In the Classroom

With new learning strategies, kids tackle higher-level math

PHOTO: Shaina Cavazos
Natalie Shaw checks subtraction and addition problems with her second-graders at IPS School 61. The school is part of the district's pilot in racial equity training.

Pia Hansen has a message for teachers and parents: math has changed.

Or, to be more specific, math teaching has changed. The new methods, she told a room full of math teachers in Indianapolis last month, are good for helping more kids understand how math works.

But sometimes it’s up to students and teachers to help parents get it, too.

Hansen’s session on teaching kids the building blocks for solving math problems at the national conference National Council of Teachers of Mathematics in late October at the Indianapolis Convention Center drew a crowded room of teachers who came to learn techniques to communicate math concepts visually with hand-held “number racks,” by having kids draw pictures to explain their answers and simply by using more precise language.

In Indiana, where new academic standards now call for students to demonstrate better mastery of math through a deeper understanding of the reasons that lead them to choose a particularly strategy to solve a problem, the ideas are especially useful.

The new standards, which detail what children must know, call for students to not just learn facts, but understand how to get answers. They learn the intuition behind borrowing in subtraction problems or figure out why an author made certain choices when writing a book. This higher level thinking and analysis helps kids be better prepared to go to college or the workforce, educators say.

Hansen, a former math teacher now with Oregon nonprofit The Math Learning Center, said it’s about time math was taught more like English, where memorization takes a back seat to understanding meaning.

“It’s not rote memorization,” Hansen said. “It’s all about thinking strategies.”

New strategies seek higher-level thinking

For some of her parents, who may have learned their basic math a generation ago, Natalie Merz’s second-grade math lesson might look pretty unfamiliar.

The long worksheets of stacked numbers to add, subtract, multiply or divide are gone. Students in her class at Indianapolis Public School 61 work on fewer problems at a time, working to explain how they came to their answers.

And although a math worksheet even five years ago would probably have a strict time limit — how many can you answer in one minute? — this activity had no such pressure.

But giving fewer problems and more time lets students work at their own paces and allows them develop better problem-solving skills. Rushing through timed tests, Hansen said, makes it harder for a struggling student to discover problem-solving strategies that work best for them. That can mean they actually learn less math and feel more frustration with the subject.

As she moved from group to group, Merz made gentle suggestions to her students who weren’t going far enough to explain why.

“Don’t try to do it in your head,” she told one group. “Draw a picture.”

Some students still counted on their fingers or borrowed to solve a subtraction problem and then went back to illustrate it. But most of them followed the directions: they drew a picture and wrote down the answer.

A correct “picture” next to the equation looked something like this, with tally marks visually representing numbers in the “tens” place and circles representing those in the “ones” place.

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Merz was reinforcing the concept that students must recognize which numbers are “tens” and which are “ones” to fully grasp the concept of place value in addition and subtraction.

In schools strained by poverty, where children come from families with limited resources, students often struggle to articulate how they got an answer, teachers said. Teachers have to work to bridge the gap with wealthier students, where extra reading, study or academic conversation at home can help prepare kids to better explain what they mean, because the benefit of understanding how they solved a problem doesn’t just end in second grade.

“My fiance does computer programming, and he has to understand the ‘why’ logic behind what he does works,” Merz said. “There’s a process behind those jobs. I think a lot of other countries have been doing that reasoning-based math a lot more. Especially with math, it builds so much. If you don’t understand math addition, you don’t get multiplication, division, algebra or calculus.”

But when kids learn math a new way, it can make it harder for their parents not just to help them with schoolwork, but to even follow the logic themselves.

An emerging parent-child divide

At the conference, Hansen told a true story that illustrated this problem.

A father and daughter she knows were working together on the problem 17 times 99, she said. The father believed his approach was best — multiplying 17 by 99 on paper the way he learned to do it:

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The daughter tried to solve it differently using a strategy called “grouping.” Her approach would break numbers down and re-group them in ways that can make the problem easy to solve quickly.

The daughter thought it was easier to multiply 100 times 17. Then, she told her dad, she would solve that equation by taking away one “group” to get the answer to the original problem.

“A group of 99?” he asked, puzzled.

“No,” she said in a matter-of-fact tone, “A group of 17.”

She calculated 17 times 100 to be 1,700 and then subtracted one group of 17 to find the correct answer: 1,683.

But her dad needed more explanation. So she drew him a picture.

The daughter illustrated her answer by drawing a grid with 17 rows and 100 columns. Altogether, the grid had 1,700 squares. When she subtracted one row of 17 squares, or taking away one group of 17 as she had said before, what was left was 1,683 boxes.

“Yeah,” he told his daughter. “I get it now.”

Visuals, Hansen said, such as number lines or grids, can help students to more quickly develop comfort with numbers and lead them to understand why a problem-solving process was used in the first place. The daughter not only knew how to get the answer, but she clearly understood the concepts behind multiplication — well enough to teach them to her father.

“Give them strategies,” Hansen told the teachers, “then drill facts.”

A different way of thinking about numbers

IPS’ curriculum team has both the new standards, and the new thinking about math, in mind when it advocates for the new strategies.

Curriculum coaches Nick Meyer and Eric Beebe believe if students learn to work through math strategies without help, it won’t just benefit them in school and in college but also better prepare them to consider the high tech jobs of the future.

“Understanding the relevance increases student engagement, but it also helps students be more successful because they can make connections from math to the everyday world,” Beebe said. “It also kind of opens the doors for them to understand what careers are associated with math and how math drives so much of what happens around us.”

But to get to there, kids have to master the basics that many adults take for granted.

Some teachers call the adult approach of doing math inside the head “mental math.” But relying on such a strategy without knowing the reasoning behind it can slow a child’s progress toward understanding.

Consider the problem 9 + 7, Hansen said. This is a problem the entire room of teachers could all do in their heads.

But when Hansen asked teachers to explain their answers, they gave a variety of different methods, but all used the same concept: grouping.

One volunteer wanted to make 9 into a 10 to make adding easier. So she split seven in two parts — a one and a six — then took the one and added it to nine. Now she had 10 and six, which add easily to make 16.

Another volunteer saw instinctively that borrowing could work the other way. She split nine in two parts — making an eight and one — then took the one to add with seven. Now she had eight plus eight, which she thought was easier to calculate to the same right answer: 16.

Hansen drew out the solutions and projected them on a screen. They looked something like this, with the arrows indicating how the broken down numbers were combined with the other to get the answer:

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This strategy, at its core, shows the kind of thinking higher-level math the new standards encourage students to employ. Many adults use them instinctively. But young children must be taught how to understand numbers that way, or they are likely to resort to counting by ones or memorizing, Hansen said.

“I don’t want you to promote one-by-one counting,” Hansen told the teachers. “I want (students) to think in chunks and groups . . . (visuals) that support that one-by-one counting are the death of us.”

If the methods to solve the new problems seem complicated, it’s because they are, she said. The goal is to help kids reach a higher standard of academic reasoning. The standard algorithm — numbers stacked on top of each other with a plus or minus sign — can lead to the right answer. But it doesn’t get at the understanding behind the math — it takes more effort and thinking for students to explain why that was the best way to solve the problem.

“We could do the algorithm we learned,” Hansen said. “But we wouldn’t be able to justify. Now, standards ask students to justify that.”

How I Teach

When the class is off-task, this fourth-grade teacher knows it’s probably time for Justin Timberlake

PHOTO: Cynthia Rimmer
Cynthia Rimmer, a fourth grade teacher at Fraser Valley Elementary School in the East Grand School District, works with students.

How do teachers captivate their students? Here, in a feature we call How I Teach, we ask great educators how they approach their jobs. You can see other pieces in this series here.

For Cynthia Rimmer, a fourth-grade teacher at Fraser Valley Elementary in Granby, building relationships with students is one of the best parts of the job. She eats lunch with them, reads to them, asks about their hobbies and attends their out-of-school events when possible.

Rimmer is one of 24 teachers selected for the 2016-17 Colorado Educator Voice Fellowship, an initiative of the national nonprofit America Achieves. The program, which also includes principals, aims to involve educators in policy conversations and decisions.

This interview has been condensed and lightly edited.

Why did you become a teacher?
I became a teacher because I love helping kids: to learn, to reach their goals, to realize their dreams, to help them to develop into the people they are capable of becoming.

I had several teachers growing up that made a big impact on my life, but none was more influential than my third grade teacher, Ms. Deanna Masciantonio. She not only taught me about space and fractions, but more importantly, she taught me how to communicate and resolve conflict, and how treat friends. She made us feel special and valued. I still carry her lessons with me today.

What does your classroom look like?
My classroom is a warm and organized space where everyone can feel comfortable learning and working together. Student writing and artwork is displayed on the walls and there are a variety of seating options where students can go to work independently or collaboratively in partners or in groups.

Fill in the blank. I couldn’t teach without my __________. Why?
Sense of humor. Teaching children can be overwhelming at times. It is important to be able to take a step back, remember what is important, and enjoy the moments we have with these incredible young students.

What is one of your favorite lessons to teach? How did you come up with the idea?
Last year, my teaching partner and I worked with our physical education teacher to create a project where students researched topics related to the Coordinated School Health Standards. While the students created their projects, I was able to address a variety of English Language Arts standards, as well as working on the students’ technology and presentation skills.

How do you respond when a student doesn’t understand your lesson?
I have tried to create an environment where students are encouraged to take academic risks and mistakes are celebrated. When someone doesn’t grasp a concept, we work together to understand things in new and different ways, making sure to address the student’s variety of learning styles.

How do you get your class’s attention if students are talking or off task?
When individual students are talking or off task, often times they simply need a quick pat on the shoulder or a friendly reminder to refocus. Some students may need a quick brain break or a few laps on the exercise bike to get back on track.

When the entire class is off task, I stop and reflect on what is happening. Often times the directions were unclear, or the students were being pushed too hard, and we all need to make time for a brain boost. But sometimes, we just need to stop and dance. Our favorite class dance break this year is Justin Timberlake’s, “Can’t Stop the Feeling.” After a few minutes of singing and dancing, the students are ready to tackle the most challenging math problems.

How do you get to know your students and build relationships with them? What questions do you ask or what actions do you take?
Building relationships with students is one of the most important and one of my favorite parts of being a teacher. Talking to the students, having lunch together, telling them about myself, reading to them, getting to know about their interests and hobbies, and letting them see that I am a real person all help build healthy relationships. I also try to attend the students’ outside events whenever possible, which I’ve found goes a long way in creating a trusting and long-lasting relationship.

Tell us about a memorable time — good or bad — when contact with a student’s family changed your perspective or approach.
In one memorable meeting, a parent requested that I move her son into a more challenging reading group. Although test scores and classroom observations didn’t dictate this switch, the parent shared some struggles that the family had recently dealt with that she felt were holding her son back from doing his best.

After I changed her child’s grouping on a trial basis, the student began to flourish. He developed more confidence and began to work harder, quickly becoming a role model and a positive leader. Parents love their children and want what’s best for them. When we take the time to partner with parents and understand where they are coming from, great things can happen.

What are you reading for enjoyment?
I just finished Fish in a Tree by Lynda Mullay Hunt. I enjoy reading the books my students are reading so that we can discuss our excitement for the stories together. I recently started My Grandmother Asked Me To Tell You She’s Sorry by Fredrik Backman. I enjoyed his book A Man Called Ove and I hope this book will just as charming.

What’s the best advice you ever received?
About 20 years ago I was considering pursuing another career. A trusted friend and mentor advised me to re-enter the teaching profession. I can’t thank her enough for that wise counsel.

school for love

Long hours, shared goals, and unbelievable stories: Why so many teachers fall in love with each other

PHOTO: Creative Commons / Timothy Brown

When Carrie and Kevin McCormack married in 2011, they quickly became known as the “teacher parents” of East Bronx Academy, the New York City school where they both worked.

But they didn’t stay the only couple on staff for long. Soon after, two other teachers paired off. Another relationship bloomed shortly afterward.

“My principal always jokes that we’re the hookup school,” Carrie McCormack says. “So many couples have met here.”

But East Bronx Academy is hardly the only school with love in the air. According to recent U.S. Census data, the most common marriages in America are between two grade-school teachers. And nearly 20 percent of people who work in education have spouses who do, too. Many of those couples met while working together.

Carrie and Kevin McCormack met as teachers at East Bronx Academy in New York City.

This Valentine’s Day, Chalkbeat has been looking at the love stories made possible by American education. Now we’re trying to answer the question of why schools are such fertile territory for love.

There are practical explanations: People who work in schools typically get started when they’re young, work together intensely, and have little time to meet other people.

“I always joke, if I hadn’t met Cornelius, I might be alone,” said Kassandra Minor, who met her husband in the bagel line on her first day teaching at a school in Brooklyn.

The benefits of pairing off with a fellow educator accumulate over time, especially as partnerships yield children. “It doesn’t hurt that we have the same vacation schedule,” says Grace Loew, a New York City teacher who met her husband when they were both first-year teachers in 2005. They’re now raising two sons together.

But educators say it’s about more than logistics. The shared task of trying to reach students who depend on schools to change their lives, they say, forges special bonds.

“Working in education, especially urban education, is an all-in job: emotionally, physically, spiritually and everything in between. The only people who can possibly understand the reward and sorrow of the work are fellow educators,” says Sally Jenkins-Stevens, who met her husband, Alex MacIver, when they taught together at a Bronx high school.

“You understand the stressors, the schedule, the unexpected days, and sometimes long nights that are associated with it,” says Brittany Monda, who met her husband Grant in a graduate program in Memphis, where they were both teachers and now each leads a school. “It’s great to know that someone has had a similar day to you without saying much when you get home.”

Or as McCormack puts it, “If I have to go home and talk to a husband who’s not a teacher, he’d probably think I was crazy.”

The possibility of falling in love has become lore at Teach For America, the nonprofit that draws many young adults to the classroom. Teach For America teachers have mentored their colleagues on the pros and cons of dating within the corps, and the number of relationships born at the organization’s summer training institute has even inspired a new piece of slang — “instiboo.”

The group’s founding CEO, Wendy Kopp, married an educator she met through Teach For America, and so did her successor, current CEO Elisa Villanueva Beard.

“Anyone seeking out a woman partner at Teach For America has a pretty good shot at finding someone, given the incredibly brilliant majority-women environment they find themselves in,” jokes Villanueva Beard.

About her own marriage, and the increasing number facilitated by Teach For America, she said, ’“There’s something powerful about being with a partner who deeply gets the urgency and the possibility, and who’s on a shared mission of being part of the solution, alongside our communities, to ensure educational equity and excellence for all.”

That work can bring together people who might otherwise not connect. Even though schools across the country struggle to attract as many male teachers and teachers of color as many would like to see in classrooms, they remain among the most diverse workplaces in America.

Ybelka Medina and Geoffrey Schmidt bonded at the New York City school where they worked.

For Geoffrey Schmidt and Ybelka Medina, a shared passion for reaching students who had struggled in their previous schools bridged what seemed like an insurmountable culture gap.

“I am a Dominican immigrant that grew up in a blue-collar family that depended on social welfare to make ends meet in Bedford-Stuyvesant, Brooklyn,” says Medina. “Geoff is American, comes from a solid white-collar family … and initially came off as a total frat boy more interested in socializing than actually teaching. I really liked hanging out with him … but didn’t take him seriously as a teacher nor as someone to date.”

Then they spent time getting to understand what had drawn each of them to the classroom, and romance bloomed.

“Education by its nature draws people who look at our world and want to make it better,” Schmidt says. “It makes sense that this kind of intense thought partnership would lead to bigger things. I know for us, it gave us an opportunity to see one another in a different way than I think we ever might have otherwise.”

The experience of seeing someone doing work they’re deeply invested in also worked its magic on Cornelius Minor, Kassandra’s husband, who said he considers teaching an art.

“When you’re doing your art, you’re your purest and best self,” he said. “If people are in your company when you’re being that person and they notice you, that’s really powerful.”