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.

yeshiva findings

After 3-year probe into yeshivas, city admits it was blocked from visiting many schools, found little instruction in math and English

PHOTO: Jackie Schechter
Mayor Bill de Blasio has been accused of delaying an investigation into whether yeshivas provide an adequate secular education.

At some of New York City’s yeshivas, attendance was voluntary when it came time to learn secular subjects like math and English. Students said they didn’t learn math beyond basic division and fractions. None of the students reported receiving steady lessons in science. 

That’s according to a long-delayed probe by the New York City education department into whether some of the city’s private Jewish schools are providing an adequate secular education for students. But even as the city released findings on Thursday, it admitted that it was never able to go inside any high schools and never received a full set of curriculum materials to evaluate — significant gaps for a report that took three years to be released.

In a letter sent to the state education commissioner on Aug. 15, schools Chancellor Richard Carranza asked the state for guidance on how to proceed after a recent change in law that put the state education commissioner in charge of evaluating the schools. The Wall Street Journal first reported on the letter. 

“We deeply believe that all students — regardless of where they attend school — deserve a high-quality education. We will ensure appropriate follow up action is taken based on guidance provided,” Carranza said in a statement.

The letter marks a new phase of an investigation sparked by current and former students and parents who complained they received little instruction in math or English while attending the schools. The city has been accused of delaying the investigation to avoid angering a politically powerful community.

New York requires private schools to provide instruction that is “substantially equivalent” to public schools, and that allows the schools to access public money for things like school security. Students and parents who were interviewed for the probe said they received instruction in math and English for only 90 minutes for four days out of the week, and all but two said they received “little to no” history lessons, according to the city’s letter.

The report finds that some schools have adopted new curriculums in English and math, but officials have not been able to evaluate the new materials because they haven’t received a complete set.

The city also said that officials at eight of the schools they were unable to visit recently gave word that they would schedule meetings.

Read Carranza’s full letter here.

In the Classroom

Carranza aims to speed up anti-bias training for educators, calling it a ‘cornerstone’ of school improvement

PHOTO: Christina Veiga
Chancellor Richard Carranza, bottom right, joined New York City principals and superintendents for an anti-bias training in Brooklyn.

After bending fluorescent pipe cleaners into loopy and angular shapes, a group of about 100 New York City principals and superintendents paired up for a chat. Their assignment: to recount their childhood aspirations of what they wanted to be when they grew up.

This was no arts and crafts class — and no ice breaker, either. The Wednesday morning session at Brooklyn Law School was an example of anti-bias training that the education department will now require for every employee who works with students across the country’s largest school system.

After committing $23 million to the work this year, Chancellor Richard Carranza announced at the session that the trainings will be mandatory, and that the city aims to speed up how quickly they happen. The goal is to compress the original four-year roll out to two.

“It’s about us as a community saying we want to change systems so that it privileges all of our students in New York City,” Carranza said. “The evidence right now, I will tell you my friends, is that not all students are being served well.”

Advocates had long agitated for the training, citing disparate rates in school discipline for black and Hispanic students, and high-profile incidents of schools accused of teaching racist lessons in the classroom. They argue that teachers need to be better equipped to serve diverse students as the city moves forward with plans to integrate its starkly segregated schools.

“We have to make school environments the most welcoming places possible for our young people. That includes adults doing personal work,” said Natasha Capers, a coordinator for Coalition for Educational Justice, a parent organization that lobbied for the training.  

Their advocacy has gotten a boost since Carranza became schools chancellor in April, bringing an approach that is bolder and more frank than his predecessor when it comes to addressing the system’s racial inequities. On Wednesday, he spent more than an hour participating in the training session just like the other school leaders, calling it “God’s work.”

“This is going to penetrate everything we do,” he said.

Wednesday’s session was lead by experts from the Perception Institute, a research and training organization, and Safe Places for the Advancement of Community and Equity (SPACEs), which provides leadership training. The pipe cleaners helped bring to life a metaphor about “bending” expectations for what educators might learn throughout the day. The one-on-one conversations were a way to “interrupt” stereotypical assumptions about other people by having sustained conversations with them, said trainer Dushaw Hockett.

“This isn’t some touchy-feely, get-to-know-you exercise,” he said.  

There is some evidence that, when done right, anti-bias trainings can work — and improve outcomes for students. But there is also research that shows it can often be ineffective.

Carranza said the city is committed to doing the work for the long-term, with the trainings designed to be ongoing and build on each other. He also said the department will keep an eye on measures such as student attendance and whether teachers report improvements in school climate to gauge whether it’s having an impact.

“This is going to be one of those cornerstone pieces in terms of, how are we going to continue to transform this immense system to really, truly serve all students?” he said. “This is going to be something that’s not going to fall off the radar. We’re going to keep pushing.”