# data[].attributes.attachment_link.readable_text
Marilyn Burns is one of today's most highly respected mathematics educators. Over the course of almost sixty years, Marilyn has taught children, led professional development sessions, spoken at conferences, contributed to professional journals, written a dozen books for children, and created more than twenty professional development publications for teachers and administrators.

In 1984, Marilyn founded Math Solutions, dedicated to improving math teaching in Kindergarten through Grade 8. Soon after, Marilyn wrote About Teaching Mathematics, now in its 4 th edition. Her other professional books include Welcome to Math Class; Math and Literature; Teaching Arithmetic; Lessons for Algebraic Thinking; Writing in Math Class; and more.

Marilyn has been the recipient of numerous honors, including an honorary doctorate degree from Bank Street College of Education in New York in 1991, the Ross Taylor/Glenn Gilbert National Leadership Award from the National Council of Supervisors of Mathematics in 1996, the Louise Hay Award for Contributions to Mathematics Education from the Association for Women in Mathematics in 1997, and induction in 2010 into the Educational Publishing Hall of Fame by the Association of Educational Publishers. In 2019, Marilyn received the Walter Denham Memorial Award from the California Mathematics Council in recognition of her advocacy for math education at the state and national levels.

Working with Math Solutions colleagues, Marilyn has developed several important school resources. , published in 2007, is a supplemental instructional program for building numerical reasoning. In 2012, was published to help teachers use children's literature for teaching mathematics. Also in 2012, Math Reasoning Inventory (MRI), a digital interview tool funded by the Bill & Melinda Gates Foundation, was made available to help teachers assess students in Grades 5 and up. In 2021, Listening to Learn was published, a digital interview tool that expands MRI to help teachers of Kindergarten and up learn how their students reason numerically.

# data[].attributes.attachment_link.description
Marilyn Burns is one of today's most highly respected mathematics educators. Over the course of almost sixty years, Marilyn has taught children, led professional development sessions, spoken at conferences, contributed to professional journals, written a dozen books for children, and created more than twenty professional development publications for teachers and administrators.

# data[].attributes.attachment_link.readable_text
Interactive Support for Professional Learning

Listening to Learn Labs are interactive, on-demand professional learning opportunities that provide support for giving interviews and learning from them.

Reasoning Labs

Practice listening to students explain their reasoning for one interview question and matching the students' reasoning to the explanations provided.

Strategy Labs

Learn about the strategies students need to reason numerically by focusing on one strategy and watching examples of students who do and do not use it.

Interview Labs

Get specific answers from Marilyn and Lynne to questions raised by teachers conducting Listening to Learn interviews.

# data[].attributes.attachment_link.description
A K-5 digital interview tool focused on students' mathematical thinking.

# data[].attributes.headline
Four Videos that Introduce Listening to Learn 

# data[].attributes.subject
Four Videos that Introduce Listening to Learn 

# data[].attributes.body
For Foundations of Numerical Reasoning, we show the full Interview 1 with one Kindergarten student. For each of the other Content Focus areas, we selected one representative problem and show a variety of students answering the same question. All videos include Marilyn's reflections.

# data[].attributes.attachment_link.authors[].name
Heinemann. A division of Houghton Mifflin Harcourt.

# data[].attributes.attachment_link.readable_text
Lynne Zolli was a classroom teacher in the San Francisco Unified School District for over forty years and taught grades 1 through 6. She also was a mentor teacher, professional development leader, Math Solutions® instructor, and conference speaker. Lynne is a grant writer, an author of Math Solutions® professional books, and a co-author of Do the Math, an intervention program that targets on number and operations, and Listening to Learn, a digital interview tool for grades K-5.

# data[].attributes.attachment_link.description
Lynne Zolli was a classroom teacher in the San Francisco Unified School District for over forty years and taught grades 1 through 6. She also was a mentor teacher, professional development leader, Math Solutions® instructor, and conference speaker.

# data[].attributes.attachment_link.readable_text
Listening to Learn is a K-5 digital interview tool that helps teachers learn how their students reason numerically. The interviews can be used throughout the year to help guide instructional planning. Listening to Learn also includes interactive professional learning labs to support teachers.

Special Offer: Save 30% off our list price automatically when you buy 31 or more.

A message from Marilyn Burns and Lynne Zolli:

"In Listening to Learn interviews, we ask students to solve problems mentally, without using paper and pencil. Students' explanations for how they reason provide important and useful insights for planning instruction. We hope that our collaboration on interviewing will help teachers learn how their students reason numerically and how to best serve their needs."
With Listening to Learn, you'll get access to:

All 10 Interviews across the four content areas

The essential reasoning strategies identified by Marilyn and Lynne

Class and individual reports for planning instruction

More than 40 unique and interactive professional learning labs that offer support and guidance from Marilyn and Lynne.

Additional resources that include an extensive video library, downloadable question cards in both English and Spanish, FAQs, instructional suggestions, and more.

District and School Inquiries
To speak with a Heinemann sales representative about purchasing Listening to Learn for a school or district, please fill out this form and we will be in touch soon. Or, you can find your area sales representative here.

For more information about Listening to Learn, visit ListeningtoLearn.com.

(click any section below to continue reading)

Components

A one-year digital subscription designed for one educator

One complete set of question cards and one jar of manipulative cubes

Reviews

"This is the mathematical partner to a reading comprehension assessment. By allowing students to sit with a question and explain their thinking you get insight into the ways they manipulate numbers, reason through problems and navigate mathematics mentally. It's the thinking that is not always able to be captured on paper." - KARA PRANIKOFF, 2nd grade teacher, P.S. 234 Independence School

"If you want amazing data to drive your instruction, then you need to conduct Listening to Learn interviews!!" -EMILY LEMAIRE, 1st grade teacher, North Riverside Elementary

"Using the interviews remotely has been amazing. It's one of the few things about teaching remotely that's been great. Just getting a chance to work with kids and get to know them one-on-one in that sort of a way has been really awesome." - JOE MANNARINO, 5th grade teacher, John Muir Elementary School

"In addition to learning about how students think about math, I also learned a lot about how students think about themselves as mathematicians. I walked away feeling like I had a sense for whether students need to work on their math mindset, number sense, or place value." - REBECCA SAWADY, 4th grade teacher, Amigos School

"I do believe all teachers should do math interviews. I don't think there's anything else out there that offers the opportunity for you to really listen and learn from your students in this way." - RASHIDA CARTER, 5th grade teacher, John Muir Elementary School

Related PD Services

# data[].attributes.attachment_link.description
Listening to Learn is a K-5 digital interview tool that helps teachers learn how their students reason numerically. The interviews can be used throughout the year to help guide instructional planning. Listening to Learn also includes interactive professional learning labs to support teachers.

# data[].attributes.headline
An Introduction from Marilyn Burns and Lynne Zolli

# data[].attributes.subject
An Introduction from Marilyn Burns and Lynne Zolli

# data[].attributes.attachment_link.readable_text
Listening to Learn is an exciting new K-5 digital interview tool by highly respected educators Marilyn Burns and Lynne Zolli. Just released from Heinemann this April, Listening to Learn math interviews are one-one-one assessments that help teachers learn how their students reason numerically - the essential information they need to plan instruction.

In this blog, we're going to keep up with Marilyn's Listening to Learn Twitter chat, so you can learn more about math interviews and share what you learn with your friends and colleagues.

Whether you've been following along with the Twitter chat from the beginning or are just seeing these video clips for the first time, we invite you to watch the clips below and share your thinking either in the blog comments or on Twitter using #ListeningToLearn. Be sure to follow @mburnsmath to see the new video every Wednesday evening.

We suggest you start with this brief overview video to get an initial sense of the importance and usefulness of Listening to Learn.

To learn more about Listening To Learn click the button below.

Below, we'll catch you up on anything you might have missed in the Twitter Chat so far-- but there's still plenty of time to join in the conversation! Look for a new Tweet from Marilyn every Wednesday through June.

Marilyn started the conversation with an introduction to Listening to Learn.

The first video clip Marilyn shared was an interview conducted by coauthor Lynne Zolli. This is Listening to Learn: Interview 2, Addition and Subtraction within 10.

The following week Marilyn shared this video, where she interviews a student using Listening to Learn: Interview 4, Addition and Subtraction Within 100

In this clip, we get a sense of Listening to Learn: Interview 1, Foundations of Numerical Reasoning from watching @amycmayfield present a problem to a Kindergarten student.

Marilyn then posted a video of Rusty Bresser presenting a student with the first question from Listening to Learn: Interview 6, Foundations of Multiplication.

Next, Marilyn shared a video featuring a word problem from Listening to Learn: Interview 10, Fractions & Decimals.

This time, Marilyn shared a pair of videos showing two students, one interviewed by Marilyn and the other by Lynne, answer the same question from Listening to Learn: Interview 8, Extending Multiplication & Division.

The next video highlights that partial understanding and confusion are part of learning in Listening to Learn; Interview 9, Foundations of Fractions.

As is evident in this video, memorization is not enough alone. As you can see, her first instinct is to lean on what she's memorized, but when she comes up short, it's her ability to reason that gets her over the finish line.

Follow Marilyn Burns and Heinemann on Twitter and check back for updates.

To learn more about Listening To Learn click the button below.

Podcast fans, Listen to our conversation with Marilyn Burns on the Heinemann Podcast.

Marilyn Burns is one of today's most highly respected mathematics educators. Over the course of more than fifty-five years, Marilyn has taught children, led in-service sessions, spoken at conferences, contributed to professional journals, and written more than thirty books and resources for children and educators.

Lynne Zolli was a classroom teacher in the San Francisco Unified School District for over forty years and taught grades 1 through 6. She also was a mentor teacher, professional development leader, Math Solutions instructor, and conference speaker. Lynne is a grant writer, an author of Math Solutions professional books, and a co-author of Do the Math.

# data[].attributes.attachment_link.title
Take a First Look at The Listening To Learn Math Interviews and Join The Conversation!

# data[].attributes.attachment_link.description
Listening to Learn is an exciting new K-5 digital interview tool by highly respected educators Marilyn Burns and Lynne Zolli. Just released from Heinemann this April, Listening to Learn math interviews are one-one-one assessments that help teachers learn how their students reason numerically - the essential information they need to plan instruction.

# data[].attributes.headline
An Overview for Principals and Administrators

# data[].attributes.subject
An Overview for Principals and Administrators

# data[].attributes.headline
(Blog) Nine Ways to Have Deeper Converstions with Students about Math

# data[].attributes.subject
(Blog) Nine Ways to Have Deeper Converstions with Students about Math

# data[].attributes.attachment_link.readable_text
, where Marilyn regularly posts blogs, videos, and podcasts to help teachers help students learn math. Marilyn tweets at @mburnsmath.
Listening to Learn is an exciting K-5 digital interview tool from highly respected educators Marilyn Burns and Lynne Zolli. Listening To Learn one-on-one assessments help teachers learn how their students reason numerically-the essential information they need to plan instruction. This blog comes from Marilyn Burns Math

In his column in The New York Times, " Nine Nonobvious Ways to Have Deeper Conversations," David Brooks offers nine specific suggestions to help us think about connecting with people in meaningful ways. Inspired by his column, here I adapt his suggestions to address having meaningful and important conversations with K-5 students about math through Listening to Learn interviews. (First a math clarification: If you count, you'll find out that I included only eight of David Brooks's suggestions. That's because I combined two of them into one.)

I begin with David Brooks's first suggestion: Approach with awe.

Approach with awe
I expect surprises when I'm in conversations with students. Earlier in my teaching career, I always knew ahead of time what I hoped to hear from students when I asked questions. It was huge for me to make the shift from listening for what I hoped to hear to listening to what students actually said. When students come up with an explanation that surprises me or throws me a bit off balance mathematically, I listen with awe and keep my focus on understanding and appreciating how they are reasoning.

Be curious about students' thinking
Here I combine David Brooks's next two suggestions: Ask elevating questions and Ask open-ended questions. When we ask students to solve problems during our interviews, their solutions are only the starting place. Whether correct or incorrect, we always ask a follow-up question, "How did you figure out the answer?" This elevates the question and opens its emphasis in a new way. We make no judgment (as David Brooks cautions us against). During class instruction, I'm in teaching mode, and my typical student-teacher interaction focuses on helping, guiding, explaining, and showing. In contrast, during interviews, I shift to asking, listening, and learning how the students reason.

Make them authors, not witnesses
Math interviews are all about giving students the experience of exploring their own thinking as they figure out answers to numerical problems. David Brooks writes, "The important part of people's lives is not what happened to them, but how they experienced what happened to them." In math interviews, we're interested in more than having students repeat what they've learned-we're interested in how they apply and make use of what they've learned.

Treat attention as all or nothing
David Brooks recommends total focus, and I agree. In interviews, we want students to know that we're interested in hearing and understanding their ideas. I also agree with his conclusion that the effect is magnetic, in the sense that it attracts and holds the student's engagement. I've experience this many, many times during interviews. When students know that we're interested in their ideas and how they think, they connect with us in ways that are often unique and special.

Don't fear the pause This rang true to me. I think of "the pause" that David Brooks describes as "
wait time," and I've learned the value of using wait time to give students time to think. During one-on-one interviews, long pauses are frequent, and I've learned not to interrupt. As long as I observe that students are thinking, engaged in working to make sense and organize their ideas, I wait patiently. That's not so easy for us as teachers, but I've gotten better at it as I've experienced the benefits.

Keep the student front and center
This is an edit of David Brooks's suggestion: Keep the gem statement front and center, which refers to resolving conflicts in conversation. In interviews, we ask students to explain their reasoning and my goal, always, is to keep the student front and center. A friend, also a teacher as many of my friends are, told me that her goal was to be sure that the students were the stars in her class. Gena was aware of the power and influence we have as teachers, and she wanted to be sure that her students knew that their school experience was all about them, that they were the stars in the classroom. I loved that then and I love it now.

Find the reasoning under the explanation
This is also a tweak from David Brooks' next suggestion: Find the disagreement under the disagreement. When two people disagree, it's important to be curious about each other's positions and dig down to better understand each other. In a way, interviews are more like one-way conversations and, as the interviewer, I often try and dig deeply into a student's thinking. I intentionally don't express my point of view and I focus entirely on learning about the student's point of view. After a student explains, I might ask, "Can you tell me more?" Or, "Would you please explain again so I'm sure I understand your thinking?" Or, "How would you explain to someone else how to figure it out?"

The midwife model
This is David Brooks's last suggestion. I wasn't sure at first that this related at all to my thinking about math interviews. After reading and rereading, I decided that it definitely does. His explanation relates to avoiding talking in order to solve someone else's problem. He references Rev. Margaret Guenter who likens a good conversationalist to a midwife "helping the other person give birth to her own child . . . patiently listening to the other person teach herself." He quotes the neuroscientist Tali Sharot who advises giving people a sense of control. That's what we do in interviews. When teaching, we focus on helping students as needed. We teach. During interviews, our focus is on finding out how students think and why they reason as they do. Then we use this information for planning instruction and interacting with students during lessons.

A final note
In his conclusion, David Brooks wrote, "You can't really know yourself until you know how you express yourself and find yourself in another's eyes." He goes on to say that deeper conversations build trust. I agree with both. For me, math interviews have been extraordinary opportunities, true gifts, to connect with students, learn how they think mathematically, and use what I learn to inform my teaching. I'm excited to share Listening to Learn.

To learn more about Listening To Learn click the button below.

Marilyn Burns is one of today's most highly respected mathematics educators. Over the course of almost sixty years, Marilyn has taught children, led professional development sessions, spoken at conferences, contributed to professional journals, written a dozen books for children, and created more than twenty professional development publications for teachers and administrators. She is also a co-author of Do The Math, which is now available from Heinemann.

Lynne Zolli was a classroom teacher in the San Francisco Unified School District for over forty years and taught grades 1 through 6. She also was a mentor teacher, professional development leader, Math Solutions instructor, and conference speaker. Lynne is a grant writer, an author of Math Solutions professional books, and a co-author of Listening to Learn and Do the Math, both of which are available from Heinemann.

# data[].attributes.attachment_link.title
Nine Ways to Have Deeper Conversations with Students about Math

# data[].attributes.attachment_link.description
where Marilyn regularly posts blogs, videos, and podcasts to help teachers help students learn math. Marilyn tweets at @mburnsmath. Listening to Learn is an exciting K-5 digital interview tool from highly respected educators Marilyn Burns and Lynne Zolli. Listening To Learn one-on-one assessments help teachers learn how their students reason numerically-the essential information they need to plan instruction.

# data[].attributes.headline
(Blog) How We Begin the School Year is More Important Than Ever

# data[].attributes.subject
(Blog) How We Begin the School Year is More Important Than Ever

# data[].attributes.attachment_link.readable_text
, where Marilyn regularly posts blogs, videos, and podcasts to help teachers help students learn math. Marilyn tweets at @mburnsmath.
Listening to Learn is an exciting K-5 digital interview tool from highly respected educators Marilyn Burns and Lynne Zolli. Listening To Learn one-on-one assessments help teachers learn how their students reason numerically-the essential information they need to plan instruction. This blog comes from Marilyn Burns Math

Over the years, I've collaborated with Lynne Zolli and Patty Clark on a variety of projects.
We worked together creating this blog to share our thinking about how math interviews can serve teachers and students.

The first month of school has always been a time to get to know our students. We build the classroom climate, establish routines, and learn to work together. The time is well spent and pays dividends throughout the entire year. Now, after a difficult year of dealing with Covid, how we begin the school year is more important than ever. We need to learn as much as possible about each of our students so that we can provide the instruction they need to grow and learn.

Returning to Full-Time Face-to-Face Classrooms
Most teachers are coming back to the classroom after a year of some combination of face-to-face and remote instruction. It may be hard to imagine adding something new to our teaching repertoires at this time, but we feel this is exactly the time to embrace a fresh approach. We suggest beginning the year with one-on-one math interviews to find out about how each student reasons numerically, which will provide an essential foundation for planning instruction. Also, interviews are a valuable tool for connecting with students personally and beginning to build the relationships that are important for supporting their mathematical learning.

About Learning Loss
We've read and heard many concerns about students' learning loss, about the gaps and misconceptions that have resulted from a year of Covid. However, instead of focusing on what students lack or might have lost, we prefer to focus on who they are and what they know. When we focus on what students know vs what they don't know, we have a foundation of understanding that helps us best prepare to serve them. To accomplish that, one-on-one interviews open the door to learning about students and can provide information not available in any other way.

The Limits of Written Assessment
We've also read and heard that we shouldn't begin the school year by giving students assessments. We agree that paper-and-pencil tests can be a dismal way for students to begin a year of learning. However, finding out what students know and understand, is essential. Sitting with students during interviews, giving them our full attention and interest, and listening to how they explain their reasoning when solving problems, has a huge payoff and can help us learn more than written assignments are able to provide. A downside of relying on students' written math assessments is that their correct answers can hide confusion while their incorrect answers can mask understanding. In contrast, we've found that talking with students one on one and listening to how they reason provides more specific, accurate, and in-depth insights.

About Listening to Learn
There is no substitute for connecting one-on-one with students, listening carefully to how they reason and giving them the time they need to think and revise their ideas. That's why we're excited that Listening to Learn is now available. This digital interview tool provides insights into where students are mathematically, useful for baseline information at the beginning of the year and also throughout the year to check on progress. Interviews not only help us uncover how students reason numerically, they also provide a way to truly get to know our students mathematically. Do they persevere when solving math problems? Are they able to use reasoning strategies to compute mentally? Are they fluent with basic facts? Are they confident? Hesitant? Persistent? Flexible? Willing to take mathematical risks?

From giving Listening to Learn interviews, we learn if our students have access to the reasoning strategies essential for their ongoing success with math. We learn if they're able to communicate and express themselves using mathematical language. We learn how they feel about themselves as math learners.

We hope that you will consider using Listening to Learn interviews with your students. Once you give the interviews a try, we think you'll wonder how you ever did without them!
Lynne Zolli and I are the co-authors of Listening to Learn, were part of the team that created Do The Math, and have worked together on many other projects. Patty Clark and I have recorded several podcasts together relating to my most recent book, Welcome to Math Class. She is the former Senior Director, Services Content Development at Math Solutions and is currently leading services and development strategy for Heinemann Math.

To learn more about Listening To Learn click the button below.

Marilyn Burns is one of today's most highly respected mathematics educators. Over the course of almost sixty years, Marilyn has taught children, led professional development sessions, spoken at conferences, contributed to professional journals, written a dozen books for children, and created more than twenty professional development publications for teachers and administrators. She is also a co-author of Do The Math, which is now available from Heinemann.

Lynne Zolli was a classroom teacher in the San Francisco Unified School District for over forty years and taught grades 1 through 6. She also was a mentor teacher, professional development leader, Math Solutions instructor, and conference speaker. Lynne is a grant writer, an author of Math Solutions professional books, and a co-author of Listening to Learn and Do the Math, both of which are available from Heinemann.

# data[].attributes.attachment_link.title
How We Begin the School Year Is More Important Than Ever by Marilyn Burns

# data[].attributes.attachment_link.description
where Marilyn regularly posts blogs, videos, and podcasts to help teachers help students learn math. Marilyn tweets at @mburnsmath. Listening to Learn is an exciting K-5 digital interview tool from highly respected educators Marilyn Burns and Lynne Zolli. Listening To Learn one-on-one assessments help teachers learn how their students reason numerically-the essential information they need to plan instruction.

# data[].attributes.headline
(Blog) How I Got Hooked on One-on-One Interviews

# data[].attributes.subject
(Blog) How I Got Hooked on One-on-One Interviews

# data[].attributes.attachment_link.readable_text
Listening to Learn is an exciting K-5 digital interview tool from highly respected educators Marilyn Burns and Lynne Zolli. Listening To Learn one-on-one assessments help teachers learn how their students reason numerically-the essential information they need to plan instruction. This blog comes from Marilyn Burns Math, where Marilyn regularly posts blogs, videos, and podcasts to help teachers help students learn math. Marilyn tweets at @mburnsmath.

♦ ♦ ♦

I clearly remember my first one-on-one math interview. It was several years after I had founded Math Solutions when I was working on a series of professional development videotapes for the Cuisenaire Company of America. The goal of the project was to capture classroom mathematics instruction that engaged students in thinking, reasoning, and solving problems. This was way before making videos was as easy as pointing and shooting with your phone-more than 10 years before the first iPhone was released!

To learn more about Listening To Learn click the button below.

Stars in One Minute: A Favorite Lesson
One of the lessons we captured on videotape was Stars in One Minute, a lesson that's long been a Math Solutions staple. I observed Carol Brooks teach the lesson. Here's how it went: As the students timed one minute on the class clock, Carol furiously drew stars on the board. When the minute was up, Carol turned to the class and said, "Wow, I have a tired arm from drawing all those stars."
Carol then asked the class how they could find out how many stars she had drawn. Several students called out in unison, "Count by tens." This wasn't surprising as the class had been learning about place value. With the students helping, Carol counted and circled four groups of stars with 10 stars in each. They then counted the extra nine stars and Carol asked, "Should I draw a circle around those?"
Cena stood up to answer. She was confident, vehement, even a little bossy. She said to Carol, "Look, you've got, um, (and here Cena stopped to count the groups of 10) four tens, and you put a four right there. And you have nine stars left over and then you put nine right there."

The class watched as Carol followed Cena's instructions and wrote 49 on the board.

My Interview with Cena
Place value is complicated for students to understand. Since Cena was so emphatic and clear, I thought it would be interesting to interview her so we'd have an example to show teachers of a student with a solid grasp of the place-value structure of our number system. That night, we contacted Cena's mom, and she gave permission for me to interview Cena. The next day, Cena arrived in her Sunday best, her hair down, brushed and ribboned, no longer the pigtailed girl in school clothes. She was excited about being interviewed.

The interview was a startling experience for me. To begin, I put out a small plastic cup with 24 tiles and asked Cena to put the tiles into groups of ten. Cena counted ten tiles into a group, ten more into another group, and then confirmed that she had two groups of ten and four extra tiles. I asked her, "Do you know how many tiles you have altogether?" Cena looked up at me and shook her head no. I tried not to let on that I was startled. "How would you find out?" I asked her. Cena answered, "Count them," and she then counted the 24 tiles, one by one. Cena seemed thrilled to find out that there were 24 tiles. I was flabbergasted.

As the interview continued, additional soft spots emerged in Cena's understanding. It was a profound experience for me. You can watch the interview here.

Fast Forward 30 Years

Even before interviewing Cena, I believed that students were always the best source for learning how to improve my classroom teaching. Now, after collaborating with Lynne Zolli to create Listening to Learn, I'm even more convinced that listening to students, one on one, provides access into their reasoning in a way that's unique and invaluable. The experiences we've had interviewing more than a thousand students have been professionally life changing. I realize that it's quite a strong statement to say that something is life changing, but when I revisit the sentence, which I've done many times, it holds true.

Lynne was a classroom teacher in San Francisco Unified School district for 41 years and we've worked together on various projects. We are two teachers who are basically intrigued, even obsessed with interviewing students. We hope to encourage and empower K-5 teachers to use Listening to Learn, a digital interview tool that can help them learn how their students reason numerically, information that we think is essential for planning instruction.

To learn more about Listening To Learn click the button below.

Marilyn Burns is one of today's most highly respected mathematics educators. Over the course of almost sixty years, Marilyn has taught children, led professional development sessions, spoken at conferences, contributed to professional journals, written a dozen books for children, and created more than twenty professional development publications for teachers and administrators. She is also a co-author of Do The Math, which is now available from Heinemann.

Lynne Zolli was a classroom teacher in the San Francisco Unified School District for over forty years and taught grades 1 through 6. She also was a mentor teacher, professional development leader, Math Solutions instructor, and conference speaker. Lynne is a grant writer, an author of Math Solutions professional books, and a co-author of Listening to Learn and Do the Math, both of which are available from Heinemann.

# data[].attributes.attachment_link.title
How I Got Hooked on One-on-One Math Interviews by Marilyn Burns

# data[].attributes.attachment_link.description
Listening to Learn is an exciting K-5 digital interview tool from highly respected educators Marilyn Burns and Lynne Zolli. Listening To Learn one-on-one assessments help teachers learn how their students reason numerically-the essential information they need to plan instruction. This blog comes from Marilyn Burns Math, where Marilyn regularly posts blogs, videos, and podcasts to help teachers help students learn math.

# data[].attributes.headline
(Podcast) A Conversation Between Marilyn Burns and Lucy Calkins

# data[].attributes.subject
(Podcast) A Conversation Between Marilyn Burns and Lucy Calkins

# data[].attributes.attachment_link.readable_text
Today on the podcast we're excited to share a special conversation between Marilyn Burns and Lucy Calkins about Marilyn's new digital math interview tool, Listening to Learn. They discuss the importance of listening, a value that is central to both Marilyn's and Lucy's work.

Marilyn Burns is one of today's most highly respected mathematics educators. Over the course of almost sixty years, Marilyn has taught children, led professional development sessions, spoken at conferences, contributed to professional journals, written a dozen books for children, and created more than twenty professional development publications for teachers and administrators. She is also a co-author of Do The Math, which is now available from Heinemann.

Lucy Calkins is the Founding Director of the Teachers College Reading and Writing Project at Columbia University. She is also the author or coauthor-and series editor-of the reading, writing, and phonics Units of Study series, which are integral to classroom life in tens of thousands of schools around the world.

Here now is Marilyn and Lucy.
Below is a full transcript of this episode.
Lucy: Well, I've been waiting for this product of Marilyn's for a long time. She's been consumed with it. Working on it for years. I'm very excited that it's coming out now. I guess one of the reasons that I feel a kinship to it, is that my first book was, Lessons from a Child. I remember someone introducing me long ago, 30 years ago and saying "This is Lucy Calkins, she's the author of Lessons from a Child." And I said "Therein lies the story." Because ultimately, this is about taking lessons from children.

I think we all remember Don Graves, after that big study that we did all those years ago. Don graves took all of our data and went off to Scotland to... Marilyn, you may not know this story, but he went off to Scotland to spend a year on sabbatical, writing about the children that we studied. He and I studied together for two years and he had all this data all around his Shepherd's hut, where he was living for that year. The shepherd in the next hut, came over to visit him. All this data, all this student work everywhere and said "Don, what are you doing?" And Don says, "I'm writing about children." And the shepherd said "Don, wouldn't you rather write a love story?" And Don said, "This is a love story." So Marilyn, I've known the product's coming, but help me to understand what it really is and what the role of interviewing is that you're so excited about.

Marilyn: The story about Don Graves is wonderful because his book has been on my shelf for years. Cause even though I'm been completely immersed in the math world, his work spoke to me because his work was about listening to children. I have a closet that I'm almost terrified to open because of that, some student work that I revisit from time to time, to help my thinking. So it's all about, for me, understanding how students think, how students make sense of math, how they come into the world of numeracy, the way you're anxious to help kids come into the world of literacy. For years, I've been honing my teaching. I've been listening to students. I've been looking at their work and then when I started having conversations with students, I realized how many times I made erroneous assumptions, how many things I missed. I learned how much talking I was doing as the teacher, rather than listening to students to get their stories. I have, maybe similar to Don Graves, I've fallen in love with the process.

Lucy: I don't think I would really know. I guess I would imagine if it's a kid's doing, 9 plus 14, you might say, how did you go about solving that problem? Is that the main question you're asking? Or what is it you ask?

Marilyn: The main question is, we ask a question. It could be a problem, like what is 9 plus 14? It could be a word problem. It could be a problem where I ask them to compare two fractions and a variety of kinds of problems, but they're all mental math, no paper, no pencil. I listen to the answer, I never give feedback as to whether the answer is correct or incorrect, but the next line is, how did you figure that out? Or how do you know, tell me more. So they tell me more, I zip it up and I listen and give them time holding their attention, curious, and not only curious, but generous to really believe that they are trying to make sense and communicate with me. So we have a conversation about a problem that could be as simple as how much is 9 plus 14? But it's their thinking that I'm paying attention to.

Lucy: We talk about architecture of mini lessons and architecture of conferences in the teaching of writing. Is there a predictable architecture to how a math interview would go?

Marilyn: Yes. The way we structured listening to learn, we have 10 interviews. Each interview has 12 questions. There are word problems sprinkled throughout there are genres of questions. But the protocol is, asks the question, hear the answer, then follow up with, how did you figure it out? And then listen. The protocol is fairly accessible to teachers. The challenge is though the product is called Listening to Learn, the challenge is learning to listen because when a child explains their language is usually imprecise or often imprecise. It's not exactly what I was expecting to hear, but I put that aside and listen to the child. On the program, there's a list of explanations that we have gotten from thousands of kids that we have asked these same questions and you see, is there a match? So you have to not only listen as a teacher, you match it to one of the explanations we gave. And that's the information that Listening to Learn, captures and creates information for you to help you analyze and interpret what the experience was.

Lucy: So Marilyn, in our reading curriculum, we have a skill, like let's say prediction. We basically say that if you're predicting like a second grader, it might sound like this. If you're predicting like a third grader, it sounds like this, a fourth grader... We have a learning progression it's called where we sort of show how a skill like prediction, looks for grade two, three, four. But in any case, then a teacher is able to listen and say, okay, that's kind of like a grade two production. Let's say they're predicting what's going to happen. Then a higher level prediction would be not only what's going to happen, but how it's going to happen. A big way that teachers learn how to teach is they listen to think, where on the learning progression is that? Then they look at what's the next step. Then that's what they teach. Is that basically what you've done?

Marilyn: Well, it's similar in a way. First of all, the progression that informs Listening to Learn are the numerical reasoning strategies that we want kids to have access to. That progression we provide to teachers. For example, when you're counting, little kids will count on often using their fingers. If they were doing 4 plus 9, which is smaller than the number you suggested, they might start with nine and count on 10, 11, 12, 13. That's appropriate when students are learning and that's appropriate when the numbers are small, but it's not an appropriate strategy later on in the progression. We have a progression of strategies that we want teachers to be familiar with and we present them. But we've also found the numbers matter. 4 plus 9 is a problem that gives us information from students at a certain grade level. It's not something I'm going to ask a fifth grader.

Well, I might. I might say, how would you explain this to a second grader? But basically the numbers matter. The same progression of strategies exists, but the problems that we ask kids to solve depend on the capacity they have for their own number sense. We see some strategies like the counting on strategy, something that we're not even interested in capturing about fourth and fifth graders. But we have things like using 25 as a benchmark, which isn't even accessible to young children.

So this progression, it's not a lot of strategies. For addition and subtraction, there are basically nine numerical reasoning strategies that we explain and present to teachers and there are four different interviews numbers within 10, 20, 1o0 and 1,000, all mentally. So the problems are problems that are reasonable to do mentally. I'm not going to say to a child, okay. Figure out in your head, how much has to be 127 plus 752 plus 521. We say, okay, if I had 825, how much more do I need to add to it, to get to 1,000. That's possible mentally, and that's something which we'll use some of those strategies, like benchmarks of 29 using multiples of 10 as benchmarks. The strategies are the essence of this and the children's reasoning give us access into the strategies that they are able to use.

Lucy: So what your product... it's interesting again, I'm kind of comparing it to the two reading assessments because in reading assessments, we have to put forward a passage with questions about it. You can take these things and apply them to any book, but to assess it's helpful to have a passage and to have watched a lot of kids work with the same passage. Basically your tool includes the problems you would have kids do. Then the ways to make sense of what kids do with those problems and how that can inform where you think this child is in a progression of math work. Is that sort of...

Marilyn: Choosing the right passage is important. If you choose a passage that's too difficult, you're not going to learn it, or if you choose the passage that is too easy. In each interview, the first three questions are kind of benchmark questions. If the child can't answer the three questions correctly and with some confidence and explain their reasoning, then we dropped down an interview. Because, it's interesting. For addition, we have four interviews. If I'm in a typical third grade class, I will typically wind up using three of the interviews with students. I may start with a particular one thinking, numbers within 20 makes sense. Then I'll adjust after the first three, that guides that. In one way, I think I've taken all that thinking that I've done intuitively when I first worked interviewing and then made it say, wait a second, I got to explain my thinking and make this accessible, so teachers will have access to it, be inspired by it, be excited by it and learn about their students.

Lucy: How do you imagine teachers using this tool? Is it beside the bed? Is it in the classroom? Is it in a summer week, long Institute? Or how will it be used?

Marilyn: My entire career, as yours in a major way, is all about professional learning. Basically I see in one way, the tool is a way to enhance your own professional learning about math. Here's my dream, whatever assessment you're using for reading to find out about your students before you start teaching, I don't understand how you can start teaching until you know who your students are, tack this 10 minutes of math on the end. You'll learn about your students mathematically as well. I know that teachers who are comfortable and find it important to interview their kids in reading, they already know about the process. They've already bought into and accepted the benefits of the process. I now want them to see that same benefit in the world of mathematics.

Lucy: So this tool that you've developed, a district could buy it on Monday and on Tuesday, a teacher could take a piece of it and work with a kid.

Marilyn: They could, because some teachers are the kind of "I'll dive in, just do it." Some teachers are trepidatious, I want to think about it. We have videos. We have learning labs for teachers. We have every access point in. You can learn by yourself. You can learn with colleagues, you can just barge in and you can look at tons and tons of video, and you can read the blogs that my colleague Lynn and I are writing and producing.

Lucy: Ideally, it would be that there's a day or two of professional development at the start of the year where people are using the resources that you've put forward to kind of immerse themselves. Ideally, a coach spends more time on this and then decides which parts of it go for which groups of your teachers and so forth. Then there's a day of professional development where people use your resources to do some PD, and then they begin working with their math kids doing some of these interviews. I've got another big question. I don't know if you're ready for it, but okay. I do the interview. What does that have to do? I've got a curriculum in math with all these books and stuff. Why am I bothering to assess if I've already got a curriculum that is non flexible?

Marilyn: Well, my snarky answer is we're teaching students. We're not teaching the curriculum. Students first. Your curriculum to me is a default path of the content and the goals for your instruction. I've never met a teacher who didn't enhance, rethink, back up and teach. They have to make it their own. Whatever program they're using, the program is there to guide their instruction.

Lucy: Right, so you said you're talking to teachers about how to adapt and infuse more into their curriculum.

Marilyn: Also here's my goal. We would talk about inclusive and including all children. What I mean by that is the lessons that I offer, I have two criteria. They need to be accessible to all students. I will know from these interviews whether I need to do some work, perhaps ahead of time with a small group or how I might have to adjust it to give access for all opportunity for kids to go further, opportunities for me to learn who I need to confer with. I think that it's very important, is to making that decision.

Lucy: What about the whole idea of ability groups and all of that?

Marilyn: I am interested in building a community of learners. So there are things that I want to do together. When I think about your mini lessons, they're really something you do with the whole class. Kids will tune in, in some way. We, in the math world, have our number talks, where we do something short to give everybody access from which I'm looking and learning, so that when they go off to their work, when you go off to do the writing work and we go off to their menu work, or their math workshop, we know who to confer with.

Sometimes I'm very leery of ability groups and labeling students. I'm more interested in giving them access to the thinking that I want them to do, and in a way that makes sense. That's where the numbers matter. If I'm playing a game with kids, whether I tell them to use four digit numbers or two digit numbers, it's the thinking, it's the strategic thinking, it's the making sense that is the essence to all of it. Teaching is not easy. Sometimes people think teaching math is easy, cause the answer is as right. But the answer is just the starting place, you got to understand how these kids are reasoning.

Lucy: Do you see yourself... I mean, I feel as if what you really will want to have is communities of math coaches coming together. I really like my office hours. Once a month I have these office hours and people just come on and ask any old question. I feel as if, with this product, you should have office hours so that people who are trying it can come. Because I just think that the conversations that will happen between schools, and particularly between both the math coaches and then the math specialists, because in some elementary schools now there's teachers who just teach math and science, they become the specialist. I wish that didn't happen, but it is happening.

But I think those teachers could really come to understand the field of math, the world of math, the thinking that a math teacher should be doing, in a way that's what this could give them access to. But I feel like it would be a community of practice for those educators would be just beautiful.

Marilyn: The two things that we've done together when I came in was a guest on your supper club, which was wonderful. And also your Saturday reunion, we had time for teachers to ask me questions and questions were so important for me, to hear the level at which they were concerned. Some very concerned with smaller issues, some very concerned with larger issues. But this is a great idea because I learn from listening to students, I can also learn from listening to teachers.

Lucy: No, it would be a beautiful thing. I do think that the teachers are going to help teach both you and me some of these crosswalks that we've been exploring. Cause I mean, we get together and we try to think about how is it the same and how's it different teaching math and reading and writing. But I think that ultimately the teachers will figure that out and they will come back and say to us, no, you don't realize there's these other things.

Marilyn: We talk here in Listening to Learn about arithmetic. You've heard me say that the third are reading, writing, arithmetic. I wanted to change it to reading, writing, and reasoning. That's what Listening to Learn is all about. But basically we're talking about anything that any adult should be able to do. It's not scary. I hope it's not scary math. I know math is scary to people. This is really, numbers within our grasp and ways to think about numbers in our heads.

Lucy: What grade levels... how low does it go?

Marilyn: It starts with kindergarten or even pre-K. I go up and so pick the last ones are fractions and decimals. It's way up there. Any kid through middle school. I've used this with adult friends of mine and I learned something from them. I say to adults, okay, how do we add 99 plus 99 plus 5. And everybody goes, humph. And I get so many different answers. We ask that in our interview five, but we ask adults. The conversation is just about honoring our own way of thinking.

Lucy: I have to confess that when you were coming on supper club, I worried you'd give me a math problem. We were in the Adirondacks together and you gave me that problem.

Marilyn: I know, and you froze!

Lucy: It was so scary! But heart's pounding, I'm sweating.

Marilyn: But it was so interesting when you got the right answer a particular way. I'll never forget the problem. It was like 99 plus 14. You figured it out, you lined it up in your head, you saw it, you got the right answer. I said, I just went 100 plus 13 light bulb went on 100 as a benchmark. I said, aha. That comes out for us, so kids will develop this. We're very tender. We all have our fears. I've been teaching remotely. And I go, oh, I'm not good enough for this. The kids are wiggling. I see their forehead. I can't hear them. I still teaching nightmares. Every teacher I've met has teaching nightmares. So we're all tender and we have to be there to support each other in the way we want teachers to support their students.

Lucy: But I think what you've made is a tool that really can help people, help teachers to encompass the bigness of teaching math. I think that people make teaching math into a little thing and that this is big, important life work. What I know about teachers is, they they've come into this field because, it's a work of the heart and of the mind because it feels so enormously important and there's ways in which schools can grind people down. I think teachers are looking for ways to recover the majesty of teaching at its finest and at its richest to really be all in, in the profession and in the mission of math and of literacy and of whatever the teaching is. I think your tool is about recovering the scope and grand juror and bigness and depth of teaching math.

Marilyn: I want to inspire teachers to tackle this with curiosity and joy, and then to bring that into their students, and I want them to use the skills they do have. If a teacher feels completely comfortable teaching literacy. What are the things you feel comfortable with? What are the things you love to do? We can do that in math. It's not like math becomes something completely separate and not related to in different and in basic ways, they're the same. We're all about helping kids grow from where they are to where they could be.

Lucy: There was a time when I imagined that I could take on math education, just because so many of the people that work with me are passionate about math. They love math. I do think that the field of math education, it needs some new breadth of energy. It's interesting because you see it in the scholars. When I meet with you and Phil Darrow and others there's this electric energy, but it hasn't encompassed the field in the way that it should. It feels like the scholars are on fire doing this, and sometimes in the field, it's a little more follow the program.

Marilyn: That's why I think I've devoted my whole life to staying in the classroom, going into the classroom and talking to teachers about what I've learned, telling my stories. I think the thing about story, which you began in our conversation is so important that, what do I actually do? Face-to-face with a class of 25 students and you saw that, we were together. We took turns. It was really an incredible impactful day. It was fun, and it was important.

So how do I say to the kids, I am interested in you and together we can do this and what's the, this, it's not just getting the answer. It's not learning how to cross out the zeros divide, subtract, multiply, and bring down it's about thinking reasoning and making sense. Let's get to work.

Marilyn Burns is one of today's most highly respected mathematics educators. In 1984, Marilyn founded Math Solutions®, an organization dedicated to the improvement of math instruction in Grades K-8. Her book, About Teaching Mathematics, now in its 4th edition, has been widely used for pre-service and in-service teachers. Her other professional books include Welcome to Math Class; Math, Literature, and Nonfiction; Lessons for Algebraic Thinking; Writing in Math Class; and others. Marilyn's children's books include classics like The I Hate Mathematics! Book and The Book of Think, and the more recent The Greedy Triangle and Spaghetti and Meatballs for All! Her children's books have been translated into eight languages.

For her educational contributions, Marilyn received the Ross Taylor/Glenn Gilbert National Leadership Award from the National Council of Supervisors of Mathematics and the Louise Hay Award for Contributions to Mathematics Education from the Association for Women in Mathematics. She was also inducted into the Educational Publishing Hall of Fame by the Association of Educational Publishers.

Marilyn and a team of Math Solutions® master teachers developed Do The Math, an intervention program that targets on number and operations, and Math Reads, a program that helps teachers use children's literature for teaching mathematics. Her most recent project, Listening to Learn, is a digital interview tool for grades K-5 based on her previous work on the Math Reasoning Inventory (MRI), for students entering middle school and beyond and funded by the Bill & Melinda Gates Foundation.

Marilyn continues to teach regularly in the classroom, finding the experience essential to developing and testing new ideas and materials. Learn more about Marilyn's work at her Marilyn Burns Math Blog, by following her on Twitter @MBurnsMath, and by visiting her Marilyn Burns Math YouTube Channel.

Lucy Calkins is the Founding Director of the Teachers College Reading and Writing Project at Columbia University. For more than thirty years, she has led the Project in its dual functions as a think tank, developing state-of-the-art teaching methods, and a provider of professional development, supporting hundreds of thousands of teachers, principals, superintendents, and policy-makers across the country and around the world.
Lucy is the author or coauthor-and series editor-of the reading, writing, and phonics Units of Study series, which are integral to classroom life in tens of thousands of schools around the world. In addition, she has authored scores of professional books and articles. Lucy is also the Robinson Professor of Children's Literature at Teachers College, Columbia University, where she co-directs the Literacy Specialist Program.

# data[].attributes.attachment_link.title
On the Podcast: A Conversation Between Marilyn Burns and Lucy Calkins

# data[].attributes.attachment_link.description
Today on the podcast we're excited to share a special conversation between Marilyn Burns and Lucy Calkins about Marilyn's new digital math interview tool, Listening to Learn . They discuss the importance of listening, a value that is central to both Marilyn's and Lucy's work.

# data[].attributes.headline
(Podcast) Jennifer Serravallo and Marilyn Burns on the Connection Between Reading and Math

# data[].attributes.subject
(Podcast) Jennifer Serravallo and Marilyn Burns on the Connection Between Reading and Math

# data[].attributes.attachment_link.readable_text
On this special edition of the Heinemann Podcast, we're bringing together authors Jennifer Serravallo and Marilyn Burns as they explore the intersections between literacy and math in the K-5 classroom.

Marilyn Burns is one of today's most highly respected math educators. She is the creator and founder of Math Solutions®, and has dedicated her career to the improvement of math instruction across grades K-8. Marilyn has taught in the classroom for many years, written children's books, led in-service workshops, written professional development publications for teachers and administrators, and created professional development videos. Marilyn continues to teach regularly in the classroom, finding the experience essential to developing and testing new ideas and materials.

Marilyn, with her co-author, Lynne Zolli, has been developing a new digital interview tool with Heinemann called Listening to Learn. It releases this Spring. Listening to Learn helps teachers and math coaches engage students in mathematical conversations without paper and pencil, understand how students' reason, and make informed instructional decisions. Marilyn says Listening to Learn is the most exciting project she's worked on in her entire professional career.

Jennifer Serravallo is the author of New York Times' bestseller The Reading Strategies Book as well as The Writing Strategies Book, Understanding Texts & Readers, and A Teacher's Guide to Reading Conferences. Her newest book publishing later this spring is Teaching Writing in Small Groups.
Below is a full transcript of this episode.

Brett: Marilyn, you're known for your math interviews, and, Jen, you do a tremendous amount of work in conferring. I'm curious about how these two approaches overlap from a math and literacy perspective. Marilyn, do you want to start us off?

Marilyn: In preparation to have this conversation with Jen, and, Jen, it's really a pleasure to finally "see you" at least online. I've been reading some of Jen's books and thinking about how the connections between math and literacy, what those connections are, how they might exist. It seems to me that the interviews that I'm working on now, that I'm just completely passionate about... Well, more than passionate, I'm sort of obsessed for quite a long time. And they're, I think, Jen, like your assessment conferences, where I'm there for me to learn.

I mean, the mantra we have is, "I ask, I listen, and I learn," so it's not a test of the child as much as it is an opportunity to hear how they think and reason so I can be a better teacher.

Jen: Yeah. I want to start off by saying it's an absolute honor and pleasure to be chatting with you. I read your, I think it was first edition of About Teaching Mathematics as a college student, and I've followed your work somewhat since. It was really great to read some of your work and watch some videos of you working with kids and see what you've been up to. Yeah, I do think there's a lot of similarities. I love your emphasis on the importance of listening as a really key part of whether it's an interview or a conference, listening and taking every opportunity with kids to really assess and, I think, evaluate what's really going on inside their heads, how they're processing things, how they're working things out. I think that's the same with literacy and with math.

I was watching today a video... I don't remember where it was. But you were working with a child, and then you were talking about all the different ways that kids can add, I think it was four and nine, and all the different ways that you're surprised by kids thinking and by kids processes.

I think what you're doing... And you can tell if I'm wrong about this. But I think what you're doing is you're trying to map a child's process and their answers onto that network of ideas. I think about it as hierarchy of goals for reading and writing and that there's progressions within each goal. So it's not just about listening, which is so crucially important, but it's also about, I think, the evaluation. What am I doing with the information as I'm hearing it, and what's the work in the teacher's mind that helps me place where a child is, what they're doing, and then what's the next step for them so that we're always working from a place of growth versus looking for deficits, looking for what they cannot do?

Marilyn: It's so important. I get nervous when we say we focus on kids' gaps or we focus on kids' misconceptions. I want to find out about where I can start doing. Where are their strengths? What do they understand? What do I have to build on? So there is a progression I have in my mind.

But there's two things. First, when I'm listening in an interview setting, I don't have the extra burden of trying to figure out, "Well, what might I do to intervene? What might I do to help?" So I'm just listening to learn, but that is hard because first of all, keeping your mouth closed and not talking as a teacher is not natural. That's not what we've been trained to do. The other thing is I'm trying to listen, not for what I hope to hear, but listening to the child, and that was a huge shift for me.

So the problem that you mentioned about, we ask kids how much is four plus nine, and that's what we're interested in thinking about, addition and subtraction within 20. So there is a progression. When kids first learn how to add, they count. Now, some kids will count starting with a nine and count on some. Some kids will start with the four and count on. Some kids will count from one, one, two, three, four, and then keep going up through nine. That progression of counting is there, and we want to help kids move from counting to using more reasoning strategies.

When I've interviewed kids, I have the progression in mind, but whatever they say is what's important to me. Whatever they understand and how they explain their reasoning is what I'm listening for. And then when I get to a situation where I'm planning class instruction, then I'll know that these are the kinds of things I need to incorporate in my number talks or in my small group work, or even my class lessons. I don't know if that answers that question, but four plus nine, I was bowled over. I mean, how many ways are there to figure out four plus nine? A lot.

Brett: Marilyn, what is it you always say about correct answers?

Marilyn: I don't know if this is what you're thinking about, but correct answers can mask confusion, just like incorrect answers can hide understanding. The answer is just the starting place. It's really how you got to the answer and how you reason that is just as important. So people say, "Well, the right answer really isn't important?" No, it's very important, but what's important is how the student reasons to get to whatever answer they come up with because sometimes wrong answers are the right answer to a different question. My job is to think about, "What was the kid thinking about?"

Jen: And when I think about literacy, of course, when we're talking about reading accurately, there's a right word and a wrong word each time you read it. There's a right way to spell that and a wrong way to spell that. But beyond that is the craft of writing and how I organize my sentences, what I'm choosing to focus my piece on. There's not a right and a wrong there. How I understand things from a story, from a non-fiction book, maybe there's a wrong sometimes if it's really not based in text, but there's a lot of possible right answers.

So I think in similar ways in math, it seems like there's a lot of right processes. There's a lot of right ways to think about a problem. I think that maybe that's a parallel to literacy, that there's a lot of right ways to, for example, infer about a character, to take what you will and come up with ideas about a character and say, "This is the kind of person who..." And based on who I am as a reader, it can change my read on that character.

I can have a different idea because of the people I've met in my life or the other stories that I've read. In math, one of the videos you sent me... So amazed by this. Was she a fifth grader maybe that you were working with trying to figure out how many notebooks she could buy? I was amazed by not only what she was saying but also what she wasn't saying. When she was hesitating, I can almost see in her head she's saying, "That can't be right. That can't be right. That can't be right." Did you take the same thing away from that video?

Marilyn: In fact, I'm about to write a blog about that, because then she came back later in the day with her whiteboard in hand to show me how she figured it out. This is interesting when you say that kids can put together sentences in any way, and it's up to them. They have that agency, and we support that. We applaud that. We encourage that in literacy. But math, I worry that too often the kids are taught a paper and pencil method, and that we don't expect them to be creative.

We expect them to apply this procedure to get this answer. There is an important role of procedures and algorithms and math, but somehow that becomes the goal. That's what concerns me. That's why I say the answer is only the starting place. Paper and pencil is a tool that you'll use, but I want the thinking to be there the same way you want the thinking to be reflected in a child's writing.

Jen: The emphasis on mental math in your interviews is really interesting to me. Can you talk about that?

Marilyn: If we think about all the ways we do arithmetic in our heads as in our lives, counting the change, figuring out what time to leave, figuring out the tip, we did so much in our heads that it's a life skill. But in school, it doesn't get the emphasis, and I think partly we have nothing to send home as evidence of what the child's doing.

I think that the movement to having number talks is really a big push towards getting kids to think, reason, and explain without paper and pencil. I see paper and pencil ideally as a way for students to keep track of their thinking rather than to reproduce a procedure, but to me, mental math is what it's all about. It's all about reasoning in your head and explaining, communicating, reacting. So I think all the same skills that you're doing in literacy are there. It's just that the content area is very different.

Jen: The ability to visualize is something else that comes in literacy as... I think of it as something that's so key to my own literacy. I'm reading a story. I feel like I'm right there in that world. I'm seeing the characters' facial expressions. When I'm writing, I'm either imagining the audience I'm speaking to... Literally when I write, I write it like I'm speaking to people, and I imagine my audience there. When I'm writing a story, I can imagine the characters coming to life, and I write down what's happening in my head.

So I wondered about this emphasis on mental math, and in particular with that fifth grader whose video I saw. What was she seeing in her head? Was it dollars and money? Was it change and money? Was she moving that around? Was she seeing the actual numbers stacked and she was adding and carrying or regrouping the... Right? I don't know. What does that make you think about?

Marilyn: Well, it's interesting because we find that some kids do visualize the actual paper and pencil problem and visualize doing it. That's what this girl on that video tape was doing. She was actually trying to add $1.39, $1.39, and she was seeing nine and nine. She was carrying in that situation. When we interview kids, we always have a way for teachers to capture how the student is thinking, and one option for certain problems is use the standard algorithm. Now, this is all mental math, and that means that they visualize the paper and pencil algorithm and apply the procedure.

But it's so interesting. I read your writing. I feel like you're talking to me. So if you're visualizing me as the audience, I think that's the way I write. We do, in our math classes, we do a lot of writing. Sometimes you're writing for your classmates as the audience, but sometimes I want the kids to write to me because if I can't interview them all the time, then tell me what you're thinking and describe your thinking.

And that's one of the math standards. Create viable arguments. Critique the reasoning of others. So I think there are so many overlaps that way, even in how we think about writing and bring that into the math class, but the visualization is so important. There's no such thing as three. It exists in your head. A kid has to have a picture of something. I had a hard time at calculus, and I have a degree in math. I think it was because I didn't realize how important it was to visualize these curves and visualize this change happening.

Brett: What Jen's asking you here. It really makes me think about the math anxiety that many of our K5 teachers feel. I think you talk often about how our teaching can be more flexible as we teach math, and that we can make space for curiosity in teaching math. Can you talk a little bit about that? And Jen, I'd love to hear your thoughts on that, too.

Marilyn: It's so interesting to think about this level of math anxiety. I think that for many people, children, and probably some adults, they don't come from the point of view that math is supposed to make sense. They come from the point of view that you're supposed to know, and if I learn how to do this, then I would get the right answer. Then I would be okay in math. It's supposed to make sense.

Now, the ultimate way, we want to make sense out of black marks on pages. I mean, that's reading, and in math, I suppose, it's making sense of those symbols on the page. But the sense-making is in your head. So the source of the knowledge for me with kids is how they're thinking, and so everything I have to do has to be to stimulate their thinking. That's why mental math becomes so important. I think that people who have fear of math... And I know so many teachers I've worked with have can tell me the time I got sent to the board. The time they felt humiliated. The time they worried. It's like, "Yours is not to question why. Just invert and multiply." That's what they were taught. They were never really taught to think reasonably, enjoy, be creative. Those words don't seem to go along with math, and that's one of my goals in life.

Jen: You know, I think I've seen a lot of math anxiety in children, and I think that part of it is about speed and some emphasis on speed and problem solving quickly. Then if kids can't, they feel like they're not good at it. I think we can make a parallel there to literacy as well.

Also, you said the publicness of getting things wrong versus being involved in math talks where you're genuinely interested in other people's thought process. That's a huge, or maybe subtle, but very huge shift.

Jen: I think the speed is one thing. Thinking that faster reader is a better reader or someone who writes more is a better writer is not true. Sometimes when kids feel like, "I'm not good at this, this isn't for me," it's because they compare their work to others and they see how quickly they can get it done or how easily it comes to them. And I think if they have to work at it, it's not good. But there are so many writers who have to really work at their craft who have to really puzzle over every sentence and do a lot of revision and a lot of work.

And the idea of revision is something too in math. You revise your thinking. You have a first draft at something, and then you go back at it and you look at it again. And I think the more across disciplines that we can emphasize that for kids that there's excitement and joy and interest in the work and in the process, not just in the final product or getting the answer. And I love what you said too about how at the end of the day, of course, it's about making sense, that math has to make sense. And I think about the parallels to reading and writing. Of course, yes, what we write must make sense. What we read must make sense.

And part of the way that we control for that in the classroom is we help to provide kids with opportunities to practice that are within their reach. So I'm not going to stick Tolstoy in the hands of a second grader because that's just going to shut them down and they're like, "I can't read this, therefore I'm a bad reader." And I think the same thing in math. I think sometimes what happens is maybe all kids get the same problems, but that problem is not right for everybody. If some are still working on adding and subtracting within 10 and others within 100 and others within 1000, the kid that's still working within 10, being presented with a within 1000 type problem, then maybe they'd shut down because it doesn't make sense anymore. It's not close enough to what they're able to do.

Marilyn: That's so true. In fact, I was working on a piece this morning about the numbers matter, the magnitude of the numbers matter because four plus nine was within reach of some of those kids you saw on the video tape, whereas 35 plus nine wouldn't be. When a kid gets out of their comfort zone, then they seem to resort back to the earlier skills in their progression, like they'll start counting. So if I have 39 plus six for example, a kid will tend to count rather than kids will say, "Well, 39 plus six, it's 40 plus 45." I mean, decompose. So once you get out of your comfort zone with the numbers, then you sometimes have something to fall back on.

And as soon as you get through with learning how to add and subtract, then along comes multiplication, which is a whole different animal. And then come fractions, then come decimals, then come irrational numbers. It goes on and on and on. So in some ways the reading and the math analogy is different. And I can see why teachers or adults would feel fear of math, because there's some point at which they fell off that ladder and they never got back on. And so you have to be able to just like in reading, find something that's accessible to the child to build the understanding, to build the strategic thinking, to build the ability to reason so you can then inch them up towards where they haven't gone. So it's subtle, it's tricky.

Brett: Jen, that brings me back to something you were saying, I think closer to the start of our conversation around goal setting and some of the work that you do in conferring. So I guess I'm wondering, how do you use the information in either Marilyn with interviewing Jen and conferring, that information that you're gathering to how you each identify the goals. And then Jen, I think we talk about this a lot, responsive teaching.

Jen: Yeah. It's all about responsive teaching, right?

Marilyn: Talk about that, because that's not a term anybody in the math world uses.

Jen: Really?

Marilyn: Really.

Jen: But isn't that what you're after with the interviews?

Marilyn: Seems like it, from what it sounds like it, so tell me a little bit about it then.

Jen: Well yeah, so I wrote down some notes about this graphic that's on a website for ... What is it called? The Listening to Learn website, right? And you have this series of boxes and then there's this list beneath each one. And so it starts with numerical reasoning. Then it moves on to addition and subtraction, and then beneath addition and subtraction to 10 to 20 to 100. I'm just saying this for listeners who may not have seen it. Then it moves on to a multiplication and division and then beneath it foundations and extensions. And I think it's similar way of thinking about, of course there's overlaps and there's times when kids might do something later on, but when they're not yet doing something earlier on, but it's the way I think about literacy and I have what I call a hierarchy of action for reading and for writing.

And it's the stuff I do first and then the stuff I do later. And then within each of those potential goals, and I'm calling goals things like print work, fluency, understanding plot and setting, understanding characters. Those are big categories. Within each, I've got this progression just like you have within the addition and subtraction, this progression within it, that lists the kind of work that you'd see as kids move into more and more sophisticated texts and reading, or learn more and more skills in writing. So for example, if I were to sort of crack open fluency, reading fluency, you might say at the beginning, I'm just trying to read words with automaticity. It might sound choppy word to word. Then I'm going to read two or three word phrases at a time.

Then I'm going to make sure I'm paying attention to ending punctuation and I'm reflecting with expression what the author wants me to. Then I'm paying attention to medial punctuation and pausing at the commas. And so if I, as a teacher and listening to a sample of a child reading aloud, I can sort of map onto that skill progression, where is the child now? And then look ahead to see what's next. And if there's a need within that goal, then that becomes the child's goal. That's what I'm going to focus my strategy instruction on, but I'm still seeing, where are they strong within that goal? And then what's next. So it's both looking for an area of opportunity for me to support the student's thinking or their skill work, but it's also looking at their strengths and then trying to move them ahead to what's next.

Marilyn: And it's so true that the only way you would know that would be sitting with a child and hearing him or her read.

Jen: Or collecting samples of work. So, I don't really need to hear a seventh grader read aloud most of the time. I could sit down in a kind of interview or an assessment conference, ask a series of questions to probe, how is the child thinking about the plot? Are they visualizing the setting? How are they thinking about the characters? And so I'd ask a series of questions that aligned to each of those possible goals. Or I could ask a child to hand in some writing that they've done about their reading, or I could look through their notebook to see what kind of writing that they've done. And I'm looking at their writing probably the same way in math you could look at their written work.

Marilyn: Well, no, that's the whole thing. If the written work is just a worksheet of problems to solve, you don't know anything. You only know that the child did or did not apply the procedure and did or did not get the right answer. And you don't have any idea about how they were thinking, and how they were reasoning. So it seems to me that in the reading community, especially with young children, you listen to them read, and that's the only way you know they are going to pause it a comma and take a breath at a period.

So interviewing, it seems to me, has become an integral part of teaching reading to young children. Why not in math? We never thought we'd give them a paper, pencil, let them "work the problem." And working the problem is very different from the kind of work you're expecting from a child who's doing a piece of writing that's integral to who they are and what they want to communicate. But we do have writing and math, but that's not really the norm. The norm is get the right answer and get it fast.

Jen: So if you notice through these interviews that you have a wide range of different needs in your classroom, which I assume you would, it's like, "Oh, these three over here really needs help with this. These three really need help with this." A question I get all the time is, how do I reconcile the differing needs in my classroom with what the curriculum tells me I'm supposed to be teaching in October? And how do I balance the curriculum and the scope and sequence with what I know the kids need and really supporting them responsively? What's your answer to that in math?

Marilyn: All right, and the snarky answer is, you're teaching children. You're not teaching math.

Jen: I maybe have said something similar in literacy.

Marilyn: But that doesn't help. But the thing is, here's what I want in my classroom, I want kids to be excited about all their learning. I want them to be excited about math. I want to have a community of learners that treats each other with respect and kindness and curiosity by modeling how I'm treating them with respect and kindness and curiosity. And then I want there to be problems that we're going to solve together. And we're all different, so we're going to have different ideas and we're going to value these ideas. So if I'm going to talk about the path to the old four plus nine if I'm working with first graders and I put this problem on the board, and I say, "I wonder how many ways could we think of figuring out the answer to four plus nine?"

First of all, let's get the answer out of the way. "In your whisper voice, when I say three, tell me what you think the answer is. I'll give you a minute to think." And then I whisper, "One, two, three." So finally we say 13, that's the answer. So we're getting that out of the way. Now how could we explain to somebody? How could we justify that answer? How could you prove that answer to somebody who agreed with you or didn't agree with you? So that's the nature of the work.

That's why I love number talks, where we have the entire community. That's where we do lessons, where the problem solving and you come to it and you work cooperatively. And then in the independent work, would you be working individually or with partners, then that's where I can tailor it more. But I don't want to give up the sense of community. I don't want buzzards or Bluebirds.

Jen: I'm thinking about how the act of doing these kinds of interviews changes the teaching that happens in the classroom and changes the learning that happens in the classroom. Yes, it's assessment, but if you assess kids by asking them to do a sheet of problems and then correcting them as right or wrong, it changes what you value, what you emphasize, how you spend your time during math class, how you talk to kids about what math is, and how mathematicians think and how they work. And I'm thinking about that from a literacy perspective, when we have a state or a district that is very bound by these standardized tests where it's about choosing the right of the multiple choice questions. It changes the way that you teach comprehension because you're teaching kids to get a answer.

But like I said before, there's many possible ways to understand anything, a character, a plot, a setting, a theme in a story. So I'm thinking about just how exciting it is to think about the way that this real inquiry mindset, I think, that a teacher has to take on to do these interviews and to benefit from these interviews, what implications that has for the classroom.

I think it's so exciting about how it changes the inquiry mindset that a teacher needs to adopt to do an assessment conference, to do an interview in math, that kind of thinking and the kind of genuine curiosity of how a child's brain works, what implications that has on how a teacher budgets their time during the classroom, during the math classroom, during the reading classroom, and how the instruction changes because of what you've now learned.

Brett: Jen, you mentioned fluency, and it reminded me that we have a lot of overlapping terms in math teaching and literature teaching. We've got fluency, prompting, searching for information. Jen, and I guess Marilyn, however you want to approach this, how do you see these terms overlapping in math and literacy and the connections that they build for teaching both?

Marilyn: Like you've talked about, responsive teaching, what do we... Can you talk about comprehension? That's not a word we use in math, we use understanding. So comprehension equals understanding. I can write a little equation like that. But responsive teaching. I get it, you're supposed to respond to who the child is. The child is the starting place, not chapter three. So in that way, I don't know if we have... I think the language is important because if we want to help literacy teachers build on their own strengths to feel more comfortable with math and vice versa, then we have to find the common ground of language, I think.

Jen: That's right. I think, just like we're saying, the advice we're giving about teaching children is to see what they can do, see where their strengths are, see where their understandings are, and help them grow from there. Same thing with teachers, with any areas that feel less comfortable. So I think the terminology, sure, that's one way, the common language. And I think about the moves you can make as a teacher, the kinds of structures you use in the classroom, whether it's small group strategy lessons, you can do that in math or an assessment conference is like an interview. You can do both in math and literacy. So finding commonalities with structure and then finding commonalities with content.

Marilyn: That's harder.

Jen: That's harder.

Marilyn: That's where the rubber hits the road, when I'm struggling with this. Like in writing, the kids are doing their own work. Even if they're all writing a how to, or they're writing a memo or whatever genre they're writing in, it's their work. What's the work in math?

Jen: To learn the algorithm to learn the...

Marilyn: Long division had a birth. It can have a death. You heard it here.

Jen: Without long division, what is there?

Marilyn: Calculators

Jen: Calculators!

Marilyn: No really. If you want to be efficient and accurate, the last thing you want to do is paper and pencil. That's a mind shift.

When I grew up we had to learn how to take square roots by an algorithm. You had to put numbers in twos... It was sort of related to division, but it was very complicated. I loved it. But nobody figures out square root of a number by paper and pencil. In fact, I was talking to a math colleague who's a real math person. He said, "I can't remember how you do that, because you just punch it in your calculator." But you have to know what to do with the number. Once you get the number, first of all it doesn't make sense, and second of all what problem are you solving with it, and what are you going to do with the information? That, to me, is math.

I had a kid interview, we have it on tape, and I asked her a question, and she said, "Can I use my fingers?" I'm thinking like, "You have to ask permission to use your fingers? They're your fingers." Doing it under the table or they're using the tongue on their teeth counting. Why are we taking these things away from our kids? You shouldn't be counting on your fingers. Yes you should. They're your fingers. Maybe we can think of some ways that... Besides that, that's it. What you're doing is fine, let's change the game. Let's think about what other ways could we think about this?

Jen: And I wonder sometimes if it's a matter of spending more time with concrete manipulative, fingers, counters, something. If it's a visualization thing. Or just spending more time with the numbers, playing games, rolling dice, subtracting, adding, subtracting, adding.

Marilyn: It's what they value as being important to know. And the important thing for me to know is what do you do when faced with a problem you've never seen before? So I got really good at long division. I got good at taking square roots. But the question was, think about... That's what math is all about. Thinking about problems you haven't seen before and wondering. So what do you notice? What do you wonder? Let's talk about it.

Jen: It changes what math is. It's not about just doing a sheet of problems. It's a totally different way of approaching math, which I think maybe contributes to some teachers' discomfort. Here's another literacy parallel. I find that teachers in general, there are more teachers comfortable with teaching reading than there are teachers teaching writing. Some teachers feel very uncertain, especially when we're talking about creative writing, like story writing or poetry. They're like, "I never had to do this myself as a child. I never really learned. I don't do it for fun. I don't do it because I need to. It's something I just don't do. And here I am trying to teach four weeks' worth of lessons to kids on how to write a good free verse poem." So it feels uncomfortable. It's so different than how they were taught.

And I think back to how I was taught math, and I'll be honest with you, I think I understood math better when I taught it when I was an elementary school teacher than how I was taught as a child, because as a child, it was only about the right answer and doing over and over and over again the same type of problem until it just stuck. Rote memorization. And now you're asking teachers to... You and other math programs that are popular nowadays are asking teachers to really understand how numbers work, the whole number bonding, and taking apart numbers and moving them around or really working on developing a conceptual understanding before they get to the algorithm, or concrete understanding before get to the algorithm.

I wonder for how many teachers that feels really different than how they were taught to do math, and that's part of the discomfort. You see the jokes all the time on social media from parents. "Oh, now that kids are home, I'm just going to teach them this way. The good old way, like I learned." And just the unfamiliarity with this way of teaching makes it challenging.

Marilyn: But what you said about when you learned to teach you then understood it.

That's because you had to take it apart and put it back together in some way so that you could explain it to the kids. You do all the work. I walk into classrooms and I see teachers doing all the work. And I want the kids to be doing the work. So I think that I... This was a painful lesson for me. I prepare my lessons, I get it clear, and then I'd give my explanation. I was trying to make it plain to the kids. Well, I was doing not only the preparation of thinking it through, I was doing all the talking.

So if I want to shift my teaching of math, then I have to shift it so that they're doing the thinking, they're doing the talking, and I'm doing... So instead of I do, we do, you do, I want to reverse it. You do, then we'll talk about we do, and then I'll tell you what I think and see if I can help you move a little bit farther. And that's completely a shift that that's turning it upside down, I think.

Jen: I visited Japan as a pretty young teacher. I got a Fulbright scholarship to go to Japan and study the schools there. And I will never forget one of the, I think it was a middle school classroom, a math classroom, just as you described. The teacher put a problem on the board. One problem. All of the kids moved their desks into groups. They talked, and almost the entire class worked. The teacher circulated. The last 5, 10 minutes of class they turn their desks back to explain their thinking, how they got their problem, the different ways they went about it. And the lesson was at the end.

We do this sometimes in literacy. We'll put up a text, a poem, let's say, and say, "Well, what is the author doing? What do you notice? What are you wondering about? Why do you think the author made these choices?" Katie Wood Ray's book Wondrous Words was really foundational of making this a regular practice in classrooms. And at the end of it all, "Oh, that's called show not tell, and here's how you do it. Here's a strategy for trying it in your own writing." And the idea of flipping that, of starting with the students, starting from what the students can do, starting from their thinking, and then having the explicitness of the teaching or the strategy or the lesson come at the very end of the class.

Marilyn: It puts a lot... It's hard, because as a teacher, when the kids are working, your job is to figure out how they're thinking, so you select the students who are going to present. That means you really have to understand, first of all, this thing about the progression, second of all, what are your kids doing, and third of all, how am I going to do this paying attention to the fact that I can't always call on the same kid and in what order? It's problem-solving teaching that's of the highest order and very, very important. So I think that you're lucky to have had that experience.

Brett: It makes me think about that question you always get, Jen, about the teacher that may not know the plot of a particular book that the student wants to read. It makes me think of that, because you always have a great answer for that.

Marilyn: I read that. I want to hear it from the voice, but I've been reading your books, and I say, "What do you do if you don't know this book?"

Jen: And that happens a lot. If you are running your classroom in such a way that kids have choice of what texts they read, and especially once you get to end of second grade up through middle school, they might be reading these really thick books that you don't know. How do you evaluate their thinking? How do you evaluate their comprehension? And I think the first piece of advice I have for teachers is to let go of the idea that there's only one "it" to get. That getting it could be a lot of different possible... There's a lot of right answers.

There's a lot of right ways to think about it. And instead, what I look for and what I advise teachers to look for is the quality of the response. So if I ask you, "Tell me about your character," and you say, "She's really kind. Well, except when she's with her sister, then she seems really bossy." Then what I'm thinking right there is the child's understanding that characters can be complex, that they're not just one way.

And then I can say how will I help this child deepen their thinking about character? And maybe it's to say that I'm noticing that the child's talking mainly about one of the characters and I can help him extend his thinking to other characters, and how the interactions between the characters gives us new insight. Or maybe it's to say, "You seem to have a really good grasp of character. So I'm ready to teach you, or I think you're ready to learn some things about how the characters and their journey helps you think about big ideas in the story."

So it's again, placing it along this progression of skills, this idea of listening for a quality of response and trying to nudge them along to think more deeply within that same goal, along that same progression, or moving to a new skill progression. That's one difference in math, you know what the right answer is.

Marilyn: But that's where I'm trying to break that mindset. The right answer is only the starting place, because right answers can, as I said before, mask confusion, whereas wrong answers can also hide understanding. So what's interesting to me is how do you think about it? Why do you come to that answer? And so that's the shift that's enormous. So if the grain size of your math teaching is correct answers are what I value and what's important, then I'm trying to make that grain into a lump a rice, whereas it's more complex than that.

I was really interested. I was interviewing this girl, Tova, and the problem I gave her to solve in her head was 36 plus nine. And she thought, and she thought, and she thought, and then she said, "I'm going to change the problem from 36 plus nine to 39 plus six, and now I can do it because 39 and one is 40, and five is 45."

And I'm sitting there thinking, "She switched these two digits. Are you allowed to do that?" And I'm thinking, "Well, when can you do that? Could I do it if it was subtraction? Can you do it in multiplication?" I mean, it opened up my whole math mind, in a way, but it was her way of thinking about that, where she got the answer 45, and that was only a starting point to think about, how does this work? She's adding the ones; does it matter if we have this one on the top and the bottom? Can you just change the quantities?

Well, if it was a contextual problem, it might not make sense to change 36 plus nine to 39 plus six. But it was fascinating. So I'm always amazed about answers are only the starting place. It's how they get to answers that really give me windows into their mathematical minds and hints about how to help them grow.

Jen: Do you find that there's a lot of kids that just aren't that able to discuss their process?

Marilyn: Yeah like last year, I just did it all. I got it all right. I said, "Oh, that was third grade. That's what you do in third grade and fourth grade. This is what we do in fourth grade math. We talk, talk, talk." I mean, that's the way I've always handled that. And you will have to do it in a safe way, so you'll have a partner and you can practice. And I sometimes even so much will ... One will sit and the other will listen. Then I'll bing, and now switch roles. Teach them to talk to each other, teach them to talk to their class, teach them to listen and ask questions respectfully. I have kids saying, "I would like to respectfully disagree." We'd all learn that phrase, so that you can participate in the discussion and we can be open to listening to each other.

So it's just a question of shifting your culture, shifting the culture so math becomes everything. Probably, your literacy teachers are more comfortable doing this with reading and writing. Why not take those skills I have and move it into the math world

Jen: Oh yeah, those same sentence starters or discussion prompts: "I'd like to respectfully disagree," "I see what you're saying," "But another way to look at that is," or, "I would like to add another point to the conversation."

Marilyn: Yes, yes.

Jen: Those same kinds of words that we use in discussing a picture book that we've read together can be used, it sounds like, to talk about math.

Marilyn: And sometimes I have kids talk in pairs and then I'd say, "Okay, now I want everyone to think about how you're going to tell the class what your partner said." So I've tried every way to get kids to really process information, verbalize it, communicate. And then later, it would be to go back and write what you think about this. So I think that it's a question about ... That would be really interesting, to take the skills ... Like when I was reading one of your books and you had all these mentor people, and there was a whole spread on Marie Clay. And I said, "Was she talking about literacy or was she talking about math?" I wouldn't have known if I hadn't known it was in your book, not my book.

Jen: Yeah, I just think there's so many parallels or could be parallels in a classroom to the moves that we make, like putting kids in a circle and having a whole class conversation, working with partners or working in a club and then coming together and sharing what you've thought about or spending some time independently and a teacher circulating around the room and doing one-on-one conferences with kids. The moves probably feel comfortable to teachers who are more comfortable with literacy than math. It's the content...

Marilyn: Exactly.

Jen: And I think developing interest and curiosity and appreciation, recognizing the relevance of what you're learning. The same with literacy, right? Not every child is going to go on to become a professional writer, but we want them to be comfortable enough to write a really well-crafted letter to their school board or to keep a journal because it helps them emotionally to do that, or whatever it is, to have that be a part of their life or have that be available to them. And same thing with math, right? I use math every day. I really do.

Marilyn: Like, we were getting some work done in the house that required a contractor coming in and he had to make a bid and I'm thinking, "Wow, this guy is doing so much math to estimate what his costs are, estimate what his time is, come up with a number that's fair." He doesn't want ... "I don't want to be greedy." He's not going to get the job. He doesn't want to feel used. He's going to feel awful. That's a lot, a lot of math.

I had a friend who an interior designer who said, "I'm not really good at math. That's why I went into interior design." And her eyes are darting around the room, and she's saying "there, and you have to have so many yards for that." And I'm thinking, "What are you telling me here?" And I met another woman who was a ballet dancer, and she really wanted to be a choreographer and said it's because she's so bad in math that she couldn't.

Jen: But she's counting. She's keeping time to know she has a rhythm to the music.

Marilyn: ... and music and the movement. I'm sure music is all math. I mean, the cross between math and music is very strong. So there's math, it's everywhere. So how did we get to this terrible, "I hate math"? I mean, the first book I ever wrote was called The I Hate Mathematics! Book. And I come into the class, and I wrote it in 1975, and I said, "How long ago was this?" And that's a good because they can do that in their heads because from 1975 to 2000, and then they only have to go ... That's a long time ago that I wrote this book. In fact, I think it's quite amazing. But I think the reason why it's still in print and successful is because children don't buy children's books, adults buy them. They look at this book and they say, "Yeah, that was me. I'm getting this for my kid." So it's pervasive. The, "I hate math" syndrome is pervasive.

Jen: Do you think that the standards or ... I mean, you don't have to speak specific to today's standards, but any standards, do you think they push too much, too soon, and that's part of what's challenging? Like if we slowed down and focused more on depth...?

Marilyn: If you saw your job as uncovering the standards, rather than covering the standards, you'd be on your way to thinking about how to teach, in your language, what would be responsively.

If I'm covering the standards, I'm doing what you and I did as teachers, we were explaining it. We figured it out, we're going to explain it. If I'm uncovering, I'm giving you a way to engage with it from which I can help you see the structure, see the big idea. It's that, "I do, you do, we do," shifted to, "You do, we do, I do." So I don't want to cover the standards, like, "Check, I taught that." It's like the used car salesman who said, "Well, I sold that car. The problem is he just didn't buy it."

So I taught it, they just didn't learn it. Who was it? John Goodlatte said there was the written curriculum, the perceived curriculum, that is how the teachers thought, and then the taught curriculum. I liked there were four different, sometimes not even intersecting, worlds.

Jen: What do you think about grading and tests as being another impediment to kids being comfortable with math or teachers being comfortable with math?

Marilyn: Yeah, timed tests are mean-spirited, useless, cruel, demeaning, and horrible. You got that clear? I think tests, it's like, are they motivating? I don't see how they're motivating. They're just ways of sorting and labeling kids. And I think that's mean. I think it promotes deficit thinking. I don't know how to get around that, because it's huge. The thing about accountability and the importance of knowing that we're doing our best as teachers and our schools are serving our kids best as we can.

And like now, they say the kids are falling behind because there's COVID. I said, "Behind what?" I mean, where is it written that every child in the third grade is supposed to learn multiplication? That's a construct. So they're not going to learn it for another year? I mean, really? The question is, you're learning the importance of what the interaction is. But, "I don't want them wasting time when they're home." You think they didn't waste time in school, and how much chatting was going on? We're in such an unnatural world right now. And I think that maybe it'll help us reset to think about what school can be. To me, I want play, work, and learning to all be the same.

Jen: I agree with that, and I think the challenge is going to be when things get back to normal, whatever that means, right? When we're back in brick and mortar schools, the whole class at the same time, five days a week, how do we approach students and how do we approach curriculum? And if we're just going to open up to the first page of the teacher's guide and teach whatever it says is aligned to that grade level standard for September, that's when people are going to feel like the kids are behind, there's a huge gap, we need to catch them up, but if...

Marilyn: Yeah, and then how do we get that language out? Okay, so my remedy is how about when we all come back together ... or that the first three weeks of school is you learning to know who your kids are and how they think.

How can you start teaching chapter one, page one, when you don't even know who your kids are? You don't know what they're thinking, you don't know if it's appropriate, of interest. What can I do to make them curious about math, and me learn as much about them, and them to feel my interest in them before I say, "Okay, I've got an idea. We're going to now spend the next three weeks learning about division. This is going to be so exciting." That's the attitude I want.

Jen: Yeah, I agree from a literacy standpoint, as well. The more we can get to know our kids first, the better the teaching is going to be from the beginning, and then just working efficiently to support kids with what they actually need to learn.

Marilyn Burns is one of today's most highly respected mathematics educators. In 1984, Marilyn founded Math Solutions®, an organization dedicated to the improvement of math instruction in Grades K-8. Her book, A bout Teaching Mathematics, now in its 4th edition, has been widely used for pre-service and in-service teachers. Her other professional books include Welcome to Math Class; Math, Literature, and Nonfiction; Lessons for Algebraic Thinking; Writing in Math Class; and others.

Marilyn's children's books include classics like The I Hate Mathematics! Book and The Book of Think, and the more recent The Greedy Triangle and Spaghetti and Meatballs for All! Her children's books have been translated into eight languages.

For her educational contributions, Marilyn received the Ross Taylor/Glenn Gilbert National Leadership Award from the National Council of Supervisors of Mathematics and the Louise Hay Award for Contributions to Mathematics Education from the Association for Women in Mathematics. She was also inducted into the Educational Publishing Hall of Fame by the Association of Educational Publishers.

Marilyn and a team of Math Solutions® master teachers developed Do The Math, an intervention program that targets on number and operations, and Math Reads, a program that helps teachers use children's literature for teaching mathematics. Her most recent project, Listening to Learn, is a digital interview tool for grades K-5 based on her previous work on the Math Reasoning Inventory (MRI), for students entering middle school and beyond and funded by the Bill & Melinda Gates Foundation.

Marilyn continues to teach regularly in the classroom, finding the experience essential to developing and testing new ideas and materials. Learn more about Marilyn's work at her Marilyn Burns Math Blog, by following her on Twitter @MBurnsMath, and by visiting her Marilyn Burns Math YouTube Channel.

Jennifer Serravallo is the author of the New York Times bestseller The Reading Strategies Book and The Writing Strategies Book, which have been translated into Spanish, French, and Chinese. These and her other popular books and resources help teachers make goal-directed responsive strategy instruction, conferring, and small group work doable in every classroom. Her newest titles are Teaching Writing in Small Groups, A Teacher's Guide to Reading Conferences, Understanding Texts and Readers, and the assessment and teaching resource Complete Comprehension for Fictionand Nonfiction.

Jen is a frequently invited speaker at national and regional conferences and travels throughout the US and Canada to provide full-day workshops and to work with teachers and students in classrooms. She is also an experienced online educator who regularly offers live webinar series and full-day online workshops, and is the creator of two self-paced asynchronous online courses, most recently Strategies in Action: Reading and Writing Methods and Content.

Jen began her career in education as an NYC public school teacher. Now as a consultant, she has spent the last fifteen+ years helping teachers across the country create literacy classrooms where students are joyfully engaged, and the instruction is meaningfully individualized to students' goals. Jen is also a member of Parents Magazine Board of Advisors for education and literacy.

Jen holds a BA from Vassar College and an MA from Teachers College, where she has also taught graduate and undergraduate classes.

Learn more about Jen and her work at Hein.pub/serravallo, on Twitter @jserravallo, on Instagram @jenniferserravallo, or by joining The Reading and Writing Strategies Facebook Community

# data[].attributes.attachment_link.title
On the Podcast: Jennifer Serravallo and Marilyn Burns on the Connection Between Reading and Math

# data[].attributes.attachment_link.description
On this episode of the Heinemann Podcast, we're bringing together authors Jennifer Serravallo and Marilyn Burns as they explore the intersections between literacy and math in the K-5 classroom.

# data[].attributes.headline
(Podcast) Marilyn Burns on Conducting Math Interviews with K-5 Students

# data[].attributes.subject
(Podcast) Marilyn Burns on Conducting Math Interviews with K-5 Students

# data[].attributes.attachment_link.readable_text
Have you ever considered that understanding is to math as what comprehension is to reading? Today on The Heinemann Podcast, we're speaking with Marilyn Burns, one of today's most highly respected math educators. She is the creator and founder of Math Solutions®, and has dedicated her career to the improvement of math instruction across grades K-8. Marilyn has taught in the classroom for many years, written children's books, led in-service workshops, written professional development publications for teachers and administrators, and created professional development videos. Marilyn continues to teach regularly in the classroom, finding the experience essential to developing and testing new ideas and materials.

We recently sat down with Marilyn to talk about her work in interviewing math students. Marilyn has been developing a new digital interview tool with Heinemann called Listening to Learn. We started our conversation on how teaching reading and math are alike and different..."

To learn more about Listening To Learn click the button below.
Below is a full transcript of this conversation.
Marilyn: I've been thinking about that question for a long time. In some ways there are similarities in that in both of the areas, in reading and math, we're trying to help children learn to bring meaning to black marks on paper. And so I'm astonished that when you read things, that literally black marks on paper will evoke huge emotional responses in me and hopefully in kids too. I'd like to think the same in math without it being just negative responses.

But I think there are differences as well. Read is a verb. We want kids to read, but we don't want kids to math. Reading requires the ability to decode, after which you have access to all the books and the library in the world. I could even read Spanish. I don't always understand, so the comprehension part is so important. So in reading, it's accuracy and fluency and comprehension. And in math it's similar. We want kids to be accurate. We want them to be fluent, and we want them to understand. And in math world we don't use the word comprehension. We use the word understanding. But basically I think of them as the same thing.

But I think there's a difference, and I'm not sure about this. In reading, the ability to decode depends on learning the system. Learning what the sounds are, having some skills to attack words, having ability with sight words. And in a way that's kind of social convention learning. You have to be taught that from an outside source. We're not born with the ability to decode words on pages.

But in math it's all based on logical structures. Kids come to school knowing that one and one is two. They learn the counting part. Those are words, but young kids count in kind of weird ways, but they have an understanding of some of the mathematical relationships that they've encountered. They sometimes they have wrong ideas like my half is bigger than your half. But the ideas in math are rooted in logic. So the logic and the learning about the symbols and the equations, the black marks, are kind of meshed together.

And I think in reading, I think kids who can read even accurately and fluently have no idea what they're reading. So they're similar and they're different. I think the people who are devoted to thinking hard about math and people who are devoted to thinking hard about reading, we can learn from each other. I'm not sure we always do.

Brett: Oh absolutely. Well with comprehension in mind, if a student in math has memorized math facts, how can that be misleading to a student's proficiency?

Marilyn: We all memorized our times tables, and you really need to know them from memory if you want access to them. It's really laborious to say, okay, 7x6, let's figure out, 6x6, whatever you have to go. You need to know 7x6=42 and it helps you reason mentally with numbers. It helps you make estimates. It's a part of what you need to know. But without understanding, that kind of memorizing isn't going to serve a child very well.

So I suppose the same is true in reading. When you memorize the sight words and you'll have had skills to get them, and you want that to be as fast as possible so you have more fluency, but the difference in math, it's different somehow.

It's kind of hard to make sense of it, but I think that the understanding is always ... The logical underpinnings are always there in all aspects of math. So for kids learning how to write numbers and count without reasoning, it's not going to work. It doesn't work for them.

Brett: You had a couple of tweets go viral recently, and I'm going to paraphrase the two of them together here, but essentially one of them said, "Correct answers can hide confusion, while incorrect answers can mask understanding." What is happening there?

Marilyn: What I have seen on paper and pencil assignments and quizzes are correct answers that when I talk to a student about what they're doing, it doesn't seem to be any understanding. It's kind of like the dumb luck approach. I Interviewed a boy about comparing fractions and he said, "One-fourth and five-sixths," he said, "Without question, five-sixths is greater." That was my question, which is greater. Now if that was on a worksheet where it would have said circle the greater fraction, he would have circled five-sixths. I wouldn't have learned anything. Then I said to him, "Well, how'd you decide?" He says, "Well, one is far away from four, but five is real close to six." And I'm thinking like, "Whoa. That was interesting." What I didn't ask him as a followup, which I kind of wish I did, what if I had asked him about five-sixths and six-sevenths? They're each one away. How would he figure out which was the greater one there? There's always a way to keep probing and pushing, but I would have assumed from the worksheet that Michael understood comparing fractions, and I would have been woefully misinformed.

Brett: And that really gets to the power of interviewing. Why is interviewing so important?

Marilyn: Interviewing is important because I really get a window into how a child is thinking. I sometimes say to kids, when I'm interviewing them, "I'm going to ask you to explain your reasoning. If I could, I would like to open up your head and look inside and say, 'Oh, that's how you're thinking,' but I can't. So you'll have to tell me. So I'm really interested because how you explain your thinking will help me understand you better and that'll make me a better teacher. So let's go."

So the interviewing is always about how did you figure that out? Even when a kid is right or especially when the student is right. I think in classroom, my early teaching you would ask a question and a child would give an answer and then you'd say, "Are you sure about that?" Or, "Would you say that again?" It's the hint like, "You've got it wrong kid. Go back to work." So I've shifted that in interviewing where we ask the kids how they think, whether they're right or wrong. We don't ever give any feedback about whether they're right and wrong. We could talk about why that's important.

But it's a question of hearing how the student is making sense. Math is all about making sense. And I think that too often students think that math is about following the rules.

Brett: Well and you take in your interviewing process, you take the emphasis off of getting the right answer by focusing on thinking.

Marilyn: Well, yes, but I'm careful about that because the right answers are important. So sometimes people say, "Well, the answers aren't important. It's more important how they think." No, the answer is important. Well, what the answers are, are important because sometimes we ask kids for an estimate or sometimes you have to be accurate. I think knowing when you have to be accurate and when an estimate would suffice is part of learning. But whatever the question I'm asking, the answer that I get is my first indication into what a student knows, but I don't stop there. I've got to find out what the student really knows. So the answers are important, but they're not the Holy Grail. I'm not looking just for the answer. I'm looking for answers and explanations. Like in reading, I'm looking at can a child read a passage accurately and fluently and can they understand what they read?

Brett: When we think about interviewing, someone might compare it to a running record, they might compare it to conferring. Interviewing is different.

Marilyn: I think it's similar and different in both of those situations. Now I don't have a lot of experience with running records, but I did go and spend some time with teachers to learn more about running records when we were working on the math interviews. So in running records you are checking for accuracy. So are we in our interviews. We are checking for fluency. So are we in our interviews. And you're checking for comprehension, but the comprehension is related to the specific passage that the student has read. So you have the questions you're going to ask.

In the interviews with math, I think it's a little more open. When I say like I did to Michael, "Which is greater, one-fourth or five-sixths," then I have to say, "How did you figure that out?" Or, "How did you decide," or, "How did you know?" And I don't know what the answer is. With the running records, you kind of know what you're listening for. I want to not pay attention to what I hope he would say and listen to what he might say. So it's similar but I think it may be subtle, but I think it's a profound difference.

Brett: One of the things that's very special about your interview style, you stay in the silence. Why is that so important?

Marilyn: I learned about wait time years ago, and it affected my teaching amazingly. Ask a question and then shut up. And I think as teachers we talk, we talk, we talk. And so if I stop and give kids time to collect their thoughts, then they have time to collect their thoughts. Otherwise, I'm the one who's doing all the learning because I'm doing all the talking. Whoever is doing the talking is probably doing more learning than the person who's listening because you're working it out in your head.

So I've learned in my classroom teaching about wait time. I've learned about ways in the classroom to make that wait time productive time when kids are thinking. And so it seems natural in an interview situation, especially when you watch the kid ... You're sitting face to face. You can watch them thinking. Their faces are scrunched up or they're kind of subvocalizing or they're tapping. Whatever they're doing, as long as the kid's involved, why would I interrupt the child?

It's fascinating. In the moment it's not hard to do because you're sort of curious about what's this kid going to come up with. But sometimes I rewatched interviews on video tape and then we have plenty of opportunities for teachers to see them. When a child sits for 20, 22 seconds, that is a long time. That's the amount of time we're supposed to be washing our hands that we're worried about the coronavirus. That's the time that I learned yesterday is how long it takes to sing the Happy Birthday song twice. Let me tell you, that's a long time to sit because I was interested in showing teachers some of these examples of wait time and I'm thinking, "Well that would be the most boring professional learning session. It's like watching paint dry." But you're not. You're watching wheels turn. I've become comfortable with silence.

Brett: And through Listening to Learn, you're showing us just how vastly different every student processes, how every student thinks. Talk a little bit about how different each student can be.

Marilyn: So here's a question that's our first question in our interview three which focuses on adding and subtracting. And interview three is numbers within 20. Interview two is numbers within 10, and then four and five, and the numbers get greater. So the first question is how much is 4+9? Well, the reason we selected that question is because when we started asking that question, we were amazed at how many different ways kids came up to solving that problem. Ways that I had never even thought were possible. From the kid who starts with the four and has to count on, five, six and gets all the way up maybe to 13 and that's a risky strategy. So the kid who says, "Well look, I'm starting with a bigger number nine," or a kid who says, "Well, you know, 4+9, 9+1=10." Every time I think I've heard it all, a kid comes up with it. There's this girl says, "Okay, I take 4+4=8." I'm thinking, "Well, all right, kids know their doubles.

Where's she going with that?" So, "Eight and then I took that four out of the nine so there's five left over. So eight and two more makes 10, and then I had three leftover and it was 13," and it's like, "Go girl." So I showed that clip to a lot of people and they say, "Well what do you do, because it's not particularly efficient." I said, "She's eight years old. Every child has a right to be eight for a whole year before they have to be nine." That's her thinking. She made sense of mathematics. I'm ecstatic.

Brett: So what is our takeaway from that in terms of what it means for classroom instruction?

Marilyn: One the things that I think many teachers are comfortable and excited about doing on number talks kind of mini-lesson discussions, 15 minutes at beginning of the class. One possible way for number talks is you put out a problem on 4+9 and you'd say, "What are all the ways we can think about figuring out that answer in our heads?" And in our heads, it wouldn't really, there's nothing to do on paper and pencil. You're just going to have to count. So one of the things on number talk, put up the problem, 4+9, you might say, "How many different ways can we think about this?" And then I want kids to hear and learn from one another. I want a community of math learners. So when the child does the counting on, I want to honor that. I want to put it up there in the board and say that's where Abel did it. But when the little girl Hanasis took out the 4+4, I want to say, "Oh, this is how Hanasis did it."

Something happens in those number talks. I had a kid do something. It's one in those areas of like, "Huh, I never thought about this." He took the nine, he took one off the nine and he put it on the four and he changed the problem from 4+9 to 5+8 and said, "That's 13." I'm thinking like, "All right. Yes, that's right," but I still to this day, don't know. Did he know ... Was 5+8 his friend and 4+9 wasn't? It's sort of like the fact that he was compensating in addition, seeing if I take one off one end and and put it on the other, the sum stays the same. He didn't verbalize that generalization, but that's pretty sophisticated mathematically.

Brett: Why do we want students to develop number sense?

Marilyn: It's part of life. I mean, I think about all the decisions that we make where we use arithmetic in our lives. What we have to add, subtract, multiply or divide to solve some problem that we need. It could be keeping score when you're playing a game. It could be buying wallpaper when I actually suggest that you overestimate, not underestimate because as soon as you run short, that dye lot's going to be gone. Understanding our finances, figuring out the tip in a restaurant.

There's so many times when we're in the supermarket, "I got $20, I don't want to go over, I don't have my credit card with me." Keep track of where things are. We think about numbers all the time. It's just part of our world. So if we've done this with teachers where we ask them to list all the ways and we get long, long lists about it, about what they do and then you say, okay, if we sort those and whether you figure it out with paper and pencil or you use a calculator or you do it in your head, how does that come out? And you know, most of the things in our daily life where we use arithmetic, cooking, gardening, playing games, we do it in our head. You figure out, "Okay, what time do I have to leave to get to the movies? The Showtime is 7:15. Will the commute traffic been done? What time do I leave?" Look at all the math you're doing.

The biggest math problem of the year? What time do you put the turkey in the oven to have it ready for Thanksgiving? Because now they say so much a pound. So much a pound with the stuffing. Turkey seems to cook more quickly these days, but what are you going to do? That gives people anxiety, but basically we think about math all the time. So people say, well, "Oh yeah, that's why we should learn fractions because of cooking." I say, "Well if I'm doubling a recipe and it calls for two-thirds of a cup, then I just take two-thirds and two-thirds. If I'm halving a recipe and it calls for three-fourths of a cup." But then again it's not really important. You kind of can measure it.

So I want kids to be playful with numbers. Think about numbers, find numbers useful to them. Not be afraid of numbers, be curious about numbers. There's so much that I want math to be playful and exploring and interesting and enjoyable.

Brett: And along with that, to you it's very important that students see the meaning in all the math. You redefined your teaching to specifically get there. Why?

Marilyn: Yeah, well without meaning, what is it? I mean, math is such a weird thing. I majored in math for an embarrassing reason. I didn't like writing. I figured you'd just had to do the problems. I was kind of goody two-shoes in school, and I was good in math. I memorized my way through a lot of college math courses.

It didn't work. Made me a better teacher. I know what it feels like to feel really dumb as the professor's filling up the board and all of a sudden, "Uh-oh, I missed a step." And then when you miss a step, you're out. And then I had to keep writing everything down that was going up on the board so I could try and figure it out later. So making sense is something that the kid does. That the source of the understanding is in the kid's head. My job is to stimulate the child with ways that they can create that understanding so they can bring meaning to math. What else is it about?

Brett: I mean selfishly as a student I would be that student that would say to the teacher, "Why are we doing this?"

Marilyn: Yes, and for many teachers it's hard because they learn math by "Yours is not to question why, just invert and multiply," and get threatened or annoyed at the kid who says that whereas you get thrown. I mean, I get thrown by questions.

A kid, third grader was convinced that 90 was an odd number because it had a nine. And so I said, "Brayden," I can still see his face, I said, "I'll get back to you tomorrow. I got to think about this." I really wanted to think about why did he think that? Well, nine is an odd number and the 90 starts with nine, must be odd. So I could have said, "No, no, no. If the nine comes first, it doesn't count. The zero is an even number." Then I realized many teachers I've asked, "Is zero even or odd?" And there are people who aren't sure or maybe it's neither because it's kind of that pivot number. So we all know what that flutter is. "Uh-oh. I don't get it."

Brett: You can see us thinking there, even in the question. I love that.

Marilyn: Kids are my laboratory. They never, never fail to amaze me and surprise me.

Brett: How did the role of mental math come in?

Marilyn: Well, that was part of the common sense thing when you realize that everything you do in life is mental math. Okay. Reading, writing, arithmetic. That bothered me so much as a child because arithmetic didn't start with R. Reading. Writing didn't start with R, but it sounded like it. But it bothers me now for a different reason. It should be reading, writing and reasoning because arithmetic is ... I don't want it to think of it as what we do with paper and pencil with following algorithmic procedures. Algorithms are important. They have an important place in mathematics, but I want the reasoning to be the leader of it. So it's the reasoning and that requires thinking mentally. But I think that as teachers, we're under a lot of pressure to send home work.

And I know there are many teachers who give their kids their work packet at the beginning of the week, and they have all week to work on. And there's a lot of practice, and it's a good way for kids to practice their skills. But what do you send home if you're doing mental math all day? The parents are going to think you didn't do any math. Especially if they say, "What'd you do in math today?" And the kid says, "Nothing," because all they did was talk and reason and exchange ideas. So I think that workbooks and textbook pages have really not encouraged teachers to give mental math the due it deserves and requires.

Brett: How do students react to your interviewing? To the interviews themselves?

Marilyn: When we developed these, I often go and borrow a class and ask the teacher if I can interview some kids. I'll go and introduce myself to the kids and explain my usual thing. "I can't open up your head. I can't look inside," the kids are a little nervous. And I've always said to the teacher, "Don't give me your top kid. Don't give me your kid who everybody knows is really having a difficult time with it. Just give me a kid, a regular kid." I take the kid out and they come back and everybody's looking, and the kid comes back and we have fun. When do kids get all this attention? This is a person they don't even know and I'm friendly, and we're going to talk about this and I'm interested and they come back. Sometimes I have kids come back, they say, "That was good." Then they're all raising their hand, "Take me, take me." I have never met a kid that didn't want to be interviewed.

I remember one time a kid did not want to be videotaped and he whispered the whole thing, which I thought was a very creative solution to this avoiding my videotaping him. But I don't know. We've been teachers for a long time. You walk into a classroom and we know how to relate to children. We know how to deal with mobs of children, and we know how to deal with individual kids. So, "Come, we're going to have a conversation. Help me out here."

Brett: Marilyn, you're developing a new project called Listening to Learn. You call it a new digital interview tool. What can you share with us about it?

Marilyn: Well, I've been interviewing kids for years, and I want teachers to have the experience of really finding out what their students understand and encouraging them to do interviews. And the reason that it's a digital tool is important because what I've figured out is it's hard to listen and learn. You have to learn to listen in order to listen to learn.

And that means really hearing what a student says and capturing that. But what am I going to do with that information? As I've thought about it, and it's kind of embarrassing to think that it was later in my career that I thought about, there are certain reasoning strategies that became evident to us as we interviewed kids that we want kids to be able to have access to. So if I think about addition and subtraction as a content focus, which is separate from multiplication and division or then fractions and decimals, or even before that, some foundation. So if I focus on addition and subtraction, I want kids to be able to decompose numbers. I want them to understand the inverse relationship between addition and subtraction. I want them to be able to break numbers apart and to place value parts. I want them to use benchmark numbers.

I'm rattling these off, but we have the 10 reasoning strategies that we want all kids to have access to in order to be able to add and subtract mentally with numbers within 10, 20, 100 and 1000. The same ten. This is not a lot. And once I figured those out I said, "Wow, this is pretty slick." But when I ask a kid, "How much is 4+9," the child's answer that I want to help teachers is listen to what the child said. And we have captured all the different ways, over 1000 kids that we've interviewed, of how they answered them and we give them, so this one is the most close to that. Then we take, in the digital tool, which I couldn't do otherwise, is the heavy lifting of mapping the kid's explanation onto one of those 10 strategies I just said.

So I want all teachers to know the 10 strategies. I don't want you to teach the strategies as if they're separate isolated skills because something will always emerge as connected to more than one strategy. If a kid says, "Well, 4+9 okay, I'm going to start with the nine and then I'm going to take one off the four, make it 10 so it's 10+3," the kid is reversing the two addends. So it's demonstrating applying the commutative property. The kid is using the benchmark number of 10. The kid is decomposing numbers within five. They're doing so many things. We capture all that. So what the digital tool can do, which has got me so excited, is it can tell you which of those strategies the student has demonstrated. And I can look across my class and say which of the strategies that kids seem to have access to and which do I need to spend more time with? That is truly information that could inform my instructional decisions.

Brett: Well that was what I wanted to ask you next. What can a teacher do with this tool in their teaching?

Marilyn: So we were interviewing a third grade class at interviewing and we found out that none of the kids use the inverse operation. For example, 11-9. That's within 20. A kid may count back 11, 10, nine, eight. It's a risky countback strategy, but 11-9 like, "9+2=11." That's the inverse of, "I can use addition to solve a subtraction problem." I have had kids, older kids, you ask 1000-998, it should be slam dunk two. For some kids it isn't. So imagine if you had that information about your entire class of who had chosen to use the inverse relationship to solve problems because it was the most efficient.

Now, if a kid says to me, "1000-998. Okay, 1000-900=100. 100-90=10. 10-8=2." A little long winded, but I'm impressed. But I want to know if they could have access, so we have several questions in each interview, which should give kids the chance to show that they could use that. But suppose I have no kids demonstrating that or suppose in my class I've got all but a third of the kids aren't. So that tells me, "Okay, in my number talks, let's talk about problems where it's more efficient to subtract, to solve it or more efficient to add, to subtract the problem." It tells me what I need to have so that kids who are either developing understanding of that important strategy or cementing it or really can extend it to even more complex numbers, greater numbers.

I have to have that information, but I want a community of learners so that I can engage it. It helps me make intentional decisions about my instruction, and that has been the most stunning thing to me. My instructional choices have become so much more intentional once I have the information from interviews.

Brett: And you've seen it strengthen the classroom community as well.

Marilyn: Oh gosh. Yes. I understand the need for differentiation and it's hard. Yes, I understand the need for classroom community. I know how hard teaching is. Some years you get a class where everybody's sort of within a range. Some years you get a class where you have kids who are so disparate in two different groups. I've seen it all. They're all tough, but at all times we are a community of learners. And that's when I need all the tools I have pedagogically.

I need to know how to do number talks. I need to know how to engage the kids in problem solving investigations that we can all learn from. I need to know how to give them independent work and truly differentiate. I need time to confer with kids and help them. I need to do it all. They do that in reading and writing instruction. I need to do it in math, but it needs to be a community even when kids are coming to it with their own way.

Brett: I've heard you say, "Math can be a way in for a teacher to really see their students."

Marilyn: Yeah. I remember a principal in New York City told me that math was easier because you can make it concrete and it's most astonishing thing when you're sitting with a young child and we have 10 counters in front of us. I agree, the child agrees we have 10. And I say, "Watch what I'm going to do," and I take one of the counters away and I say, "How many are there now?"

Some kids have to count them. Other kids will just say, "Well nine." The difference between those two kids, I would not know that one kid understands that nine comes before ten, nine is nested in 10, 10 ... There's so much that happens. We think of counting as being simple, but it's really pretty complex and without the ability to see it, I could actually see it there. That gives me understanding about what that child does and doesn't know.

So the child who isn't sure probably needs some work with smaller quantities. I tweeted out recently a question that came to me one morning and it was like, if you look at the pips on a di e, if you look at the arrangement of dots, you don't have to count one, two, three, four, five. Well you don't, but some kids do. It's a brain function. You can see five so it's subitizing. Is that the same as sight words? And I tweeted that out. A bunch of people sent me some really interesting information to think about with this idea of subitizing. What do I see? What do I know? And I want teachers to be curious about that with their kids.

So one of the things we suggest in Listening to Learn, we help teachers with the protocol of giving interviews. We interpret the students' explanations and map them onto the strategies. And we also provide some "what next" instructional suggestions. Teachers have their programs and they're basically, those are their default roadmaps for instruction, but we give some suggestions. It's common for many teachers to do dot patterns where you show kids random dot patterns. Sometimes few enough to see if they will ... You just sort of show-hide, take a quick look. But if you have a bunch of them arranged in such a way, a quick look where you can't subitize that many, but you could see perceptually a group of four and a group of two and you'd say, "Oh, that's six."

So it's kind of like a conceptual subitizing rather than just perceptual subitizing. I mean, I'm amazed how complicated counting is, and I taught secondary math. I encourage secondary math teachers to go down the grades and talk to the kids about what they understand. Things that we took so much for granted. When the professor in the math class said, "It is now obvious that," I was the kid to whom it was not obvious.

Follow us on Instagram @heinemannpub to stay up to date on the latest books, your favorite authors, and upcoming events!

Marilyn Burns is one of today's most highly respected mathematics educators. In 1984, Marilyn founded Math Solutions®, an organization dedicated to the improvement of math instruction in Grades K-8. Her book, About Teaching Mathematics, now in its 4 th edition, has been widely used for pre-service and in-service teachers. Her other professional books include Welcome to Math Class; Math, Literature, and Nonfiction; Lessons for Algebraic Thinking; Writing in Math Class; and others.

Marilyn's children's books include classics like The I Hate Mathematics! Book and The Book of Think, and the more recent The Greedy Triangle and Spaghetti and Meatballs for All! Her children's books have been translated into eight languages.

For her educational contributions, Marilyn received the Ross Taylor/Glenn Gilbert National Leadership Award from the National Council of Supervisors of Mathematics and the Louise Hay Award for Contributions to Mathematics Education from the Association for Women in Mathematics. She was also inducted into the Educational Publishing Hall of Fame by the Association of Educational Publishers.

Marilyn and a team of Math Solutions® master teachers developed Do The Math, an intervention program that targets on number and operations, and Math Reads, a program that helps teachers use children's literature for teaching mathematics. Her most recent project, Listening to Learn, is a digital interview tool for grades K-5 based on her previous work on the Math Reasoning Inventory (MRI), for students entering middle school and beyond and funded by the Bill & Melinda Gates Foundation.

Marilyn continues to teach regularly in the classroom, finding the experience essential to developing and testing new ideas and materials. Learn more about Marilyn's work at her Marilyn Burns Math Blog, by following her on Twitter @MBurnsMath, and by visiting her Marilyn Burns Math YouTube Channel.

# data[].attributes.attachment_link.title
On the Podcast: Marilyn Burns on Conducting Math Interviews with K-5 Students

# data[].attributes.attachment_link.description
Have you ever considered that understanding is to math as what comprehension is to reading? Today on The Heinemann Podcast, we're speaking with Marilyn Burns, one of today's most highly respected math educators. She is the creator and founder of Math Solutions®, and has dedicated her career to the improvement of math instruction across grades K-8.