Creating a Community of Mathematicians through Number Talks

One of the primary goals of a math educator is to support the growth of mathematicians who are strong thinkers and problem solvers.  In order to do this, the math classroom needs to become a community of thinkers, where students feel safe and welcome sharing their ideas and different methods of problem-solving and where students regularly learn from each other.  A great way to build a culture of problem-solving in a classroom is through Number Talks (also called Math Talks).  I have been inspired by so many wonderful math talk scenarios that I have seen in the first few weeks at of school at GEMS World Academy Chicago, so I want to take some time to share some resources and best practices for number talks in the classroom.

What is a Number Talk?
A Number Talk is a brief (5-15 minute) discussions about a single, strategically chosen mental math problem or situation.

• Students are presented with the mental math problem and are provided adequate wait time to think to themselves about the math problem.  Giving a silent thumbs-up hand signal on their chests notifies the teacher when they are ready to share.  Placing the thumbs-up on the chest is more discrete rather than raising a hand so others are not made to feel self-conscious if they are taking longer to think.
• In a non-judgemental way, the teacher allows all willing members of the class to share their answers only. 
• The teacher then follows up by asking students to share their problem-solving strategies orally, which the teacher charts on the board to compile a visual representation of the various strategies the students share.  
• The teacher invites students to ask questions of each other and make connections between the various strategies.  The teacher may also ask strategic questions to prompt thinking and help students compare/contrast strategies.

Why use Number Talks?
Through independent thinking and then communicating and comparing/contrasting various strategies, Number Talks are one way teachers can engage students in the Five Strands of Mathematical Proficiency as explained in the National Research Council's book Adding It Up: Helping Children Learn Mathematics.

Image from Adding It Up: Helping Children Learn Mathematics

Jo Boaler, Standford Professor of Mathematics Education and faculty director of YouCubed, also argues that Number Talks are one of the best ways to build number sense.  The focus of a Number Talk is not necessarily on the answer, but on how you arrived at the answer since problems can be seen in many different ways.  When students verbally share their thinking, the role of the teacher is to visually model/record the multiple strategies with the purpose of making connections among the students' many different methods for thinking mathematically.  (You can hear from Boaler herself about how routines are established and what these number talks look and sound like in this 15-minute video, which is an excerpt from her Stanford online course.)

Where can I find ideas for Number Talk prompts?

• The book Good Questions: Great Ways to Differentiate Mathematics Instruction in the Standards-Based Classroom by Marian Small provides ideas for open questions that are accessible to a variety of learners and allow for mathematical debate and conversation.
• Fractiontalks.com provide images that can be great prompts for fraction-related number talks.
• VisualPatterns.org provides images that can be used as prompts for number talks.
• MathTalks.net provides math talk prompts used with 6-8th grade students.
• Which One Doesn't Belong? is a "website dedicated to providing thought-provoking puzzles" which allow for rich mathematical conversation. You can also follow the #WoDB hashtag on Twitter for more ideas.
• Use any mathematical problem that allows for multiple ways of thinking!  This graphic organizer from SFUSD may be helpful to use as you start to plan your own.

What if I want to read more about Number Talks?
Check out the following resources for more information about how to implement number talks in your classroom with students!

• The article Number Talks: Building Numerical Reasoning from NCTM's Teaching Children Mathematic's provides a wonderfully detailed overview of a Number Talk's key components. "The heart of number talks is classroom conversations focused on making sense of mathematics."
• Inside Mathematics, an education non-profit focused on supporting high-quality math education, has a series of number talk video clips which allow you to see number talks in action in a variety of classrooms with a debrief afterward.
• Number Talks: Whole Number Computation Grades K - 5 is a fabulous (but pricey) resource that details how to start doing number talks, ask strategic questions to follow and prompt students' thinking, and advice for developing grade-specific number talk prompts.
• The Teaching Channel (Tch) also has created a page called "Dig Into Math Talks" with links to many additional resources.

Spread the Number Talk Love!
What are some of your favorite resources for number talks?  What have been some of your most successful number talk prompts?  Do you have any advice for someone new to doing number talks?

Thank you for growing our community of learners by sharing in the comments section!