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. 

Building Better Schools

Hundreds of teachers will be displaced by Indianapolis high school closing plan

PHOTO: Dylan Peers McCoy
Teacher Tina Ahlgren spoke to the Indianapolis Public Schools Board in June about the importance of making the high school closing process easier for teachers.

If the Indianapolis Public Schools Board approves a plan to close three high schools, students won’t be the only ones facing transition: Hundreds of teachers will need to find new positions.

Just what will happen to those educators remains uncertain. District leaders say most teaching positions will be moved, not cut. But educators have raised concerns that the process for reassigning teachers is murky and that the prospect of school closings will push teachers to flee.

A proposal from Superintendent Lewis Ferebee released last month calls for closing Broad Ripple High School and John Marshall Middle School, and converting Arlington and Northwest High Schools to middle schools. Those four schools combined had 329 certified teachers in 2015-2016, the latest year available in the state performance report.

The district would also roll out a new career academy model, where students choose their high schools based on focus areas in fields such as business, construction and medical science.

All that transition means a lot of changes are in store for the hundreds of educators who work at the schools slated to close — and those at the high schools that will launch career academies and take the influx of new students.

For now, the district is not providing much information on what is in store for teachers. The details are expected to come after the IPS board votes on which schools to close in September. Eleven days after the board votes, central office staff are scheduled visit the high schools to discuss the timeline, next steps and personnel decisions.

But Ferebee said it will be even longer before the district has a full picture of how many teachers are needed at the career academies in each school because it depends on where students choose to enroll.

“Much of what we do with certified staff will be driven by enrollment interest of students,” he said.

By closing schools, the district expects to save $4.35 million in “classroom resources,” or expenses from the general fund, according to the report recommending closing high schools. The general fund is typically used to pay for costs including salaries for teachers and other school workers, equipment like computers and supplies needed to run the schools.

The administration does not expect it would save much from shrinking the teaching force, because they anticipate that the number of teachers will stay relatively stable, said deputy superintendent Wanda Legrand. “Our student enrollment will stay about the same.”

IPS union president Rhondalyn Cornett, who leads the Indianapolis Education Association, said that she also expects the number of teachers to remain steady — as long as students don’t start leaving the district for charter and township schools.

The career academies may also lead to more jobs for teachers with new skills and credentials, but it’s not entirely clear how that will play out. Some teachers may already be qualified to teach in the new programs and others may be able to get the extra credentials relatively easily.

Even if the district maintains the same number of students and teachers in its high schools, however, the transition is hard for teachers at the schools that are expected to close, Cornett said.

“They are afraid. They don’t understand how this process works,” she said. “They don’t know what the future holds.”

Cornett said that the district should make the closing process easier for educators by being clear about how they can get jobs at other schools and giving teachers who lost their jobs because of  school closings priority for open positions.

Tina Ahlgren, the 2014 IPS Teacher of the Year, spoke to the board in June about the urgent need to make the process transparent for teachers. Ahlgren has been through this before. She lost jobs at two prior schools after one school was taken over by the state and a magnet program at another school was abruptly moved.

“During each of these transitions, I watched dozens of loyal, effective, IPS educators leave the district due to the chaos that ensued and the broken promises from this district,” she said. “I speak here today to remind you of those challenges in the hopes that we will learn from our past and not repeat those mistakes this time around.”

size matters

NYC class size limits could boost learning — but in practice, they often don’t. A new study explains why.

PHOTO: Erin Einhorn

A contentious debate about how much class size actually matters is getting some new data — and ammunition for both sides.

While former Mayor Michael Bloomberg dreamed of firing half the city’s teachers and paying the remaining superstars twice as much to teach larger classes, Mayor Bill de Blasio has argued that small classes are essential. But as classrooms have become more crowded, how much pressure should there be to reverse that trend?

A new study focusing on New York City offers some evidence for both poles of the debate: Reducing class sizes can significantly increase student learning, but those gains are often cancelled out in the short run by the lower-quality teachers who wind up staffing them — and disruptions linked to their quick hiring.

“My paper is quite supportive of the argument that class size [reduction] boosts student achievement,” explains Michael Gilraine, the study’s author, who will start this fall as a professor at New York University. But “when you reduce class sizes you’re going to have a trade-off because you need to bring in new teachers — and that might have its own independent effect.”

Gilraine’s findings come at an opportune moment for organizations like Class Size Matters and the Alliance for Quality Education, which recently filed a complaint with the State Education Department claiming the city has failed to meet required class size reduction targets.

Using data from 473 city schools, Gilraine isolated the effect of class size reductions by looking at third- through sixth-grade classes that moved just above or below the 32-student cap required for elementary grades. Classes that moved from 32 to 33 students, for instance, would have to reduce class sizes by adding a new teacher, while classes that moved from 33 to 32 students could reduce class sizes without adding a new teacher — isolating the effect of the newly added teacher.

Looking at schools near the cap between 2009 and 2014, Gilraine found that reducing class size by an average of four students produced gains in reading and math scores equivalent to roughly two and a half months of extra learning.

But there’s a big catch: The classes that shrank by bringing in a new teacher saw essentially no boost in student achievement. And since roughly 50 percent of the classes Gilraine examined depended on newly hired teachers, the overall effect of the class size reductions was cut in half.

Though Gilraine did not rigorously assess why half of these class size reductions didn’t boost student learning, he said there are a couple of likely reasons. For one, newly hired teachers may be less experienced or lower quality.

Second, there could be disruptions associated with bringing in new employees. Since class sizes were frequently lowered after the teachers union filed grievances, some reductions happened after the school year had already started — potentially disrupting classes mid-year.

The study has not been published or peer-reviewed, but Thomas Dee, director of Stanford’s Center for Education Policy Analysis, said it appeared to be rigorous. He said the findings are not entirely surprising but illustrate the importance of understanding how class size policies play out across systems, not just in the context of smaller experiments.

Dee pointed to the gold standard of class size research: a landmark randomized experiment in Tennessee conducted in the 1980s that found significantly reducing class sizes in early grades improved student learning. “That really established in people’s minds that small class sizes — though they’re expensive — are effective,” he said. But “the kinds of things that might work in a small-scale study may not scale well.”

Gilraine’s findings dovetail with research on California’s billion-dollar effort to systemically lower class sizes in the 1990s, which showed reducing class sizes led to gains in reading and math but was dampened by hiring less experienced teachers.

Dee added that one conclusion to draw from Gilraine’s study is that class size reductions may be more effective when they’re targeted — at high-need schools, for example — rather than enforced system-wide.

Leonie Haimson, executive director of Class Size Matters, said the study shows the city must do more to reduce class sizes — and do so more proactively. She emphasized that the city could avoid disruptive hiring practices, and that there’s no reason to assume hiring more teachers would reduce the overall quality of teaching in the long run.

“In a well-crafted class size reduction, you’re going to hire teachers earlier on and those teachers are going to be higher quality and stay longer and become more effective” she said. “If anything, this paper is an indictment of the current system.”