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

As a first-year teacher, he wanted to quit. Watching ‘the greats’ helped him stick it out.

PHOTO: Caroline Bauman

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.

A few months after Kevin Vaughn took his first teaching job in a third grade classroom in Arizona, he decided to quit.

“Teaching was way beyond me,” he said.

Vaughn went to his principal and apologized profusely for his imminent resignation. But then things went off-track. His principal told him to calm down and suggested he visit other classrooms in the building to see what good teaching looked like.

Vaughn, now an art teacher at Dolores Elementary School in southwest Colorado, agreed and ultimately stuck with the job. He talked with Chalkbeat about his habit of “stealing” ideas from other teachers, the challenge of getting to know students he sees once a week and his love of fidgeting.

Vaughn is one of 20 educators selected for the state’s new Commissioners Teacher Cabinet. The group will provide input to officials at the Colorado Department of Education on the impact of education policies in the classroom.

This interview has been condensed and lightly edited.

Why did you become a teacher?
At the age of 30, I gave up a career in the food and beverage industry. I realized I was just feeding people. It might have been a wonderful dining experience and good food, but it was no longer something I could hang my hat on. I wanted something more. I wanted to make a difference in somebody’s life.

What does your classroom look like?
I like to run an organized classroom, so even though there is a great deal of creativity and energy in the room, I’d say the students are rather focused on their work while music from the era we are studying plays in the background.

Fill in the blank. I couldn’t teach without my __________. Why?
Fidget. Yes, believe it or not, I’ve always had a fidget — even before it was a fad. For the 20 years I’ve been teaching, I’ve played with clay, rubbed a rock, squished a sponge, rubbed a piece of cloth all the while providing instruction or walking around assisting students as they work. It keeps me calm and collected. It is great to be able to model for students how fidgeting should really look. It doesn’t need to take away one’s focus from the teacher or cause distraction to other students.

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

I’d have to say my current favorite lesson since becoming an art teacher is one in which I teach the kindergarteners about Wassily Kandinsky. We look at some of his work, discuss his style and his use of color, and then create our own using shaving cream and food coloring. The work is so individual, and almost instantaneous as it is revealed, that the kids just beam about the art they have produced. As with so many other lessons, I found this one online and just tweaked it to fit my personality and teaching style. There really are a plethora of high quality teachers out there willing to share their ideas.

How do you respond when a student doesn’t understand your lesson?
When a student doesn’t understand a lesson, I’ve always just taught it again, and again, and again — with different examples and from different perspectives. With art, it is usually the technique that troubles the students as it is often the first time some students have used a particular medium. So, sitting down with students and breaking it down into smaller steps usually works well.

How do you get your class’s attention if students are talking or off task?

Rarely is the whole class off task, but usually when a student is off task I slowly walk by and refocus attention with a soft comment. However, if I need the attention of the whole class I’ll call out the first name of the artist we are currently studying, and have them call back — in chorus — the last name of that artist. Me: “Leonardo,” Students: “DaVinci.” They know that is the time to put down their tools and put their eyes on me.

How do you get to know your students and build relationships with them? What questions do you ask or what actions do you take?
It was so much easier when I was a classroom teacher to build relationships with the students. I saw the same students on a daily basis and could slowly develop that relationship as I learned more about their personalities and academic needs. Now, as an art teacher, I only see my students once every six days, so I have to make an effort to engage them outside the classroom as often as possible as well as in the studio. The cafeteria, in the hallway, at recess are all good times to just get to know the students.

Tell us about a memorable time — good or bad — when contact with a student’s family changed your perspective or approach.
I started my teaching career on the Navajo reservation and later moved to a small migrant community in Oregon. In both of these areas I was working with students of very different cultural backgrounds than the one I came from. I wouldn’t necessarily say that meeting the families of my students changed my perspective or approach, but it certainly gave me insight into my students lives that I could use to help me be a better teacher for them.

What are you reading for enjoyment?
The first book this summer I picked up was “The Generals: Patton, MacArthur, Marshall, and the Winning of World War II” by Winston Groom.

What’s the best advice you ever received?

My first principal and mentor, Ron Mansfield, told me to, “Watch the great teachers and learn.” Everything I know and do as a teacher I stole from someone else. I have my own personality and ways of doing things for sure, but being a good teacher has come by seeing how it is done by the best. Over 20 years I’ve had the opportunity to work with some tremendous people, and I’m so thankful that I’ve had the opportunity to learn the art of education from each and every one of them.

try try again

Why this Bronx middle school believes in second — and third — chances

PHOTO: Christina Veiga
Vincent Gassetto, the principal M.S. 343, hugs a staff member after winning the Teaching Matters prize in July 2017.

Teachers at M.S. 343 in the South Bronx had a problem: Their lessons weren’t sticking.

Students initially would test well on fundamental concepts — such as multi-digit long division or calculating the rate of change. But that knowledge seemed to melt away on follow-up exams just months or even weeks later.

The solution that teachers developed, based on providing constant feedback to students and encouraging regular collaboration among staff, has helped M.S. 343 beat district averages on standardized tests. It has also landed the school a $25,000 prize.

This week, M.S. 343 won the Elizabeth Rohatyn Prize, which is awarded to public schools that foster great teaching. Presented by the nonprofit Teaching Matters, the award money will go toward building a digital platform that students and teachers can use to track their progress from anywhere, at any time.

The work at M.S. 343 starts with determining which skills teachers will emphasize and test throughout the year. Working together, teachers draw on what they already know about which concepts are most likely to trip students up, contribute to success in later grades or appear on standardized tests. A key concept could be understanding ratios in sixth grade or mastering scientific notation by eighth grade.

“It’s all in the teachers’ hands,” said Principal Vincent Gassetto.

Students are regularly tested with “learning targets.” But they’re also given three chances to prove they’ve mastered the skills. Gassetto said the approach is backed by neuroscience, which suggests the best way to learn is to use the knowledge multiple times, instead of cramming for a single test.

“That actually tells the brain: You’re being tested on this, it’s important. And that stores it in a part of the brain that’s easily retrievable,” he said.

Only the highest score will be recorded, which serves a different purpose: boosting students’ confidence in themselves as learners.

“We’re celebrating their progress, not necessarily the end result,” math teacher Lola Dupuy explained in a video the school produced. “It can be very confusing for a student to receive a failing grade and very discouraging for them if they don’t know … what they’re doing wrong and what they need to do to improve it.”

In between tests, each department comes together to analyze students’ answers. They zero in on common misconceptions and come up with a list of questions for students to ask themselves when reviewing their work.

Using the questions as a guide, it’s up to the students to figure out where they went wrong, often by working in groups with peers with varying skill levels.

“Students are more engaged in their work and the outcomes are better because they’re self-reflecting,” Dupuy said.

M.S. 343’s approach also gets at a common knock on testing: The results are rarely used to improve teaching and students often don’t have the opportunity to learn from their mistakes. At M.S. 343, teachers spend entire weeks meeting as a team to go over results and fine-tune their instruction. That time, Gassetto said, is a valuable resource.

“Most of the time, when you give a big assessment,” Gassetto said, “you’re testing, but for what purpose? We don’t do that. If we’re going to ask kids to sit down and take an assessment, we need to look at it and get it back to them right away, so it’s useful.”