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. 


Colorado schools are getting a major bump in the state’s 2018-19 budget

Students waiting to enter their sixth-grade classroom at Kearney Middle School in Commerce City. (Photo by Craig Walker, The Denver Post)

Colorado’s strong economy has opened the door for state lawmakers to send a major cash infusion to the state’s public schools.

As they finalized the recommended budget for 2018-19, the Joint Budget Committee set aside $150 million, an additional $50 million beyond what Democratic Gov. John Hickenlooper had asked for, to increase funding to schools.

“We believe this is the most significant reduction in what used to be called the negative factor since it was born,” said state Rep. Millie Hamner, the Dillon Democrat who chairs the Joint Budget Committee.

Colorado’s constitution calls for per pupil spending to increase at least by inflation every year, but the state hasn’t been able to meet that obligation since the Great Recession. The amount by which schools get shorted, officially called the budget stabilization factor, is $822 million in 2017-18. Under state law, this number isn’t supposed to get bigger from one year to the next, but in recent years, it hasn’t gotten much smaller either. 

But a booming economy coupled with more capacity in the state budget created by a historic compromise on hospital funding last year means Colorado has a lot more money to spend this year. In their March forecast, legislative economists told lawmakers they have an extra $1.3 billion to spend or save in 2018-19.

The recommended shortfall for next year is now just $672.4 million. That would bring average per-pupil spending above $8,100, compared to $7,662 this year.

Total program spending on K-12 education, after the budget stabilization factor is deducted, should be a little more than $7 billion, with the state picking up about $4.5 billion and the rest coming from local property taxes.

The budget debate this year has featured Republicans pressing for more ongoing money for transportation and Democrats resisting in the interest of spreading more money around to other needs. The positive March forecast reduced much of that tension, as a $500 million allocation for transportation allowed a compromise on roads funding in the Republican-controlled Senate. That compromise still needs the approval of the Democratic-controlled House, but suddenly a lot of things are seeming possible.

“We knew we were going to have more revenue than we’ve ever had to work with,” Hamner said of the status at the beginning of the session. But that presented its own challenges, as so many interest groups and constituencies sought to address long-standing needs.

“The fact that we’ve been able to reach such incredible compromises on transportation and K-12 funding, I think most members will be very pleased with this outcome,” Hamner said. “Where we ended up is a pretty good place.”

The big outstanding issue is proposed reforms to the Public Employees Retirement Association or PERA fund to address unfunded liabilities. A bill that is likely to see significant changes in the House is wending its way through the process. The Joint Budget Committee has set aside $225 million to deal with costs associated with that fix, which has major implications for teachers and school districts budgets.

The Joint Budget Committee has also set aside $30 million for rural schools, $10 million for programs to address teacher shortages, and $7 million for school safety grants.

The budget will be introduced in the House on Monday. Many of the school funding elements will appear in a separate school finance bill.

Going forward, there is a question about how sustainable these higher funding levels will be.

“It does put more pressure on the general fund,” Hamner said. “If we see a downturn in the economy, it’s going to be a challenge.”

outside the box

Program to bring back dropout students is one of 10 new ideas Jeffco is investing in

File photo of Wheat Ridge High School students. (Photo by Nic Garcia/Chalkbeat)

Jeffco students who drop out will have another option for completing high school starting this fall, thanks to a program that is being started with money from a district “innovation fund.”

The new program would allow students, particularly those who are older and significantly behind on credits, to get district help to prepare for taking a high school equivalency test, such as the GED, while also taking college courses paid for by the district.

The idea for the program was pitched by Dave Kollar, who has worked for Jeffco Public Schools for almost 20 years, most recently as the district’s director of student engagement.

In part, Kollar’s idea is meant to give students hope and to allow them to see college as a possibility, instead of having to slowly walk back as they recover credits missing in their transcripts.

“For some kids, they look at you, and rightfully so, like ‘I’m going to be filling in holes for a year or two? This doesn’t seem realistic,’” Kollar said. “They’re kind of defeated by that. As a student, I’m constantly looking backwards at my failures. This is about giving kids something like a light at the end of the tunnel.”

Jeffco’s dropout rate has decreased in the last few years, like it has across the state. At 1.7 percent, the rate isn’t high, but still represents 731 students who dropped out last year.

Kollar’s was one of ten winning ideas announced earlier this month in the district’s first run at giving out mini-grants to kick-start innovative ideas. Kollar’s idea received $160,000 to get the program started and to recruit students who have dropped out and are willing to come back to school.

The other ideas that the district gave money to range from school building improvements to comply with the Americans with Disabilities Act at Fletcher Miller Special School, from new school health centers to a new district position to help work on safety in schools. One school, Stott Elementary, will create a “tinker lab” where students will have space and supplies to work on projects as part of the school’s project-based learning model.

The Jeffco school board approved $1 million for the awards earlier this year. It was an idea proposed by Superintendent Jason Glass as a way of encouraging innovation in the district. This spring process is meant as a test run. The board will decide whether to continue investing in it once they see how the projects are going later this spring.

Officials say they learned a lot already. Tom McDermott, who oversaw the process, will present findings and recommendations to the board at a meeting next month.

If the board agrees to continue the innovation fund, McDermott wants to find different ways of supporting more of the ideas that educators present, even if there aren’t dollars for all of them.

That’s because in this first process — even though educators had short notice — teachers and other Jeffco staff still completed and submitted more than 100 proposals. Of those, 51 ideas scored high enough to move to the second round of the process in which the applicants were invited to pitch their ideas to a committee made up of Jeffco educators.

“We’re extremely proud of the 10,” McDermott said, but added, “we want to be more supportive of more of the ideas.”

McDermott said he thinks another positive change might be to create tiers so that smaller requests compete with each other in one category, and larger or broader asks compete with one another in a separate category.

This year, the applicants also had a chance to request money over time, but those parts of the awards hang on the board allocating more money.

Kollar’s idea for the GED preparation program for instance, includes a request for $348,800 next year. In total, among the 10 awards already granted, an extra $601,487 would be needed to fund the projects in full over the next two years.

Awards for innovation fund. Provided by Jeffco Public Schools.

The projects are not meant to be sustained by the award in the long-term, and some are one-time asks.

Kollar said that if that second phase of money doesn’t come through for his program, it should still be able to move forward. School districts are funded per student, so by bringing more students back to the district, the program would at least get the district’s student-based budget based on however many students are enrolled.

A similar program started in Greeley this fall is funded with those dollars the state allocates to districts for each student. So far, eight students there already completed a GED certificate, and there are now 102 other students enrolled, according to a spokeswoman for the Greeley-Evans school district.

But, having Jeffco’s innovation money could help Kollar’s program provide additional services to the students, such as a case manager that can help connect students to food or housing resources if needed.

And right now Kollar is working on setting up systems to track data around how many students end up completing the program, earning a high school equivalency certificate, enrolling in a college or trade-school, or getting jobs.

Helping more students on a path toward a career is the gold standard, he said, and what makes the program innovative.

“It’s not just about if the student completes high school,” Kollar said. “It’s are we making sure we are intentionally bridging them into whatever the next pathway is?”