**I have used the Number Talks from your original book, Number Talks: Helping Children Build Mental Math and Computation Strategies, with my students for a number of years now, and I’ve seen tremendous growth in their ability to work flexibly with numbers. For those who might not be familiar with Number Talks, can you briefly explain what they are and why they are important for our students?**

A Number Talk is a five to fifteen minute classroom conversation around purposefully crafted problems that are solved mentally. During a Number Talk teachers ask students to mentally solve problems to help students focus on number relationships, encourage and elicit students’ individual strategies, and help students construct important mathematical ideas. As students share and defend their solutions and strategies, they have opportunities to collectively reason about numbers while building their mathematical understanding.

Number Talks are rooted in Jean Piaget’s theory of learning which centers on the idea that there are actually three different types of knowledge. (We discuss this more in Number Talks: Fractions, Decimals, and Percentages.) Knowledge that has its ultimate source in other people, and changes from society to society, like the names for things or how something is written, is something we have to tell students. It’s called social knowledge. Things like, “This is called the distributive property,” or “You can write the multiplication sign as an ‘x’ but you can also write it as a dot,” are social conventions and can change from society to society or over time.

We ask instead of tell, however, when we are dealing with logico-mathematical knowledge. Logico-mathematical knowledge has its ultimate source in the mental relationships that students make for themselves. There are different ways to solve the problem 16 x ¾ because there is logic involved. When we ask students, “How could you solve this? How do you know?” it’s because we know we are dealing with logico-mathematical knowledge and that the source of this knowledge is students’ own mental relationships.

Understanding the difference between different types of knowledge changed our classroom practice from giving students procedures to asking students to create or “invent” strategies based upon mental relationships they were making.

**Teachers operate under a wide variety of instructional routines and utilize many different math programs. How can teachers fit Number Talks into what they are currently doing? **

Teachers often wonder about:

- how often to do a Number Talk;
- time constraints;
- the best time to do a Number Talk; and
- connecting the Number Talk to their lesson.

We recommend doing whole-group Number Talks at least three times a week to develop a community of learners that are focused on accuracy, flexibility, and efficiency. A whole-group setting offers an opportunity to exchange and consider a greater range of diverse ideas. Some teachers also incorporate small group Number Talks into their weekly routine to allow them to focus on students with similar needs.

Our instructional time is precious, so we encourage teachers to limit their Number Talk to somewhere between 5 and 15 minutes. We have even set a timer to help keep us mindful of the time! If you only have 5 minutes, consider using an individual problem or using the problems from a Number Talk string over several days. For example, on Monday you might pose 1/2 + 1/2; on Tuesday introduce the second problem in the string, 1/2 + 3/4, and on Wednesday share the final problem, 1/2 + 5/8. Keeping the previous problems and their solutions posted, provides students support as they think about the new problem.

A Number Talk can be used at any time during the day; however, our preference is to begin our math time with a Number Talk. There is something about coming together and exchanging different perspectives in a Number Talk that sets the tone for the rest of our lesson. When we begin with Number Talks, we notice students’ mathematical dispositions shift toward sense making and justification of ideas.

A Number Talk does not always have to connect to your lesson content. For example, if your lesson is focused on geometry, your Number Talk might incorporate problems to address multiplication strategies or “soft spots” you notice from a particular operation.

**As an instructional coach who was trying to help my teachers implement Number Talks, I found that some teachers were intimidated because they didn’t understand the strategies themselves and they weren’t sure they would be able to scribe the strategies the students used. What advice can you give teachers who are hesitant to try Number Talks for those reasons? What supports does the book provide to help teachers feel more comfortable as they get started?**

We completely understand. It can be uncomfortable to ask students to share their strategies and then not understand their way of solving the problem. The good news is that the more you do Number Talks, the more strategies you hear and the less often you find yourself in that uncomfortable position.

When we first started doing Number Talks, we found ourselves asking co-workers, friends and family members how they would solve the problems we were going to give our students. The more strategies we heard, the more we were able to anticipate what our students might do and the more we were able to plan how we would record those strategies.

We also found that depending on the problem, as we asked several people how they would solve it, there were usually only 3 or 4 common solutions. Anticipating students’ solutions helped build our confidence to open the classroom discussion with Number Talks.

When a student does share a strategy that we haven’t considered before, we usually handle the situation in one of two ways.

- We ask another student if they can explain the first students’ strategy. Sometimes a peer can understand another students’ thinking when we can’t.
- We let the student know that we are having trouble following their solution right now, and we record and put that solution to the side until we can have a private discussion to try to understand their thinking. Then if it’s appropriate, we come back to that discussion the next day with a fresh understanding and acknowledge that student’s thinking.

**I find that in classrooms that are the most successful with Number Talks, the teacher has fostered a culture of respect and helped students develop strong mathematical communication skills. How do number talks support mathematical discourse and why is that important?**

Number Talks are based on the ability to exchange ideas and consider other people’s points of view. A classroom culture of respect is critical to successful Number Talks. As soon as you ask students questions such as, “What do you think?” or “How do you know?” or “Who would like to defend their thinking?” you are asking students to be vulnerable. That can be frightening unless our classroom is a place where it’s okay to be wrong, where mistakes are viewed as opportunities to learn, and where the class a whole is trying to learn from each other.

Turn and Talk is an important instructional strategy that can help build students’ confidence in sharing their ideas. When you pose a problem and ask students to turn and talk about what they are thinking, everyone gets a chance to share their ideas. Then when you ask students to share, they are not only sharing their own ideas, but ones they have collaborated on and had a chance to solidify by talking them through with a partner. It takes some of the pressure off of sharing your own ideas.

When students are new to sharing their ideas and discussing the reasoning of others, it is often helpful to post a list of open-ended prompts to support students as they learn to engage in mathematical discourse. We have found the following to be useful in our classroom discussions.

I noticed ________________________________________.

Can you explain why you __________________________?

Will it always work if we __________________________?

I understand ________but am confused about _________.

I am confused about ______________________________.

**What are some of the reasons that students have such a poor understanding of fractions and decimals?**

There are three primary reasons students have difficulty with understanding fractions and decimals.

- A fraction can have multiple representations and interpretations; For example, 3/4 can be represented as a fraction, a decimal, or a percentage. Three-fourths can also be interpreted as a part-whole relationship, a measure, a ratio, a quotient, or an operator. Navigating between these different representations and interpretations can be confusing and problematic for students.
- When a student’s knowledge of fractions rests solely on memorized procedures, their foundation for making sense of solutions when operating with fractions is fragile. Tricks such as “yours is not to wonder why, just invert and multiply” or “keep, change, flip,” may produce quick results but often result in errors when students forget steps to procedures they do not own. By intentionally focusing on building conceptual understanding first, student use fractional reasoning and number sense to decide whether a solution is reasonable.
- One of the biggest barriers to understanding fractions is when students think about fractions as two whole numbers stacked on top of each other instead of as distinct quantities. Examples of students using inappropriate whole-number reasoning are when they add or subtract across numerators and denominators or when they order fractions by focusing solely on the denominator (such as ½, 1/3, 1/4). These kinds of mistakes are not careless errors, but indications of students trying to use what they know about whole numbers to understand fractions. These student misconceptions do not have to be inevitable. Number Talks can be an important vehicle for helping students to make sense of fractions.

**The floor is yours! What do you feel teachers ought to know about this new book?**

We hope teachers will begin with Number Talks that focus on building fractional reasoning before moving into computation. Students’ ability to reason and make sense of the mathematics is what supports them when they begin operating with fractions.

While the book is organized by chapters, please do not feel you should go page by page and use the Number Talks in the order in which they are presented. Listen to your students and let them guide you as you select individual problems or Number Talk strings. The Number Talk strings are provided as a way to support students as they look for and make numerical relationships; however, it is certainly fine to select an individual problem.

Finally, enjoy the journey! Enjoy learning with and from your students. We hope you will be comfortable becoming a part of the learning community and that your own fractional reasoning and strategies will grow through this process. The strategies in the book were ones we learned from students, so we urge you to resist teaching the strategies by telling.

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What a thrill for me to have the opportunity to interview Sherry and share her words of wisdom with you!

Arlee Hall says

Thank you so much for this incredible resource! My students (and I) have a deeper understanding of mathematics, thanks to your book!

Arlee Hall says

I WON!! Oh MY GOODNESS! Thank you so very much for this incredible gift! I cannot wait to sink in my favorite arm chair and devour this incredible book. I am so very grateful!

Tammy Stotler says

So thankful for the work you have done and continue to do!

Brooke Hipp says

I’m just starting to use Number Talks with my students, the results are amazing. I can’t wait to see the new book!

Beth Alfonso says

LOve using number talks. Great discussions that support deeper understanding.

Amy DeLon says

I have only recently heard of this resource and am interested to learn more! It sounds great!

Kellie Gunter says

I am an Intervention Specialist and my focus for the upcoming year is Math. I had previously heard a bit about Number Talks, but now I am so excited to read and learn more! Thanks for the post!!

JUANA says

I very much appreciate this article since I try to improve my use of number talks. Looking forward to reading this new resource.

Jenni says

I can’t wait to get my hands on this book!

Tara says

I’ve ordered 6 for my campus! I can’t wait to start using with our 3rd, 4th, and 5th graders!

Tami Broomall says

Love the first book, so I can’t wait to check out the new one.

Suzanne says

I love Number Talks! I would love a copy of this book!

Desiree says

I love number talks. Thank you for posting about this book. It sounds like a great resource

April says

This looks like an amazing resources to share with my students! I would love to get my hands on a copy!

Liz says

I love the idea of number talks. Next year i need to do them a lot more!

Danielle says

I have really enjoyed Number Talks with my students to see where their thinking takes them.

Anne Vopal says

As a math specialist, I have the privilege to work with students in K-8. I love using Number Talks with my students. It is a wonderful way to have students explain their thought process and share with their classmates. This new book sounds like a great way to further Number Talks into the upper elementary grades and middle school. Thank you!

Sharee Hebert says

I can’t wait to read this book. I want to be able to share about teaching understanding rather than just the tricks.

Beth says

The first book was such a great resource. Can’t wait to read the second.

Siew says

I’ve read the first book and have been using number talk with my child to see how thinks through the problem. Sometimes just talking through his strategy helps him figure out where his mistakes are.

Colleen Williams says

Can’t wait to read it! Thank you for offering the giveaway!

Amanda Vollmer says

I have the first Number Talks book and believe getting students talking about math and their thinking is SO important! Trying to figure out how to get my buildings on board too!

Kelly Malloy says

I love using number talks in my classroom! Can’t wait to check out this version!

Amy says

Love you Facebook page and blog. I love sharing your posts!

Kelly says

I have used Number Talks with third graders and saw amazing growth! I would love to try this approach with my fifth graders using fractions!

Becky Stegall says

Thanks for sharing the interview. I am excited about this book as I will venture into 6th grade math next year and think this could be a great help to bridge from elementary to JH. Thanks!

C Kirk says

Listening to students is extremely important!

Penny Young says

I use something similar, but love how this goes into it more in depth.

Caitlin says

I love the confidence that number talks has built with my students during my student teaching semester! I can no wait to implement number talks next year with my own classroom!

April Kisner says

Number Talks are an amazing resource…it gets our kids talking mathematically and thinking!

Can’t wait for this version!

Debra Smith says

I love Number Talks and try to incorporate them several times a week. So useful to understanding for my kiddos.

Lisa Wild says

Our students have grown tremendously since our school began implementing Number Talks!

Lori Kizer says

NUmber Talks truly changed the level of thinking and discussion in math in my classroom! It helped my students be effective in their strategies as well as to think outside of the conventional box.

Christine says

I love the original Number Talks book!

Jan says

Number talks are an awesome resource! I look forward to reading this new book.

Jan says

Number talks are so valuable. I would love to read more about number talks with fractions.

Melanie Meredith says

I really want to integrate Number Talks into my classroom so that my students will start working together and actually talk about Math! Thanks for this opportunity!

Laura says

Looking forward to using number talks next year in my 3/4 multiage as a may to bring the two groups together!

Diane Herman says

I have just started Number Talks in my Grade 1 class in Sydney, Australia. My students really enjoy talking about their thinking. Thanks for such a valuable resource.

Kelli says

Love Number Talks. I’ve seen the benefit with increasing fluency of basic facts. Can’t wait to get my hands on the new fraction and decimals one. Thx for sharing this interview!!

Donna says

Thank you so much for providing all the information in this interview! It was so helpful. It made me think differently about how I teach my students.

Candy says

The article was very helpful. I feel that I have a better understanding about number talks. I will try one this week.

Carrie says

I use Number Talks in my 3rd grade class and LOVE the math talk, thinking, reasoning, and making sense of math that happens! Looking forward to checking out the fraction talks since that is a topic many of my third grade students struggle understanding!

Thanks!

Crista says

One of the most exciting things I’ve done this year as a math coach is modeling number talks in SDC special education classes. Every time I’ve done it, teachers have been excited to see the thinking and understanding that their kids were able to do, that they had never been able to get students to demonstrate. Dot Talks are my favorite to get kids exercising their voice and recognizing that there are multiple ways to make sense of the problem.

Cindy Elkins says

I have been advocating use of Number Talks with the teachers I work with. I first learned about it from a math professor when working on math specialist certification coursework. It was one of our required “textbooks.” I absolutely love it!! Because of it, I soon realized there were so many different strategies out there that I was personally neglecting. It has made me a better teacher and a better math coach. You are right — too often teachers want to quickly go to the “tricks” to teach operations with fractions without building understanding. I think your book will go a long way toward helping teachers understand this information themselves – and then pass along to the students.

Dee Ann says

I use Number talks every week several times and this is the student’s favorite part of our math block. They LOVE it!!!!!

Danielle says

I student taught in a school that did Number Talks everyday and I fell in love with it. When I became a teacher myself, not a single teacher did Number Talks in their room. However, from the first day of school, I implemented Number Talks into my own classroom and my students were able to understand and use all strategies that were introduced to them. My kids look forward to it everyday and love discussing with their peers about the different ideas on how to solve the same problem. Now, my school knows that it’s my favorite thing and I even talk about it at district meetings, hoping other teachers will see the advantages! When I found out there was a new book, I was over the moon and want to hopefully be able to bring those new strategies to my kiddos. Thank you for everything!

Sharon says

Thank you so much for all the information! I will be trying number talks in my class this week.

Brittany Bright says

I want this as a mom and teacher. My son struggles with fractions and decimals. I look for quick but good ways to work on these mor in addition to what school does with them. Would love to give one to our math team.

Elisa Gray says

This is my first year teaching algebra. (the last time I spent much time in an algebra class was when I was in high school in the 70s!) My students ALL (It’s the way the class make up is designed) have terrible number sense. I’m wondering if Number Talks might help them, even if they are already in High School.

Annette says

Thank you for another great resource!

Beate Pryor says

I work with many teachers and students. I enjoy modeling the number talks with students while teachers observe. My hope is that this new book will allow me to work with more of our intermediate students and teachers.

Kim says

I am amazed at the mental computation and flexibility my students have shown this year after implementation of number talks. Number talks are a part of the day my students look fiat forward to.

Mandy says

After reading this post, I am very interested in this book and starting Number Talks with my 5th graders. Thank you for the resource!