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Talk Moves: Developing Communication Skills

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Here's an interactive tip to help develop student communication skills in your elementary school classroom. This communication tip is perfect for language learners.

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Good discussion in math class is essential for student learning. Mathematical discourse helps students reflect on their own understanding, make sense of and critique the reasoning of others' ideas, and most importantly, build mathematical confidence.

This is a great resource to help prompt students to engage in small group and whole class conversations. Print a copy for each student's math journal and print a big version to display in your classroom.

This shares more information about the importance of mathematical discourse, what good math discussion looks like, and strategies you can try now to improve discussion in the classroom. Pin it, print it, and share it with a teaching colleague today!

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Poster and Infographic: Improving Math Discourse in the Classroom

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Good discussion in math class is essential for student learning. Mathematical discourse helps students reflect on their own understanding, make sense of and critique the reasoning of others' ideas, and most importantly, build mathematical confidence. This is a great resource to help prompt students to engage in small group and whole class conversations.

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The importance of engaging students in meaningful mathematical discussion has long been identified as an essential component of students' mathematics learning.

When students share and exchange their ideas, both they and their teachers benefit.
Dr. Gladis Kersaint
Understanding the Importance of Mathematical Discourse

Talking about mathematical concepts allows students to reflect on their own understanding while making sense of and critiquing the ideas of others. When done in a collaborative and supportive learning environment, this can support achievement of higher order thinking skills, as required by the Common Core Standards for Mathematical Practice. Students can make conjectures, link prior knowledge to current understanding, reason about mathematics, refine and amend their approaches, and take ownership of their mathematical knowledge.

Students benefit greatly from learning to use the tools of mathematical discourse-including words, symbols, diagrams, physical models, and technology-to present and defend their ideas. Imparting these new skills on students allows teachers to access, monitor, and evaluate students' mathematical understanding and development.

Mathematical Discourse in Action

One approach to giving students the information needed for a mathematics lesson involves the teacher simply telling the students what they need to know. Far more productive, however, is more a thoughtful approach to student engagement that encourage a productive dialogue, as seen in the example below. As educators, we need to structure lessons to encourage student interaction, address gaps in student understanding, and help students express mathematical concepts more precisely. Providing opportunity for conversation does just that.

Does this look like a classroom dialogue you've seen before? To further your understanding of the importance of facilitating mathematical discourse, ask yourself:

How did these students benefit by sharing what they knew as part of the mathematics discussion?

Why did the teacher allow students to evaluate the correctness of Julie's answer?

Why did the teacher ask another student to restate what James said?

Establishing a Discourse-Rich Mathematics Learning Community

To engage students in productive mathematics discussions, it is important to establish a learning environment that welcomes student involvement. The first step is setting the expectation that every student will contribute to the discourse community.

Students must be encouraged to use their problem-solving, reasoning,and communication skills to make conjectures, explore their own ideas and approaches, and find solutions to routine and non-routine mathematics problems.

In particular, the five process standards-problem solving, reasoning and proof, communication, connections, and representation-can be seen in action in a discourse-rich mathematics community as students interact, question one another and convey their understanding. During this dialogue, teachers can recognize errors in context and reinforce that they are natural occurrences that enhance learning.

What does a classroom rich with mathematical discourse look like? Walk into one and you'll likely see:

Students and teachers acknowledging and discussing errors and the reasons behind them to help students build greater understanding.

Students questioning each other using mathematics arguments to establish the correctness of solutions.

Students reaching and justifying conclusions based on their own mathematics knowledge without relying on the authority of teachers.

Students engaging in "productive struggle" with appropriate scaffolds for support.

Students encouraged to use a variety of approaches to convey their knowledge and solution strategies, including oral presentations; written explanations; and physical, graphical, pictorial, or symbolic representations.

Understanding Student and Teacher Roles in Mathematical Discourse

Facilitating student engagement in mathematical discourse begins with the decisions teachers make when they plan classroom instruction. The tasks they use, the ways in which they organize the classroom, and the behaviors they model communicate expectations for classroom norms, including the ways students are expected to engage in classroom discussions.

Depending on prior experiences, students might find these new expectations for engagement uncomfortable and may not be ready to plunge into mathematical dialogue feet first. Teachers must ease the transition to a dialogue-rich mathematics classroom and prepare students to engage in such discussions. It is also important to carefully consider the best ways to coordinate student interaction in pairs, small groups, or whole-class interactions to ease transitions and maximize learning.

To support students, teachers must help students create avision for expected behaviors and actions, prepare them for their roles by modeling or role-playing, and reinforce these behaviors consistently. Teachers need to monitor progress as students engage in mathematics discussions, supporting them as their mathematical knowledge grows and they become more skilled at expressing ideas coherently and using vocabulary, syntax, and semantics precisely.

Teachers should observe, listen to and monitor students to support instructional decision-making. Determining what questions to ask, which students to call on, when to intervene and when to extend student thinking provides opportunities to understand student thinking, monitor growth and assess knowledge. A discourse-rich classroom enables teachers to gain insights not only about what students know, but also about the approaches they use, how-and how well-they understand the ideas, and the ways they present their knowledge.

In addition to content knowledge, mathematical discourse allows teachers to monitor students' dispositions and gauge their developing confidence, interest, and perseverance. Teachers can use this information to determine areas of confusion or frustration in order to decide when an intervention might be needed. They also examine understandings and misconceptions revealed during classroom discussions and adjust lesson plans accordingly.

Asking the right questions can help support instructional decision making and direct student focus. Some examples are below:

Engaging Every Student in Mathematical Discourse

All students are mathematics language learners, regardless of their level of English language proficiency, and discourse allows ALL students to develop mathematical language.

While it is important to build scaffolds to support students who are learning English and mathematics at the same time, it is essential to recognize that mathematics is a technical language that all students must learn. Students who are English speakers also require support as they learn the language of mathematics.

As outlined in the Standards for Mathematical Practice, students should become fluent in mathematical language, including vocabulary, symbolic representations, syntax, semantics, and linguistic features. In addition, they must have ample opportunities to use the language of mathematics as they engage in various forms of communication. Discourse allows students to practice precision in multiple areas, including:

1.Vocabulary

English words with a different meaning in mathematics, such as "negative," "table," or "rational."

Specialized terms, such as "hypotenuse" or "trapezoid."

Terms with multiple meanings in mathematics, such as "median" or "base."

2. Symbols

Ways to read and interpret symbolic representations. For example, "a × b" can be expressed as "a times b," "the product of a and b," or "multiply a and b."

3. Syntax

Understanding the rules that govern the structure of sentences. For example, "A number y is 4 more than a number x" is translated symbolically to "y=x+4."

4. Semantics

The process of making meaning from language.

The same mathematics word may be interpreted differently depending on the context. For example, the median of a set of numbers versus the median of a triangle.

Teachers support mathematical language development by asking key questions and encouraging students to ask for clarity. By doing this, teachers motivate and encourage students and facilitate productive discussion, fostering a supportive classroom culture that maximizes learning.
This blog is part of a three post series on the importance of mathematical discourse from Curriculum Associates Dr. Gladis Kersaint is a Professor of Mathematics Education at the University of South Florida Stay in-the-know with all things EdTech and innovations in learning by signing up to receive the weekly Smart Update. and an author of the Ready Mathematics program. , a Getting Smart Advocacy Partner, and Dr. Gladis Kersaint, the author of the recently published whitepaper Orchestrating Mathematical Discourse to Enhance Student Learning. Download your free copy here.
For more on Curriculum Associates, check out:

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Talking Math: How to Engage Students in Mathematical Discourse

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The importance of engaging students in meaningful mathematical discussion has long been identified as an essential component of students' mathematics learning. When students share and exchange their ideas, both they and their teachers benefit. Dr. Gladis Kersaint Talking about mathematical concepts allows students to reflect on their own understanding while making sense of and critiquing the ideas of others.

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Teaching Tools | Resources for Teachers from Scholastic

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This article and the free download at its conclusion are adapted from Intentional Talk: How to Structure and Lead Productive Mathematical Discussions (Stenhouse, 2014). Used with permission. by Elham Kazemi and Allison Hintz
Leading mathematical discussions can be both invigorating and challenging. It's easy to start a discussion by asking children to share their thinking. And nothing beats those moments when children proudly share something they figured out.

But then what? Math discussions aren't just about show-and-tell: stand up, sit down, clap, clap, clap. Knowing what to do with students' ideas and teaching children how to meaningfully participate in discussions can be a lot more daunting.

We often worry during a discussion that students might get lost trying to keep up with what everyone is saying or that they may simply tune out when a lot of ideas are shared. And no teacher likes that uncomfortable feeling of putting a child on the spot.

Yet when teachers plan for and steer productive discussions, children realize it's worth listening to one another and that it's okay to be pressed to say more.

Our four principles for good math discussions

Not all mathematical discussions have the same aim or should be led in the same way. In our book Intentional Talk (Stenhouse, 2014 - see the MiddleWeb review here), we describe how considering your teaching goals for math talk can help you better design discussions to meet those goals and teach children to participate meaningfully.

Our work with classroom discussions is guided by four principles:

1. Discussions should achieve a mathematical goal, and different types of goals require planning and leading discussions differently.

2. Students need to know what and how to share so their ideas are heard and are useful to others.

3. Teachers need to orient students to one another and the mathematical ideas so that every member of the class is involved in achieving the mathematical goal.

4. Teachers must communicate that all children are sense makers and that their ideas are valued.

These principles are at the heart of creating classrooms where children can participate equitably. Sarah Michaels, Mary Catherine O'Connor, and Megan Williams Hall ( 2010) write about classroom communities that live by these principles as engaging in "accountable talk,"or "talk that seriously responds to and further develops what others in the group have said" (1). The challenge, of course, lies in putting these principles into action.

The classroom vignettes in our book reflect insights we have gained into leading mathematical discussions while working closely with teachers who are committed to equity in students' achievements and learning opportunities.

These vignettes do not take place in gifted classrooms or in schools in the most affluent neighborhoods. We hope the everyday brilliance of the teachers and children shared in our book will help us all strive toward creating classrooms that disrupt longstanding assumptions about who can and cannot excel in mathematics (Delpit 2012).

Here's a bit more about what we mean by each of the four principles. This will give you a glimpse into the ways particular mathematical goals can help you run a discussion.
Principle 1: Discussions Should Achieve a Mathematical Goal
The mathematical goal acts as your compass as you navigate classroom talk. The goal helps you decide what to listen for, which ideas to pursue, and which to highlight. In Orchestrating Productive Mathematics Discussions (2011), Margaret Smith and Mary Kay Stein describe the importance of teachers clearly specifying the mathematical goal before planning out a discussion. The mathematical ideas at the heart of a lesson will help you distinguish between different types of classroom discussions you can have with your students.

Sometimes your aim is to have students share as many different ideas as possible in the discussion so they see a range of possibilities. We call this "open strategy sharing," because we're working on building students' repertoire of strategies. The class generates lots of ideas, and the discussion likely moves across a broad terrain that includes mathematical concepts, procedures, representations, and explanations. Students listen for and contribute different ways to solve the same problem.

At other times you might want to focus the discussion on a particular idea. We call this "targeted discussion." Through targeted sharing the discussion zooms in on a particular idea. This more focused sharing involves specific goals, like defining and using key terms or concepts correctly, revising an incorrect strategy, or making sense of a particular representation. The students listen to and contribute ideas in order to move toward consensus. In the table above are the targeted discussion structures that we focus on in chapters of Intentional Talk.
Principle 2: Students Need to Know What and How to Share
To make classroom discussions come alive, students need help knowing how to participate. When students have the chance to express their ideas, teachers have more information about what students do understand, what they are grappling with, and where they might be stumbling or confused.

Students learn through classroom discussions what to share. In our book, we provide guidance for how to structure each type of discussion. We also pay attention to how students learn to contribute meaningfully in different types of discussions.

We need to provide clear models for what an explanation sounds like and we need to judge, based on learning goals for students, what mathematical ideas require an explanation at any particular time. Students learn what to share as we prompt them to articulate important parts of their explanations.

We can use and offer sentence starters that cue students to know what to say: "Explain to me what you meant by ____," "What would you do if the number was ____?" and "How is your way different from ____?"

We also help students learn what to listen for so they can contribute to the conversation: "Listen for how she broke apart the numbers," "Think about whether you are understanding how she used the number line to show her thinking."

Similarly, students learn how to share through our explicit support. Reinforcing norms supports students in knowing how to share. For example, you might need to reinforce where to place oneself ("Stand here so we can see your work"); how loudly to speak ("Speak loudly so everyone can hear your idea"); and what tools to use ("Use the drawing in your journal to help").

We want to help children crack the code of being successful in meaningful mathematical learning at the same time as we tap into and draw on the resources they bring to the classroom (Aguirre, Mayfield-Ingram, and Martin 2013).
Principle 3: Teachers Need to Orient Students to One Another and the Mathematical Ideas
One of the challenges of leading discussions is bringing the whole class into the discussion. Most classrooms have several students who are eager to share and will always raise their hands and volunteer their thoughts. If we always call on these students, it's easy for others to remain passive or become anxious about how to enter the discussion.

But that's not the only problem; if students have their hands raised just to get in their two cents, you'll end up with a bunch of ideas that don't build on each other or go anywhere. Teachers have to use strategies that help students learn how to attend to each other's ideas and the mathematics. We call this orienting students to one another and the mathematics.

Teachers can draw attention to the meaningful contributions that all students make and can encourage students to take risks by "assigning competence," or identifying and naming students' specific contributions. The vignettes in our book demonstrate many different ways that teachers advance the mathematical agenda of a discussion by strategically highlighting a student's insight or contribution, especially when a student might not be feeling confident about his or her standing with the rest of the class.
Principle 4: Teachers Must Communicate That All Students Are Sense Makers and That Their Thinking Is Valued
Our last principle is also the most important principle to put into action, because children have to be willing to take risks and put their ideas out there.

Discussions obviously open up the possibilities that students will share their partial and incorrect understandings. How we as teachers respond to errors and partially developed ideas sends important messages about taking risks. It is not easy for students to express their ideas if there is a high burden to be correct and understand everything the first time around.

We need to remember that there's always a logic behind why students think the way they do, even if they seem off base. We also need to recognize publicly students' ideas, making sure we don't single out just a few students as mathematically "smart."

There are many ways to be smart in mathematics, including making connections across ideas, representing problems, working with models, figuring out faulty solutions, finding patterns, making conjectures, persisting with challenging problems, working through errors, and searching for efficient solutions (Featherstone et al. 2011). Being smart in mathematics is not just about speed and accuracy.

Vivian Paley writes that being curious about children's ideas signals to them that they are respected: "What are these ideas that I have that are so interesting to the teacher? I must be somebody with good ideas" (1986, 127). We want all students in the class to regard themselves as mathematical thinkers and to see themselves as people who can grow and be successful.

Read more to see the 4 principles applied

Want to see the four principles in action? Download this PDF and you'll be able to eavesdrop as Ms. Lind moderates a discussion with her class, using an open strategy share and two types of targeted discussions. Student work included!
Elham Kazemi is a professor and associate dean of professional learning at the University of Washington Seattle, where her focus is elementary mathematics education and school-based professional development. In 2012, Kazemi was nominated for the university's faculty award for Distinguished Contribution to Lifelong Learning. She is a frequent presenter at national conferences. Allison Hintz is an assistant professor of mathematics education at the University of Washington Bothell. As an elementary teacher, Allison participated in the Developing Mathematical Ideas professional development with University of Washington professor Elham Kazemi - See more at: http://www.stenhouse.com/html/intentional-talk.htm#sthash.4vKpSZQV.dpuf Allison Hintz is an assistant professor of mathematics education at the University of Washington Bothell. As an elementary teacher, Hintz participated in the Developing Mathematical Ideas professional development.
Allison Hintz is an assistant professor of mathematics education at the University of Washington Bothell. As an elementary teacher, Allison participated in the Developing Mathematical Ideas professional development with University of Washington professor Elham Kazemi - See more at: http://www.stenhouse.com/html/intentional-talk.htm#sthash.4vKpSZQV.dpuf

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Four Steps To Deepen Student Discussions about Math

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This article and the free download at its conclusion are adapted from Intentional Talk: How to Structure and Lead Productive Mathematical Discussions (Stenhouse, 2014). Used with permission. by Elham Kazemi and Allison Hintz Leading mathematical discussions can be both invigorating and challenging. It's easy to start a discussion by asking children to share their thinking.

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- Informed Consent
- Confidentiality
- Anonymity

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A little young for my students, but similar concept.

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Number talks ( Kindergarten, 1st Grade & 2nd Grade) offer a bridge between conceptual understanding and mental math. During mini-lessons and Guided Math, I am ALL about manipulatives. Base 10 pieces, unifix cubes, cuisenaire rods - give me all the math things. Especially in 1st grade, manipulatives offer a concrete way to represent a number and their thinking. At some point, this concrete thinking has to begin to transition into abstract and mental math processes. Number Talks offer a daily, short, structured way for students to talk about math with their peers.

What is a Number Talk?

Number Talks are short (10ish minutes), daily exercises aimed at building number sense. Number sense is the ability to play with numbers meaning students can visualize problem solving, perform calculations quickly, and are flexible in their mathematical strategy. Students who have strong number sense solve problems in more than one way and check that their answers make sense. As a part of this routine, students are thinking, asking their peers questions, and explaining their own thinking all while the teacher records the thinking.

Sherry Parish has written the book Number Talks (Amazon affiliate link) and it offers awesome ideas for Kindergarten to 6th grade. It is definitely an expensive (up to $60 if bought new) but offers great ideas and real-life examples of Number Talks.

What Do Number Talks Look Like?

When possible, I love slipping a number talk ( Kindergarten, 1st Grade & 2nd Grade) in at the beginning of our Guided Math block. If we're running late, I'll slip a Number Talk in during an awkward transition or at the very end of the day. A traditional talk follows this routine -
Present the class with a problem. Students are seated in a common area with no math tools. Number Talks are mental exercises. I store my number talks ( Kindergarten, 1st Grade & 2nd Grade) on binder rings next to my Document Camera for easy access.

Give think time. (When a student raises their hand, it tells other students they were not fast or good enough in their thinking. To account for this, students give me a sly thumbs-up on their chest to signal that they have thinking they want to share. Then, they put up multiple fingers (on the same hand) to indicate they have multiple ways to answer/solve the problem.

3. Call on a student - "_______, what are you thinking?" Have the student explain their thinking and then give their answer. My focus is always on the process not the answer.

4. Offer the strategy to the class. Student will elaborate (if correct) or ask questions (if misguided). If students aren't sure they understand a friend, they will say "I'm a little confused. Could you tell me in a different way?" If students agree with the student sharing they will do sign-language for 'me too' (thumb near chest and pinky pointing at friend). This builds the student's confidence and offers the student sharing positive affirmations.

5. Invite other students to share their strategies.

Scaffolding Students

If students have never been expected to explain their mathematical thinking, students may be very resistant to share their own strategies. So, how do I encourage students to share their own thinking/strategies?

Model, Model, Model - The first 2 days of Number Talks, I do a lot of modeling. After this, I completely release the Number Talks to the students.

Sentence Stems - "In my head I saw..." "My first step was..." "At first, I decided to try..." "I needed to..." "Since I wasn't sure what to do, but I noticed..."

Force It - Awkward silence is your friend. Sometimes I will wait (for extended periods of time) for students to share their thinking. Even if a friend is STRUGGLING with a problem or sharing their thinking, I do not come to the rescue. Growth comes when friends are able to sort out their own thinking and my 1st grade friends are able to do this...even if it is a little painful for me.

Examples of 1st Grade Number Conversations

So, it all sounds great, right?? But what do number talks actually look like? My first talks ( Kindergarten, 1st Grade & 2nd Grade) each year are always subitizing patterns (dot patterns). They are the perfect introduction into composing and decomposing numbers. Slowly that transitions into the 100s chart and eventually into word problems and balancing scales.

In the 2nd grade number talks, the focus is on building fluency within 20 and 100, as well as, layering skills in different ways. From missing addends, to algebraic thinking, over 400 prompts offer students dozens of chances to spiral review math skills each month.

Subitizing Quick Images

Subitizing ( Kindergarten, 1st Grade & 2nd Grade) is the ability to quickly identify the number in a group of objects without individually counting the objects. It is a concrete way to explore composing and decomposing numbers. Students will see dot patterns in different ways, and that is a great thing. When showing students 6, made from a pyramid students might see 3 and 3, 5 and 1, or 3 and 2 and 1. These are all ways to build 6 and lead students to understand that numbers can be composed and decomposed in many different ways.

Composing Numbers

Flexibility in number thinking is a critical skills in beginning mathematicians. Students must understand that 7 can be made from 4 and 3, 2 and 5, 6 and 1, or 7 and 0. Below students are provided with a "Target Number" and ask students to use some of the provided numbers to hit the target. Students then have to decide how many numbers to use, which operation to use (addition or subtraction), and then, decide if number order matters. ( 1st Grade Prompts, 2nd Grade Prompts)

Flexibly Composing AND Decomposing Numbers

An important part of teaching primary students is to build number fluency and flexibility. Students should be able to encounter numbers in a variety of formats and engage with them in a variety of ways. During our Representing Numbers conversations ( 1st Grade & 2nd Grade), I encourage students to branch outside of the typical ten frame, plus one, etc. These are great strategies when we first start, but after the first few days students can build on these basic representations to develop different relationships and understanding.

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Number Talks: How and Why? - The Brown Bag Teacher

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Number talks ( Kindergarten, 1st Grade & 2nd Grade) offer a bridge between conceptual understanding and mental math. During mini-lessons and Guided Math, I am ALL about manipulatives. Base 10 pieces, unifix cubes, cuisenaire rods - give me all the math things. Especially in 1st grade, manipulatives offer a concrete way to represent a number and their thinking.

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Use these five strategies to encourage meaningful classroom discussions.

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- Expectations of students - Assuming if students will or will not be able to handle the task
-Prompting more than needed or not allowing for full discussion

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- How to best facilitate discussion in the classroom?

- How to make students feel comfortable enough to share with other?

- Ways to promote sharing even when uncertain of an answer.

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Math Talk Moves Poster - Math Solutions Books & Resources Store

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- Student based discussion
- Students solve problem and explain their thinking
- Students allowed to come to conclusions, whether right or wrong

-Ability to return to the discussion problem later in the lesson to correct any misconceptions

- Teacher observing, asking questions