Number Talks

How one Tennessee school district is getting students excited about math

PHOTO: Grace Tatter
First-graders at Pleasant View Elementary in Cheatham County work on a math problem. Cheatham County is one of a handful of districts in the new Mid-Cumberland Math Consortium.

In a burst of “mental math,” Cheatham County teacher Amy Castleberry challenges her first-graders to have fun exploring numbers. There are no paper-and-pencil drills, no right or wrong ways. She’s just using a quick free-thinking exercise to inspire each child to figure out how numbers work.

That’s the basis for Number Talks, a 10-to-15-minute conversation about math that elementary schools in her Middle Tennessee district have integrated into their daily routines this school year to complement existing math lessons and curriculum. It’s all to encourage critical thinking skills and a deeper understanding of math concepts under the state’s academic standards.

During one Number Talk this spring, for instance, Castleberry watched her students at Pleasant View Elementary School easily answer a series of single-digit addition problems. Then she introduced a double-digit problem.

“You’re going to show off now — 32 + 14!” she says.

One boy squeals with delight at the challenge as he and the other students begin to think. Some count on their fingers. Others enthusiastically wave their thumbs to signal that they have an answer. Still others sit with furrowed brows. But no one seems anxious. There’s nothing to be graded. The answers are in their heads.

One by one, the children share their answers with the group and how they came up with them — whether by counting up, using an algorithm, or another method of their choosing — as long as they can explain their processes. Their comments reveal how much they understand, and Castleberry interacts with her students to help them sort out the correct answer and which computation methods make the most sense.

Number Talks was developed beginning in the 1990s when two U.S. educators began giving teachers mental math experiences during professional development settings. Impressed with the response, the exercises grew into a mental math format and a toolkit to help children learn math concepts.

America’s students struggle with math. Just one-third of eighth-graders are proficient, according to last year’s National Assessment of Educational Progress. Teachers have long faced challenges to help their students grasp math concepts. Tools such as Number Talks help to bridge the gap in critical computational thinking skills.

Cheatham County math coordinator Joseph Jones learned about Number Talks last year in Nashville during the Tennessee Department of Education’s LEAD conference for district and school leaders. When he went home to research it, he was hooked. This year, he trained his academic coaches to lead mental math exercises, so they could in turn train teachers in grades K-5. He’s also working with middle and high school teachers to weave in the concepts in their classrooms too.

A frequent visitor to classrooms, Jones is constantly surprised by the inventive way students come up with the right answers to math problems. For example, a student recently solved 15 x 35 in his head by multiplying 5 x 35, and then multiplying that by 3, quickly getting the correct answer of 525.

Number Talks don’t dismiss or disavow the algorithms that most teachers and parents learned when they were in school. Algorithms, or a basic set of operations that can be memorized, are still useful. “It’s just we don’t stop there now,” he said.

“Even when (students) don’t remember something, maybe they can think their way to it. That’s honestly at the bottom of it all. What we’re driving at are critical thinking, collaboration … things that go beyond mathematics,” Jones said.

Jones served last year on the panel of Tennessee math educators who reviewed and revised the Common Core math standards. He knows both the state’s current and future math standards well. Number Talks jibe perfectly with them, he says.

“(The talks) allow children to make sense of mathematics in their own thinking, to express themselves, to communicate their reasoning,” he said. “All of that is perfectly in line with the math practice standards.”

Cheatham County teachers are still getting used to the talks, especially since they often involve listening to students detail mathematical mistakes that teachers are eager to correct. But they’re learning to be patient.

"We use numbers every day. ... We've got to be able to have conversations about them."Susan Collins, academic coach

“Sometimes (students) catch themselves and fix it themselves, and also the other kids around them will give them feedback, especially if they’re wrong,” said Emily Wong, a fourth-grade teacher at East Cheatham Elementary School. “I love watching them learn from each other.”

Teachers learn too, including how to think of math in conversational and conceptual terms. Academic coach Susan Collins, a former English teacher, said the transition was challenging at first but has been rewarding in the end.

“We use numbers every day. … We’ve got to be able to have conversations about them,” she said.

How I Teach

Crazy contraptions, Chemistry Cat, and climbing stories: How this Colorado science teacher connects with kids

PHOTO: Courtesy of Shannon Wachowski
Shannon Wachowski, a science teacher at Platte Valley High School, holds a toothpick bridge as a her students look on.

Here, in a feature we call How I Teach, we ask educators who’ve been recognized for their work how they approach their jobs. You can see other pieces in this series here.

Shannon Wachowski once started a parent-teacher conference by sharing that she was concerned about the student’s lack of motivation. The boy’s mother quickly began adding criticisms of her own — alarming Wachowski enough that she started defending the teen.

It was then the student’s behavior began to make more sense to Wachowski, who teaches everything from ninth-grade earth science to college-level chemistry at Platte Valley High School in northeastern Colorado. She realized that school, not home, was the boy’s safe place.

Wachowski is one of 20 educators who were selected to serve on the state Commissioner’s Teacher Cabinet. The group provides input to officials at the Colorado Department of Education.

She talked to Chalkbeat about how she uses parent conferences and classwork to learn students’ stories, why making Rube Goldberg contraptions boosts kids’ confidence, and what happens when she raises her hand in the middle of class.

This interview has been condensed and lightly edited.

Why did you become a teacher?
Originally a practicing chemical engineer, I became a teacher because I wanted a more fulfilling career. I had tutored chemistry in college and really enjoyed it.

What does your classroom look like?
Because my students work in teams 90 percent of the time, my tables are arranged so that students can sit in groups of four. I wrote a grant last summer for standing desks so each two person desk raises up and down. They are convenient for labs or when students need a change of scenery. My walls contain student-made license plates (an activity I do on the first day of school) and other student work from class, including various Chemistry Cat memes!

Fill in the blank. I couldn’t teach without my ________. Why?
My heart. Initially I became a teacher because I loved my content. I soon realized however, that while content is important, developing relationships with students is paramount. No learning will happen if positive relationships are not established first. When I am frustrated with student behavior, I try to put myself in their place and respond in a caring and compassionate manner.

What is one of your favorite lessons to teach?
One of my favorite lessons is when my students build Rube Goldberg devices. It gets somewhat chaotic because they are working in teams and materials are everywhere, but every single student is engaged. In the end, they can apply what they know about energy to design a multi-step contraption. I have seen very low-confidence students excel at this activity, and it is very rewarding to see them experience success in a science class.

How do you get your class’s attention if students are talking or off task?
One strategy I’ve recently started using came from my experience leading professional development for other teachers. I will be somewhere in the middle of the room (usually not the front) and raise my hand. When students see me raise my hand, they will raise theirs and pause their conversation. Then other students see those students and raise their hand, etc. Once everyone is quiet, then I’ll make my announcement. Like all other strategies, I need to practice being consistent with it.

How do you get to know your students and build relationships with them? What questions do you ask or what actions do you take?
I always plan the first couple of days for “get to know you” activities. My students design their own paper license plates using whatever letters, numbers, or design they would like. They then have 30 seconds to talk about their license plates.
I noticed that in some of my more challenging classes I needed a way to better connect with my students. At the beginning of most class periods I share some sort of funny story about what happened to me the evening prior — for some reason, I am never short of these stories — or a picture of my dog, or my latest climbing adventure. Sharing this information does not take long and eventually, students will ask if I have a story to share if I haven’t done so in a while. This also leads to them sharing stories with me, and finding that we may have more in common than we think.

Tell us about a memorable time-good or bad-when contact with a student’s family changed your perspective or approach.
At parent-teacher conferences one year I had a parent come in with their student. This student was not the most motivated individual — not disrespectful, just did not seem to want to do anything with his time. As I was explaining this to his parent, the parent started talking very negatively to and about the student, so much so that I found myself trying to defend the student and bring up positive qualities about his character. This interaction helped me to understand some of the student’s behavior in class, as well as realize that for some students, school is their safe place. There are often lots of reasons for a student’s behavior that I may not be aware of, which is why it is important to get to know each student and their situation as best as possible.

What are you reading for enjoyment?
When I have time outside of school, one of the things I enjoy doing is throwing pottery. I am currently reading “Science for Potters” by Linda Bloomfield. It combines my love of science and art into one book.

What is the best advice you ever received?
Since I teach a variety of levels, I often have one class that challenges my classroom management skills. This can be frustrating as I am the type of person that would like to achieve perfection in every circumstance. When I have a discipline issue in my class, I often see it as a personal failure. My husband often reminds me that “You can’t control other people’s behavior, you can only control your response to it.”

behind the music

‘We just wanted to help the movement’: Meet the NYC teacher whose students wrote a #NeverAgain anthem

PHOTO: Kyle Fackrell

Among the many creative displays of protest that stood out during Wednesday’s national student protest against gun violence was an original song by Staten Island students: “The truth: We need change.”

The song, uploaded to YouTube Wednesday morning, features John W. Lavelle Preparatory Charter School students in a soaring anti-gun counterpoint, led by seniors Jerramiah Jean-Baptiste and Aeva Soler.

“Don’t run away from the truth,” Soler sings during one exchange. “If we don’t act now, what should we do?”

Jean-Baptiste picks up where she leaves off: “We need change in this time of doom. It shouldn’t be the case that we’re losing lives too soon. I shouldn’t feel afraid inside my school. We need change.”

We checked in with Kyle Fackrell, Lavelle Prep’s longtime music teacher, who has worked with Jean-Baptiste, Soler, and their classmates for nearly five years, since their introductory eighth-grade music class. Here’s what he told us about the song, his students, and their ambitions.

How the song came to be: “I knew that my students were very passionate about this subject. When I learned about the walkout coming up and that it would be coming up soon, I was aware of these students and their songwriting abilities, and I suggested the idea of writing a song. They really just ran with it.”

What the process was like: “We’ve worked together a lot and have made a lot of music together. When I proposed this idea it was like clockwork. It was really exciting to see how fast Jerramiah could come up with the ideas.”

On the students’ goals: “We just wanted to help the movement. I was having that conversation with my students today, should the song get the success we hope it gets, that would be great, but really want we to maintain our genuine interest in making a difference with the song. I’m just supporting them.”

What the reaction has been: “It’s been very positive. … Everyone who hears the song is blown away. It really is thanks to the talent of the young students that I’m blessed to be helping them develop.”

On what motivates his students: “None of them were coming at it from knowing people who were in a shooting. They’re just very aware and intelligent students. I think the point that the students in Florida are making is that a lot of people underestimate kids and youth, and I think these students are also underestimated — about how much they are aware of what’s going on in the world, and that they should have a say.”