Develop Number Sense with Number Talks

One of the reasons Number Talks are so important is that they give students, and adults, a whole different perspective on mathematics—a perspective that turns out to be critical for future learning.”  ~Jo Boaler, Professor of Mathematics Education, Stanford University

In Cathy Humphreys and Ruth Parker’s Making Number Talks Matter and their newest companion title, Digging Deeper: Making Number Talks Matter Even More, teachers learn not only how to use Number Talks to develop number sense, but how these short, daily routines can help create a thriving classroom community where students actively share their thinking and teachers become expert listeners.

What Are Number Talks?

Number Talks are routines in which students reason mentally with numbers. It is a time when students put their pencils and paper away to think about and try to solve a problem mentally, then share their thinking and strategies with their peers. The teacher’s role is to listen, to record the students’ thinking on the board, and to hold back on explaining or correcting. This can be difficult for some, but it is essential to making Number Talks work. “Number Talks turn students’ roles in math class upside down. Now they are supposed to figure something out rather than be told the steps to follow. Now they are supposed to explain what they think rather than waiting for us to explain” (Humphreys and Parker 2015).

Why Are Number Talks Important?

Number Talks allow students to take back the authority of their own reasoning, but they also bring interest, excitement, and joy back into the math classroom. Number Talks allow students to make sense of mathematics in their own ways by practicing making convincing arguments while critiquing and building on the ideas of their peers. “As students sit on the edge of their seats, eager to share their ideas, digging deep into why mathematical procedures work, they come to like mathematics and know that they can understand it,” (Humphreys and Parker 2015). Number Talks can help students build competence, flexibility, and confidence as mathematical thinkers.

How Do I Start Digging Deep Into Number Talks?

For practical guidance as to how to start Number Talks in your classroom, pick up a copy of Making Number Talks Matter, an introduction and how-to guide to Number Talks. In order to get a full grasp of Number Talks, however, and see exactly what they look like, Digging Deeper is a must-have. This essential companion book uses extensive video footage of teachers and students practicing Number Talks in real classrooms. This personal and accessible book shows teachers:

  • The kinds of questions that elicit deeper thinking
  • Ways to navigate tricky, problematic, or just plain hard exchanges in the classroom
  • How to more effectively use wait time during Number Talks
  • The importance of creating a safe learning environment
  • How to nudge students to think more flexibly without directing their thinking.

“The process of engaging students in reasoning with numbers is one we hope you will consider as a problem-solving venture—an investigation that will help you to learn to listen to your students and learn along with them as you build your lessons around their thinking” (Humphreys and Parker 2015).

Ruth Parker co-created Number Talks with Kathy Richardson in the early 1990s. Cathy Humphreys has been instrumental in extending Number Talks to the secondary level. Together, Cathy and Ruth have developed a deep knowledge of the best ways to teach Number Talks with students of all grade levels. Their extensive knowledge is packaged nicely into these two highly accessible books. Order them HERE today.


Humphreys, Cathy, and Ruth Parker. 2015. Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4 – 10. Portland, ME: Stenhouse.

Add comment December 3rd, 2018

Profiles in Effective PD Initiatives: The Power of Book Study Groups

In our series focusing on effective PD initiatives, Holly Holland revisits a wildly successful online book study group that attracted over 700 educators from around the world. One teacher in Oregon was trying to get her colleagues to engage students in Number Talks and the book study group gave her ideas and efforts a boost.

Making Number Talks Matter
By Holly Holland

making-number-talks-matterLike many educators, Marcia Trujillo often feels professionally isolated. Varied schedules and interests make it tough to connect with colleagues who want to deepen their knowledge of particular math topics she cares about. As a math coach for three elementary schools in the South Lane School District in Oregon’s Willamette Valley, Trujillo has encouraged teachers to engage students in Number Talks—short, daily routines during which they solve problems in their heads, with no paper and pencil, and explain their reasoning.

“The teachers whom I work with are busy, and time is always an issue,” she said. “When someone like myself goes in and tries to help teachers learn something new, it’s difficult because teachers often don’t have time to think, to plan, to try something new. Inevitably, I begin to second-guess myself: ‘Is this a practice that will positively impact student achievement and teacher knowledge over time?’”

Then, last summer, Trujillo saw on Twitter that teachers were participating in an online book study of Making Number Talks Matter (Stenhouse, 2015), Cathy Humphreys and Ruth Parker’s new resource for educators serving grades 4–10. Within a few weeks, Trujillo was collaborating with about 700 educators from fifteen countries who were reading the same book for professional study. Over several months they reviewed chapters together, wrote blog posts, shared and watched classroom videos, and conversed about commonly asked questions using social media platforms, including Facebook and the Teaching Channel. The experience proved transformative for Trujillo, who has used the skills from her personalized professional development to support other teachers in her district.

The interactive book study “takes me out of my isolated world and surrounds me with other people who love math or either are coaching other teachers in best practices or trying to learn something new,” she said. “Being able to read the book with other people, write about it, and also watch the videos helps me feel confident that I’m on the right track, and that the practice is worth teachers’ valuable time to learn about and to implement in their rooms.”

Such stories also inspire Crystal Morey and Kristin Gray, the two math teachers who started the collaborative book study of Making Number Talks Matter. Both are Teaching Channel Laureates who met last summer and discovered their mutual love of Number Talks. Morey, a middle school math teacher in Enumclaw, Washington, had worked with Ruth Parker for three summers through a state grant that supports professional development for teacher leaders. Gray, a K–5 math specialist in Lewes, Delaware, had presented on Number Talks at education conferences and built up a large following on social media. They decided to reach out to colleagues to see who might be interested in exploring the book together. The Teaching Channel agreed to host the free exchange—the first of its kind.

“I knew a lot of people would be interested, but as far as spreading internationally, I had no idea,” Gray said. “So many components about this make it unique. In book studies in the past, when you are in your school it’s always limited to what your colleagues have to say, what their experiences are, and what is the culture of your own building. This opens it up to so many different grade ranges and different school populations. You see the professional work as bigger than your school. It’s amazing to me to have the same focus point and so many people around the world using it but with different experiences than mine.”

Gray and Morey developed a study guide for the book. Gray also posted weekly questions about the book chapters to guide discussions and distributed a digital newsletter to recap what had happened during the week, along with related resources. Some teachers worked quickly through the chapters whereas others took a more leisurely pace, in both cases personalizing their learning. Through an online platform called Teaching Channel Teams, the collaborative enabled teachers who were working at the same pace and on similar topics to align. All of the participants could communicate through discussion boards and blogs and were able to upload videos, which could be annotated.

In addition, Morey interviewed Parker about the book and posted their insightful conversations. Morey also videotaped herself using Number Talks strategies with students and asked Parker to critique her work so that others could learn from it. After she posted the videos on the Teaching Channel site, other teachers began videotaping their own classroom exchanges and sharing them.

“They’re taking pictures of their Number Talks boards and posting them. Some started blogging for the first time because of this—they’re super excited,” Gray said. “I think it says a lot about Number Talks and how incredibly valuable it is to hear students converse about math. It just feels like a cultural shift in how we listen to our students and dive into their thinking.”

Gray and Morey said Making Number Talks Matter is such a rich resource because it reaches across the trajectory of mathematical operations and then extends them. Although the book targets grades 4–10, teachers below and above that span have found ways to adapt the strategies.

“The book allowed me to understand the operations even more,” Morey said. “It was a learning tool for me mathematically. It also allowed me to understand how to open up instruction and provide opportunities for flexibility in thought.”

Morey and Gray stress that Number Talks are not about teachers’ direct instruction but rather about their students’ mathematical thinking. Instead of trying to please the teacher by simply uttering the “right” answer, for example, Number Talks are designed to help students move beyond memorization, express their understanding as well as their confusion, and use a variety of problem-solving strategies so they can become flexible mathematical thinkers.

Brian Bushart, curriculum coordinator for elementary mathematics in the Round Rock Independent School District in Texas, liked the book so much that he decided to share it with a cohort of about thirty local educators, including K–5 teachers, instructional coaches, and interventionists. They started by meeting for two days last July and then scheduled nine more after-school sessions throughout the school year. To deepen their study, participants joined the Teaching Channel collaborative and participated in a Google Hangouts chat with Gray. Bushart also asked them to reflect on their experiences through blog posts and to share a related lesson. The goal was to have each of the participants reach out to at least one other colleague at his or her school, spreading the influence of Number Talks. So far, more than 150 educators in the district have participated in some component of the book study, including the online collaboration and related workshops.

The book was very practical, grounded, and approachable, Bushart said, and “turned out to be exactly what they wanted.” In addition, the Teaching Channel videos enabled teachers to see colleagues “trying out the things we were talking about. It was so current: ‘Hey, I just did this on Tuesday.’ It felt like they were in the book study with us. It wasn’t canned or stale.”

Gray and Morey hope to repeat the interactive book study in the coming year. They have collected all of the Twitter hashtags and blogs and responses to tell the story of their collaborative work.

“It’s exciting to me to see so many people being open and sharing, whether it’s perfect or not,” Gray said. “That’s so brave. I think it shows we all learn better together.”

3 comments February 15th, 2016

Now Online: Making Number Talks Matter

making-number-talks-matterCathy and Ruth have developed incredible knowledge of the best ways to teach Number Talks with students of all grade levels. That knowledge is packed into this highly readable book.
—Jo Boaler, from the Foreword to Making Number Talks Matter

Believing that mathematics is mostly about using procedures correctly, many students have learned to focus on getting the right answer, whether or not the process makes sense to them. As a result, they disengage and lose confidence in their reasoning.

In Making Number Talks Matter, veteran math educators Cathy Humphreys and Ruth Parker show you how to help students take back the authority of their own reasoning through this 15‑minute daily routine. With skillful facilitation, your students will reason mentally with numbers, develop a strong sense of the meaning of quantities and operations, and gain proficiency with mathematical practices.

Teachers who are new to Number Talks will find a solid introduction, guiding principles, and tips on how to set up the routine. And teachers of all experience levels will learn new ways to extend and enhance their practice, with multiple strategies for each of the arithmetic operations; sample problems; examples of discussions and how to record student thinking; and ideas for increasingly challenging problems—including fractions, decimals, and integers.

As your students come to know that they have mathematical ideas worth listening to, as they learn to defend their ways of knowing with sound mathematical arguments, and as they learn the value of listening to one another and building on the ideas of their peers, their view of mathematics will be transformed.

Preview the full text of Making Number Talks Matter online!

Add comment March 23rd, 2015

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