories, and I was able to connect with my student on a much deeper level, and let her know that I am here for her any times she needs an ear to listen. From that day on, the student confided in me as she needed to and improved her effort and behavior in the classroom.

What’s the best advice you ever received?

A colleague told me that, “As educators, we learn best from our students.” I thought that had been the silliest thing as I had considered myself the head of the classroom who was supposed to know everything. As I began to dive deeper into my career, I couldn’t agree with her more.

My students have taught me that teaching is not black and white. There is no perfect science to it. Everything we do as educators is based off of what our students know and do, resulting in continuous reflections on our own practices. What needs to be modified? What needs to be revisited the following day? What shouldn’t be done anymore? What can I do further to push or help my students? What worked and what didn’t work? [These] are things we reflect about regularly. My students are the reason my toolbox of promising practices is so strong.

To read more stories in the How I Teach series, click here. 

By the numbers

Early reports indicate New York opt-out rates are decreasing statewide, a possible sign of eased tension

PHOTO: Ann Schimke

Early opt-out estimates started rolling in Wednesday, the day after students sat for their first round of New York state standardized tests this year.

The number of families refusing to take the controversial tests seems to have decreased slightly in Rochester, the Hudson Valley, Buffalo and Albany. In Long Island, typically an opt-out hotbed, the rates thus far seem similar to last year. It’s still too soon to tell in New York City, but the number of families refusing to take tests has been traditionally been much lower in the city than in the rest of the state.

These are only preliminary numbers, based mostly on reports from school districts. Both High Achievement New York and New York State Allies for Public Education are tracking these reports closely and providing early tallies. The state will release an official tally this summer and would not provide any information at this time. But if it is true that opt-out rates are declining, it could be a sign that tension is slowly seeping out of what has been a charged statewide education debate.

“I think slowly and steadily, the situation is calming,” said Stephen Sigmund, executive director of High Achievement New York, a coalition of groups that promotes testing. “The changes that the state made are good changes and have helped calm the water.”

On the other side, Lisa Rudley, a founding member of New York State Allies for Public Education, said the numbers still look strong, the decreases are “very minor” and there is still a lot of information to be collected.

“The reality is, whether the numbers go up or down, there’s still a major problem with the testing in our state,” Rudley said.

Over the past few years, the number of families opting their children out of tests statewide has been on an upward trajectory, as teachers and parents protested what they saw as an inappropriate emphasis on testing. (There are currently three testing sessions each for English and math administered to students in public school grades 3-8.)

Backlash to the tests heightened in response to the state’s decision to adopt the Common Core learning standards and to tie those test results to teacher evaluations. The opt-out rate climbed to one in five students in 2015.

Partly in response to the movement, the state began to revise learning standards and removed grades 3-8 math and English tests from teacher evaluations tied to consequences. The Board of Regents selected a new leader, Betty Rosa, endorsed by opt-out supporters. Last year, the tests themselves were shortened slightly and students were given unlimited time to complete them. But, officials were unable to quell the tension. Roughly the same number of students sat out of the tests last year as the year before.

It’s difficult to estimate whether the opt-out rate has increased or decreased in New York City yet, said Kemala Karmen, a New York City representative for NYSAPE. She said that, anecdotally, in schools she has been in contact with, opt-out rates have either remained constant or decreased. Yet she has also heard of opt-outs in schools that had not reported them in the past. Karmen is also critical of the state’s changes to testing, which she thinks do not do nearly enough to assuage parents’ concerns.

New York City has traditionally had much lower opt-out rates than the rest of the state. While statewide 21 percent of families opted out last year, less than three percent did in the city. In part that’s because the movement hasn’t taken hold with as strongly with black and Hispanic families, who make up the majority of the city’s student body. Still, the movement’s political ramifications are being felt statewide.