research on number talks

How Number Talks Assist Students in Becoming Doers of Mathematics

• First Online: 16 June 2023

Cite this chapter

• Dawn M. Woods 4  

298 Accesses

1 Citations

Number talks are discussions where teachers encourage their students to mentally solve mathematics problems and then come together as a class to share their mathematical reasoning. As students share, listen, and discuss their solution strategies, they begin to make connections between how procedures are the same, different, and/or more efficient. In this chapter, I explore how a teacher leverages number talks to support students in becoming doers of mathematics. Findings from this study reveal how the teacher supported students to (a) develop agency, (b) distribute authority, and (c) share mathematical reasoning. Further, it was found that mental computation played an important role since it supported students to discover ingenious, effective, and efficient ways of solving mathematical problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime
• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Available as EPUB and PDF
• Compact, lightweight edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info
• Durable hardcover edition

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Focusing on Mathematical Structure and Sensemaking in Courses for Future Teachers

Number Sense and Flexibility of Calculation: A Common Focus on Number Relations

Number Work: Recovering the Original Complexity of Learning Arithmetic

Aguirre, J., Mayfield-Ingram, K., & Martin, D. M. (2013). The impact of identity in K-8 mathematics: Rethinking equity-based practices . National Council of Teachers of Mathematics.

Google Scholar  

Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93 (4), 373–397. https://doi.org/10.1086/461730

Article   Google Scholar  

Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38 (4), 333–339. https://doi.org/10.1177/00222194050380040901

Blöte, A. W., Klein, A. S., & Beishuizen, M. (2000). Mental computation and conceptual understanding. Learning and Instruction, 10 (3), 221–247. https://doi.org/10.1016/S0959-4752(99)00028-6

Boaler, J., & Greeno, J. G. (2000). Identity, agency, and knowing in mathematical worlds. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 45–82). Ablex.

Chapin, S. H., O’Connor, C., & Anderson, N. C. (2013). Talk moves: A teacher’s guide for using classroom discussions in math . Math Solutions.

Cobb, P., & Merkel, G. (1989). Thinking strategies: Teaching arithmetic through problem solving. In P. Trafton & A. Shulte (Eds.), New directions for elementary school mathematics (pp. 70–81). National Council of Teachers of Mathematics.

Cobb, P., Gresalfi, M., & Hodge, L. L. (2009). An interpretive scheme for analyzing the identities that students develop in mathematics classrooms. Journal for Research in Mathematics Education, 40 (1), 40–68. https://doi.org/10.4324/9780203879276

Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Retrieved from http://www.corestandards.org

Dubbels, B. (2011). Cognitive ethnography: A methodology for measure and analysis of learning for game studies. International Journal of Gaming and Computer-Mediated Simulations, 3 (1), 68–78. https://doi.org/10.4018/jgcms.2011010105

Engle, R. A., & Greeno, J. G. (2003, April). Framing interactions to foster productive learning. Paper presented at the annual meeting of the American Educational Research Association.

Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. The Journal of Special Education, 33 (1), 18–28. https://doi.org/10.1177/002246699903300102

Gerstenschlager, N. E., & Strayer, J. F. (2019). Number talks for statistics and probability. Mathematics Teaching in the Middle School, 24 (6), 363–368. https://doi.org/10.5951/mathteacmiddscho.24.6.0362

Greeno, J. G. (1998). The situativity of knowing, learning, and research. American Psychologist, 53 (1), 5–26. https://doi.org/10.1037/0003-066X.53.1.5

Greeno, J. G. (2006). Learning in activity. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 79–96). Cambridge University Press.

Hammerness, K. (2001). Teachers’ visions: The role of personal ideals in school reform. Journal of Educational Change, 2 , 143–163. https://doi.org/10.1023/A:1017961615264

Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Oliver, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25 (12), 13–21. https://doi.org/10.3102/0013189X025004012

Horn, I. S. (2010). Teaching replays, teaching rehearsals, and re-visions of practice: Learning from colleagues in a mathematics teacher community. Teachers College Record, 112 (1), 225–259. https://doi.org/10.1177/016146811011200109

Humphreys, C., & Parker, R. (2015). Making number talks matter: Developing mathematical practices and deepening understanding, grades 4–10 . Stenhouse Publishers.

Hutchins, E. (1995). Cognition in the wild . MIT Press.

Jackson, K. (2009). The social construction of youth and mathematics: The case of a fifth-grade classroom. In D. B. Martin (Ed.), Mathematics teaching, learning, and liberation in the lives of Black children (pp. 175–199). Routledge.

Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. The Elementary School Journal, 102 (1), 59–80. https://doi.org/10.1086/499693

Lannin, J., Ellis, A. B., & Elliot, R. (2011). Developing essential understanding of mathematics reasoning for teaching mathematics in prekindergarten-grade 8 . National Council of Techers of Mathematics.

Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life . Cambridge University Press. https://doi.org/10.1017/CBO9780511609268

Book   Google Scholar  

Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation . Cambridge University Press.

Martin, D. B. (2009). In my opinion: Does race matter? Teaching Children Mathematics, 16 (3), 134–139. https://doi.org/10.5951/TCM.16.3.0134

Munter, C. (2014). Developing visions of high-quality mathematics instruction. Journal for Research in Mathematics Education in Mathematics Education, 45 (5), 584–635. https://doi.org/10.5951/jresematheduc.45.5.0584

Nathan, M. J., & Knuth, E. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and Instruction, 21 (2), 175–207. https://doi.org/10.1207/S1532690XCI2102_03

National Research Council. (1987). Education and learning to think . The National Academies Press. https://doi.org/10.17226/1032

National Research Council. (2001). Adding it up: Helping children learn mathematics . The National Academies Press. https://doi.org/10.17226/9822

Parker, R., & Humphreys, C. (2018). Digging deeper: Making number talks matter even more, grades 3–10 . Stenhouse Publishers.

Parrish, S. (2010/2014). Number talks: Helping children build mental math and computation strategies . Math Solutions.

Parrish, S. D. (2011). Number talks build numerical reasoning. Teaching Children Mathematics, 18 (3), 198–206.

Parrish, S., & Dominick, A. (2016). Number talks: Fractions, decimals, and percentages . Math Solutions. https://doi.org/10.5951/teacchilmath.18.3.0198

Reys, R. E. (1984). Mental computation and estimation: Past, present, and future. The Elementary School Journal, 84 (5), 546–557. https://doi.org/10.1086/461383

Reys, R. E., Reys, B. J., Nohda, N., & Emori, H. (1995). Mental computation performance and strategy use of Japanese students in grades 2, 4, 6, and 8. Journal for Research in Mathematics Education, 26 (4), 304–326. https://doi.org/10.2307/749477

Russell, S. J. (1999). Mathematical reasoning in the elementary grades. In L. V. Stiff (Ed.), Developing mathematical reasoning in grades K-12, 1999 yearbook of the national council of teachers of mathematics (pp. 1–12). National Council of Teachers of Mathematics.

Sowder, J. T. (1988). Making sense of numbers in school mathematics. In G. Leinhardt, R. Putman, & R. Hattrup (Eds.), Analysis of arithmetic for mathematics . Erlbaum.

Sowder, J. T. (1992). Making sense of numbers in school mathematics. In G. Leinhardt, R. Putman, & R. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 1–51). Lawrence Erlbaum Associates.

Sriraman, B., & Umland, K. (2014). Argumentation in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education . Springer. https://doi.org/10.1007/978-94-007-4978-8_11

Chapter   Google Scholar  

Staples, M., & Newton, J. (2016). Teachers’ contextualization of argumentation in the mathematics classroom. Theory Into Practice, 55 (4), 294–301. https://doi.org/10.1080/00405841.2016.1208070

Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10 (4), 313–340. https://doi.org/10.1080/10986060802229675

Sun, K. L., Baldinger, E. E., Humphreys, C., Sun, K. L., & Erin, E. (2018). Number talks: Gateway to sense making. The Mathematics Teacher, 112 (1), 48–54. https://doi.org/10.5951/mathteacher.112.1.0048

Torbeyns, J., & Verschaffel, L. (2016). Mental computation or standard algorithm? Children’s strategy choices on multi-digit subtractions. European Journal of Psychology of Education, 31 (2), 99–116. https://doi.org/10.1007/s10212-015-0255-8

Trafton, P. (1978). Estimation and mental computation: Important components of computation. In M. Suydam & R. E. Reys (Eds.), Developing computational skills (1978 NCTM yearbook of the national council of teachers of mathematics) (pp. 196–213). NCTM.

Wenger, E. (1998). Communities of practice: Learning, meaning, and identity . Cambridge University Press.

Wood, T., & Turner-Vorbeck, T. (2001). Extending the conception of mathematics teaching. In T. Wood, B. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 185–208). Lawrence Erlbaum Associate.

Wood, T., Williams, G., & McNeal, B. (2006). Children’s mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37 (3), 222–255. 30035059

Woods, D. (2018). Developing ambitious mathematics instruction through number talks . ProQuest Dissertations Publishing, 2018. Print.

Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27 (4), 458–477. https://doi.org/10.5951/jresematheduc.27.4.0458

Download references

Author information

Authors and affiliations.

Oakland University, Rochester, MI, USA

Dawn M. Woods

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Dawn M. Woods .

Editor information

Editors and affiliations.

Department of Psychology, Campion College at the University of Regina, Regina, SK, Canada

Katherine M. Robinson

Faculty of Education, University of Western Ontario, London, ON, Canada

Donna Kotsopoulos

Department of Educational & Counselling Psychology, McGill University, Montreal, QC, Canada

Adam K. Dubé

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Woods, D.M. (2023). How Number Talks Assist Students in Becoming Doers of Mathematics. In: Robinson, K.M., Kotsopoulos, D., Dubé, A.K. (eds) Mathematical Teaching and Learning. Springer, Cham. https://doi.org/10.1007/978-3-031-31848-1_8

Download citation

DOI : https://doi.org/10.1007/978-3-031-31848-1_8

Published : 16 June 2023

Publisher Name : Springer, Cham

Print ISBN : 978-3-031-31847-4

Online ISBN : 978-3-031-31848-1

eBook Packages : Education Education (R0)

Share this chapter

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

• Skip to content
• Skip to search
• Staff portal (Inside the department)
• Student portal
• Key links for students

Other users

• Forgot password

Notifications

{{item.title}}, my essentials, ask for help, contact edconnect, directory a to z, how to guides, mathematics k–12, using number talks and number sense routines across k–6.

Deepen your knowledge about number talks. Discover the difference between a number talk, a dot card talk and a routine like ‘Which one doesn’t belong’? Learn more about what makes teaching routines effective so you can refine your practice.

Research evidence indicates that providing opportunities for students to share and justify their mathematical ideas and respond productively to the ideas of others, helps them to see themselves as, and to become, competent mathematicians (Kazemi & Hintz, 2014; Smith & Stein, 2011).

Using Number Talks and Number Sense Routines across K-6 is a NESA-accredited opportunity that delves into how different teaching routines in mathematics can be used well to support student learning. This course is designed to build upon and enrich existing teacher knowledge of various teaching routines of mathematics. 

Who this course is for

Participants may complete this professional learning individually or together as a team. Participants could include:

• any teacher or leader interested in enhancing their understanding of some important big ideas in mathematics across K-6
• Assistant Principals, Curriculum and Instruction (AP, C&Is)
• specialist support teachers
• graduate teachers with a specialisation in mathematics
• Stage 4 teachers and leaders focussed on supporting the transition between Stage 3 and Stage 4.

Learning as a school team

Learning together is usually more impactful than learning alone, however, it’s not always possible for schools. Participants can be:

individual teachers who want to learn more about number talks and number sense routines

small teams from within a school

Assistant Principals, Curriculum and Instruction, Deputy Principals and Principals participating in the learning alongside teachers

whole school teams who learnt together, who may choose to use professional learning meetings and staff development days as time to come together to refine, affirm and deepen their understanding

teachers at different schools forming communities of learners, to participate together and share what they’re doing in their classrooms as a result.

What you will learn about

This professional learning opportunity aims to:

deepen teacher understanding in what makes a number talk a number talk

investigate other number sense routines that can be used to support student understanding in maths

explore how number talks and other number sense routines can be used in classrooms across K-6 and beyond

deepen understanding around dialogic practices in mathematics

support knowledge for teachers across the horizon of learning from K-6 and beyond.

Curriculum Reform and syllabus implementation

The NSW Curriculum Review identified the importance of teaching and learning focused on developing students’ deep understandings of important concepts and strategies (NESA, 2021)​. Number talks and other number sense routines have been shown to be powerful teaching routines we can use to achieve that goal. Additionally, this course offers school communities the opportunity to explore these routines which help promote reasoning, a proficiency which lies at the heart of the NSW Mathematics syllabuses and the Curriculum Reform agenda.

Course commitments

‘Becoming Mathematicians: Using Number Talks and Number Sense Routines across K-6 is registered with NESA, recognising 7.5 hours of accredited professional learning. It is available online through Open Learning which teachers across NSW can access as best suits them. The course involves:

five self-paced course modules (approximately 90-120 minutes each)

opportunities to play with mathematics and discuss, reflect and respond to ideas throughout each module.

Release dates

Participants may like to access this learning:

over a few days

by exploring a few of modules as part of a professional learning day.

Registration for Becoming Mathematicians: Using Number Talks & Number Sense Routines across K-6 is open for NSW Department of Education teachers and school leaders.

You will need to consider the time commitment and discuss this learning opportunity with your principal and get their approval to participate. There is no cost associated with this professional learning. However, if casual relief is used, that will need to be covered by the school.

Each person taking part in the learning must register. You can complete the registration individually or one colleague can register each participant in your school team. Allow up to 2 weeks to receive an email with access information for the professional learning.

Register now

If you are in a non-school based teaching (NSBT) role, please register using the K-6 Mathematics Professional Learning – NSBT form .

Contact the  NSW Mathematics Professional Learning team for further information.

• Early Stage 1

Business Unit:

• Educational Standards

Number Talks

• Number Talks Project – Washington
• Upcoming Events
• Number Talks Online Mini-Sessions
• Number Talks Institutes and Online Series
• Number Talks and Multilingual Learners
• Ratio & Proportional Reasoning
• Rational Numbers
• Expressions and Equations
• Probability: A Study of Chance
• Reasoning About Data
• Patterns I: Foundations for Algebraic Reasoning
• Patterns II: Foundations for Algebraic Reasoning
• Numerical Reasoning
• Geometry & Proportional Reasoning
• Extending Algebraic Reasoning
• Studio Days
• Community Math Nights
• Community Math Night Leadership Workshops
• Model Components
• Higher Education-MEC Partnerships
• Math Games for Learning
• Helping with Homework
• Parents as Questioners
• Math Websites
• Number Talks Books
• How to Work with Parents and the Public
• Mathematical Power: Lessons from a Classroom
• Alternative Procedures & Algorithms
• Mathematically Powerful Students
• Two Mathematics Cultures
• Instructional Practice: Focused Survey
• Websites and Resources
• MEC Principles of Design
• Instructional Approach
• PD Approach
• Board of Directors
• Ruth Parker
• Patty Lofgren
• Debbie Olson
• Instructors
• Support Team
• Development Collaborators

Math is a problem solving venture that requires critical thinking not steps and procedures. Number Talks start the journey toward that realization. 3-8 Instructional Coach, OH

This feels necessary, powerful and possible! 4th Grade Teacher, WA

Number Talks For Multilingual Learners A new professional learning opportunity 

Find  Number Talks events  near you 

Learn about MEC’s 2-day Number Talk Institute  

Read what teachers are saying about Number Talks 

Schedule a Number Talk Institute in your area

Order one or more of our Number Talks books  

“After attending the Number Talk Institute with Ruth Parker, I knew I needed to bring Number Talks back to the teachers and students at my school. One of the components that stood out to me the most from this institute was the ability Ruth had to make the teachers feel comfortable and safe in exploring new strategies. Creating this safe atmosphere allowed us to think through the problems without the fear of being put on the spot. As much as I appreciated this as an adult learner, it became clear we need to provide our students with this comfort as well. Collaborating with teachers to implement Number Talks in their classrooms, I was amazed to watch students take strides in not only their ability to think about numbers and operations but in communicating their thinking as well. When given the opportunity to share on their own terms, students were eager to explain their strategies and learn from each other. As we begin year two of Number Talks in our school, I look forward to seeing the impact it makes on these young mathematicians.” Hailey Gilmore, LAP Teacher/Instructional Specialist, Lacey, WA, Fall 2016

We hadn’t met these 3rd graders before videotaping the Number Talk in April, 2016. This Number Talk was filmed first thing in the morning, and this was the first time these 3rd graders had ever been videoed. Thank you Hailey for the gift of sharing your practice with us. We hope it will provoke interesting conversations!

Please share your comments and questions about this video and about Number Talks using our contact form . We look forward to hearing from you!

Number Talks are a 10-15 minute mental math routine created by Ruth Parker and Kathy Richardson in the early 1990s to engage students in meaningful mathematical discourse and sense-making as well as transform the culture of the classroom to one of inquiry and curiosity. Cathy Humphreys has been instrumental in extending and studying their use at the secondary level.

In 2015, Ruth and Cathy wrote  Making Number Talks Matter to support teachers interested in learning more about this powerful instructional routine. In 2018, they wrote the companion book, Digging Deeper: Making Number Talks Matter Even More . In addition, MEC has developed a 2-day Number Talks Institute and 7-session Number Talks Online Series to bring Number Talks directly to teachers.

Now, educators all around the world are experiencing first-hand the power of Number Talks to empower students to make sense of mathematics and build a solid base of understanding that allows them to be flexible and creative mathematical thinkers at all levels of study!

Copyright © 2024 MEC | Mathematics Education Collaborative. Need Help? Contact our support team.

Remember Me

Number Talk

This short but powerful activity develops students’ number sense and flexibility with numbers, while also honoring the creativity in the different ways people see math.

Planning For It

When you might use this practice.

• At the start of a new year, to establish the value of the many ways we see mathematics
• Throughout the school year, as often as 5-10 minutes each day, to create a productive climate of equitable group work and build a growth mindset culture for students around mathematics class

Time Required

• ≤ 30 minutes
• Chalkboard or whiteboard

Learning Objectives

Students will:

• Practice calculating without paper and pencil
• Increase their flexibility with numbers
• Honor the fact that we all see math differently and that these differences are interesting and should be respected
• Develop a growth mindset toward mathematics

Additional Supports

• Making Practices Culturally Responsive
• Adapting Practices for Students with Special Needs
• Making Classrooms and Schools Trauma-Informed and Healing-Centered

SEL Competencies

• Self-Awareness
• Social Awareness
• Relationship Skills

How To Do It

Reflection before the practice.

• Watch mathematics teacher and author Cathy Humphreys demonstrating a number talk , considering different ways to approach the problem from a number sense standpoint.
• How will you react if/when students make mistakes? Are you prepared to welcome all mistakes as valuable learning opportunities? (Here is an example of a student making a mistake during a number talk at youcubed summer camp.)

Instructions

Note: Practice 3 of 5 in youcubed Mathematical Mindset practice collection.

To the Teacher

Number talks honor the fact that we all see math differently and that these differences are interesting and should be respected. Number talks also help students learn flexibility with numbers and how to calculate without paper and pencil.

With number talks, students have a chance to think through their understanding of numbers and explain their reasoning. In the number talks we did with our students , they had a chance to think about multiplication problems. The problems allowed for students to think flexibly about multiplication and develop number sense through their reasoning and the reasoning of their classmates.

We love when there is more than one answer because making and discussing mistakes lead to much more learning, and it also allows us space to give mindset messages about mistakes. When we did the 12×15 number talk, there was a student who got 168, and as she was explaining her thinking, she stopped and said, “Oh, wait! I made a mistake.” Jo’s response was, “That’s great! That means you have synapses firing in your brain because you made that mistake.” Jo then invited her to explain her thinking when she made the mistake so that the class could understand what she did (see video here ). This was an important moment because the student who was sharing, and the rest of the class, saw that her thinking was respected and her mistake was celebrated.

Remember to value mistakes and say things like “This is great we have three different answers; we will have a really good discussion.”

Launch (2-5 minutes)

• Introduce students to the purpose of the number talk. Explain that students will see a number problem and be asked to determine the answer without paper or pencil. They will be asked to share their answers and to describe how they completed the calculation.

Explore (2-5 minutes)

• Show a number problem, e.g., 17 x 15. You may also choose to start with a two-digit number multiplied by a one-digit number like 21 x 3. (The first is appropriate for middle school or higher, the second might be used for elementary). Ask students to solve the problem using as many strategies as they can think of without using pencil and paper.
• This is a better way of signaling to you than raising their hand. Hands shooting up can be intimidating and/or distracting to other students.
• If there are multiple answers, put all of them on the board and do not identify the correct answer or label any answer as incorrect. The purpose of the number talk discussion is for students to share and justify their answers. Students will oftentimes identify and correct mistakes on their own during the discussion.

Discuss (8+ minutes)

• Start by inviting students to share strategies by saying something like, “Who would like to justify their answer?” If there are different answers ask, “Who would like to defend one of these answers by sharing how you found it?”
• Capturing a student’s method can be challenging. Make sure to ask clarifying questions if you do not understand. Number talks are about communication. It is a good time to model how to interact when you do not understand what is being said. This is a great time for students to see you struggle and work to understand what is being shared. This is important modeling and it is also the reason we do not ask students to come to the board to share their thinking.
• If students are challenged with finding or sharing methods, it is OK to introduce a method and share it with them. We recommend you do this by saying the method you are sharing is one you got from another student. This is an important message for them and a time when they should not see you as the expert in the classroom. By sharing a method created by another student you maintain the culture that you are a community of math learners.
• Record students’ work horizontally rather than the traditional vertical method that students are taught. This will help students make sense of the numbers rather than working from the traditional algorithm. If a student says they used the traditional algorithm, ask the student to describe what they saw and record accurately. Then ask for other strategies.
• It is also important to create visuals for student strategies. Choose a strategy and model how to draw a visual representation for the numerical calculations. Using color is helpful when creating visuals for student strategies. After creating a visual, ask students to choose a different strategy and create a visual that represents the calculation. (See PDF for examples of recorded student strategies to the problem 18 x 5.)
• Is it like this? (Referring to a part of your representation)
• Is this what you saw?
• Is it a little bit like this other one? What was different about it?
• What did you do after that?
• Maybe we could draw this one out because that would be helpful. Does this look like what you did?
• Do you feel like this represents your thinking?
• A main goal during number talks is to get as many students sharing as many strategies as possible. One of the things we do to encourage more students to share is to invite more strategies by asking, “Did anyone do it differently?” “Did anyone see it differently?”
• Ask students to sketch the visual for a strategy.
• Ask students to solve a new problem using one of the strategies shared.
• How are students engaging with mistakes? Multiple answers in number talks are an opportunity to honor and discuss mistakes. It is important to make sure that you keep your responses to right and wrong answers the same. When students recognize their teacher’s reactions and can connect them to right and wrong answers, they become fearful of their ideas being respected and will stop sharing.
• How are students taking numbers apart and putting them together? There are many ways to create equivalent expressions by composing and decomposing numbers. This is called number flexibility and it is very important for number sense and algebra. The more students experience number flexibility the more creative, confident, and fluent they will become. When you start number talks for the first time, you might notice students not sharing a variety of strategies and not breaking apart numbers beyond making 10s. This is likely connected to an absence of number flexibility. When students see different ways to compose and decompose numbers when doing a calculation, they often say, “We thought that wasn’t allowed.” Understanding that numbers represent quantities that can be redistributed and arranged is one of the reasons we love number talks.
• Which students are sharing strategies? While the number talk problem itself is often a simple looking arithmetic problem, there are many ways of solving the problem. Like most activities, some students participate vocally and others do not. This is not the kind of activity in which every student needs to share. There are many ways to think about engaging students who do not offer strategies. You might invite them to use one of the strategies shared on a new problem, create a visual for a strategy, or complete a reflection in their journal.

Reflect (5 minutes)

• Acknowledge the group for honoring all approaches to the problem as well as accepting and learning from mistakes.
• Ask students to reflect on their experience in their journal with a prompt like, “What is something you learned you could do with numbers that you did not know before?”

This is a practice developed by prominent practitioners including Sherry Parrish, Ruth Parker, and Cathy Humphreys. It is recommended by Jo Boaler and featured on the website of youcubed , a center at Stanford University that she leads. In addition to classroom ideas and videos, youcubed offers a variety of resources for mathematics educators, including research summaries and professional development.

Reflection After the Practice

• Did this exercise invite more open thinking by students as well as more acceptance of mistakes by peers?
• Did any of the students’ strategies surprise you? Do you feel any change in your own openness towards different ways of approaching math problems?
• How can you leverage this concept, accepting multiple approaches to math problems and promoting number sense as you teach math?
• Did you make any adjustments in the way you react to students’ mistakes? How can you continue to promote a growth mindset in math?

The Research Behind It

Evidence that it works.

Research has shown that students who learned about growth mindset with regards to mathematics reported more positive beliefs about math, were more engaged in math class, and did better on standardized math achievement tests. Mindset interventions in math benefit all students, but have demonstrated even more power for groups that may be more affected by myths about math learning, including girls, English language learners, and economically disadvantaged students.

In addition, a four-year study of high school students in different types of math classes showed that the students who learned math in mixed-ability classrooms that emphasized cooperative group work, open problem-solving, and the use of multiple strategies–compared to those in traditional math classrooms, which were often ability-grouped and focused on teacher lectures and individual work–demonstrated greater gains in math achievement and greater reductions in achievement gaps, enjoyed math more, and treated each other with more respect, support, and equity .

Why Does It Matter?

A substantial body of research has indicated that students who have a growth mindset about intelligence–who believe that, with effort, intelligence can be changed over time–are more likely to do well academically .

Importantly, evidence shows that growth mindset can be learned : in a nationally representative study, students who were taught about a growth mindset of intelligence went on to earn better grades (especially if they started out lower-achieving) and select more challenging classes. Grades improved even more in schools with more supportive learning climates, in which peer norms supported the growth mindset message.

Though much of the research on growth mindset has to do with beliefs about intelligence, other research suggests that social and emotional growth mindsets (e.g., believing that personality, emotions, etc., can grow and change) can reduce bias and promote well-being , social competence , and prosocial behavior .

GGIE Online Courses for Educators

Do you want to dive deeper into the science behind our GGIE practices? Enroll in one of our online courses for educators!

Number Talks

Want to help students to build computational fluency, important reasoning skills, and confidence in mathematics? Number talks are the way to go! Check out the resources below to see how and why.

Meredith's Must-Know Info

I love Number Talks. When I start working with schools, Number Talks are what I usually recommend we explore first because they are bite-size and easy to implement, yet they give students so much bang for their mathematical buck. They are a great entry point for teachers to practice facilitating productive mathematical discourse (engaging students in communicating math ideas) and for students to learn the ropes of talking about math. Number Talks are also a key tool in boosting the mathematical mindsets of your students because the framework of a number talk gives students a safe platform to take math risks and feel valued for their ideas. Here are some important things to understand about Number Talks and why you should start implementing them right away.

What is a number talk?

A Number Talk is a short number sense routine (5 -15 minutes long) through which students practice mental computation. During a number talk, teachers present carefully chosen sequences of computation expressions or equations and students communicate their thinking about the answers through reasoning and justification.

What are the goals of a number talk?

• Building computational fluency (flexibility, accuracy, and efficiency).
• Boosting mathematical mindset and confidence.
• Increasing student abilities to reason and justify.

What are the protocols that I should implement for an effective number talk?

• Have students sit in a circle. This sends an important message that all ideas are equally valued and moves emphasis towards the collective conversation and away from a back and forth discussion with the teacher at the center. It’s also a great management tool for inviting participation… students can’t hide behind other students or desks, negative behaviors are less likely because students are physically open to each other, and if negative behaviors do occur, the teacher can get to the student quickly and subtly for redirection (without tripping on anyone else!).
• Use the quiet thumb. Establishing a signal like a thumb in front of your chest to indicate you are ready with an idea is an important characteristic of a number talk. This private signal helps students to not feel rushed. Sometimes seeing that someone else’s hand is waving in the air is an invitation to stop thinking. “So-and-so has the answer. I don’t need to try anymore.” It also sends a dangerous message that speed is what makes a “good” mathematician, a message we do not want to send! Plus, this is a tool for keeping students engaged who figure out an answer and are waiting for others to have time to think… “Show me two fingers if you’ve figured out another way to solve. Show me three fingers if you can find three ways!”
• Use wait time. Make sure all of your students have ample time to think privately before inviting answers. This will boost participation and help all learners feel they have access to the conversation.
• Value mistakes It’s important that mistakes are accepted and discussed as part of what it means to be a mathematician. Setting up protocols for revising ideas together on a different day, modeling the importance of making mistakes as a learning process, and honoring what IS RIGHT in an idea that is not yet fully formed, are all important in building growth mindsets and ensuring that everyone feels welcome and capable of contribute ideas.
• Record student names next to ideas One key feature of a number talk is that the mathematical ideas are recorded by the teacher as students present them. This helps to make visible that mathematics is about creativity and multiple approaches. When we record the student’s name next to each offered idea, we can further send the message that all ideas are valued and welcomed. (And yes, it’s ok to record an incorrect idea. That leaves record for later revision, emphasizes that ideas can grow and change, and provides formative assessment data for you.)

How do I choose sequences to present?

Being intentional about the computation and visual sequences that we present students in a number talk is really important in helping students to make mathematical connections. Lucky for us, a lot of the work in choosing sequences has already been done for us. See the links in my lesson resources for places to start with choosing appropriate sequences.

Jo Boaler Why Number Talks

Jo Boaler, founder of YouCubed.org and mathematical mindset pioneer, offers reasons for why number talks are very important in every math class, across the grades.

Jo Boaler Teaching A Dot Card Number Talk

Another one from Jo Boaler: This is a classroom demonstration of a dot image number talk with a group of middle school girls. This example shows that dot image number talks can be done appropriately with K-12 students (or even adults!) and shows how visual number talks are a great place to start number talks with any class.

Lesson Support

NumberStrings.com

This website gives examples of number strings to use by grade level, accompanied by helpful blog descriptions of classes engaging in the presenting strings. Lots of great resources here.

FractionNumberTalks.com

Nat Banting is a genius and one of my new heroes. He has brilliantly taken the protocols of Number Talks and adapted them to images of fractions that invite students to explore, reason, and engage in dialogue around deep conceptual ideas about fractions. This one is a keeper.

Additional Research

Number talks build numerical reasoning.

Sherry Parrish, who wrote the book that helped start the number talk revolution, wrote this article that outlines five key components of effective number talks: classroom environment and community, classroom discussion, teacher's role, the role of mental math, and purposeful computation problems.

Fluency Without Fear

From the first time I read this article, the way I thought about fluency was forever changed. Though Jo Boaler engages us in thinking about brain research around fluency development, she does so in a way that's easy to understand and is accompanied by clear classroom practices to boost fluency. Number talks are her number one suggestion... check this one out.

Number Talks

Number Talks were created by Kathy Richardson and Ruth Parker in the early 1990s to engage students in meaningful mathematical discourse and sense-making as well as transform the culture of the classroom to one of inquiry and curiosity.

Number Talks in the Primary Classroom  by Kathy Richardson and Sue Dolphin, provides all the information teachers need to present powerful Number Talks that ensure ALL children succeed in building number sense and computational fluency. Teachers will see how to make Number Talks purposeful based on how children learn number concepts and the mathematics their students know so far. An abundance of ways to use models to help children see the mathematics they are learning will keep every child engaged, eager, and learning.

What is a Number Talk?

Number Talks are an approach to developing facility with computation that engages  children in thinking  about numbers and allows them to add, subtract, multiply and divide using the mathematics that is meaningful  to them, rather than following procedures that are not.

Read more about Number Talks and find resources here .

Number Talks in the Pre-Kindergarten Classroom  by Kathy Richardson and Sue Dolphin, shows teachers how to bring meaning to the math for their students, how to engage them in thinking, and it presents the kinds of models, problems, and questions that are needed to support learning.

Number Talks is a valuable 3-5 minute routine where the teacher is interested in how the children think, and interacts with children in ways that let them show the teacher what they know so far and what insights they are developing over time.

Order your copy of Number Talks in the Pre-Kindergarten Classroom

Number Talks in the Primary Classroom  by Kathy Richardson and Sue Dolphin, identifies the mathematics that children must learn, describes the stages that children naturally move through on their way to proficiency and shows teachers how to use models, questions, and experiences to support children’s development of mathematical understanding. This book comes out of the author’s combined experiences doing Number Talks for more than 30 years.

Order your copy of Number Talks in the Primary Classroom

Blacklines for Number Talks Cards to accompany these books can be found here .

Schedule a Number Talks Course in your District

To schedule a Number Talks: Thinking With Numbers K-2 or 3-6 course in your district, contact us at (360) 715-2782 or email Sheryl Russell at [email protected] .

Number Talks

Description

• Author: Dan
• Posted: Fri, November 20, 2015, last modified October 12, 2022
• Topics: Common Core Math Practices
• Grades: 1 , 2 , 3 , 4 , 5 , 6 , K , Pre K
• Keywords: Mental Math Games

About This Lesson

Topics: Mental math, numerical fluency; argument & critique Materials: White board or projector Time: 5 – 15 minutes Common Core: Variable, but especially MP3

This mental math routine creates powerful positive habits for students.

Why We Love Number Talks

Number talks don’t replace other instruction, but they are a powerful complement to it. They get all students involved, help them strengthen fluency, intuition, and mental math strategies, improve students’ ability to explain and critique solutions, and allow teachers a valuable window into their students’ thinking. A well-run number talk is an excellent example of Common Core Math Practices 1, 2, 3, 6, 7, and 8.

How Number Talks Work

If you implement one type of activity into your class routine, Number Talks might be the most bang for your buck. In many ways, they’re familiar. The teacher writes a simple problem down on the board, and students solve it mentally. The difference is that the students aren’t just looking for the answer: they’re trying to find as many different ways to solve the problem as they can. The key elements to number talks are a de-emphasis on speed and right answers and an added emphasis on process and communication. Here’s how they work:

• The teacher writes a problem on the board. It can be as simple (like 9 + 17) or complex (500 ÷ 24) as long as it is appropriate as a mental math problem for the class.
• Students mentally solve the problem. They show the teacher whether they have the answer by (quietly) giving a thumbs up at their chest. This prevents a small batch of quick students from shutting everyone else down. If students can come up with a second way to solve the problem, they hold up a second finger at their chest. This means that everyone can keep thinking about the problem even after they have the answer.
• Students share their answers. After enough time has passed that everyone or nearly everyone has a solution, the teacher asks students what their solution are. She writes down all solutions; none are given preferential treatment, and she doesn’t say whether they are right or wrong.
• Students explain their thinking. Once all solutions are written down, the teacher asks students to explain how they got their solution. Students explain (from their seat) while the teacher writes the steps they describe on the board.
• Discussion and consensus. Ideally, by the end of the discussion, the class should have a list of 3-6 different approaches to the problem, plus a consensus as to what the correct answer is.
• Followup. The teacher then has the option to ask a followup questions that builds on the last. (If 9 + 17 was the first question, 9 + 27 or 19 + 17 might be good followups.)

Example Number Talk

Teacher: Time for our morning Number Talk. Everyone consider this question. (She writes 9 + 17 on the board). (A student starts waving his arm in the air.) When you have the answer, show me with a thumb at your chest. (The student puts his arm down and holds up a thumb.) If you get more answers, show me by holding up more fingers. (She waits for 30 seconds. Several students are holding up multiple fingers, though many have just a thumb. The teacher is noting to see if anyone hasn’t solved the problem—this is a great opportunity for formative assessment. Finally, she begins calling on students for their answers, starting with those who have only one solution.)

Teacher: Lucy? Lucy: 26. (Teacher writes 26 on the board.)

Teacher: Charles? Charles: 107 (Teacher writes 107 on the board.)

Teacher: Michelle? Michelle: 25. (Teacher writes 25 on the board.)

Teacher: Any other answers? (No one has any.) Who would like to explain how they got their answer? Tyrone? (The teacher records what the students write as they explain.)

Tyrone: I know that 9 + 7 is 16, and then I added another 10 to get 26. Sarah: 10 + 17 is 27, and 10 is 1 more than 9, so 9 + 17 must be 26. Charles: 9 + 1 is 10, and then you put a 7 after, so it’s 107. Lucy: I counted one by one, but I just realized that I miscounted. I agree with 26 (Teacher crosses out 25 and replaces it with 26.) Sam: I respectfully disagree with Charles. You can’t add the 9 + 1 because the 1 stands for 10. Charles: But that’s how you add. I did it right. (Teacher lets conversation continue until class consensus, or near-consensus, is reached. Meanwhile, she’s noting where students are in their understanding of place value and addition.)

Tips for the Classroom

• Start with easy questions that are accessible to everyone.
• Students will be looking to see if you indicate what the right answer is. Don’t favor right answers over wrong ones. Make sure that the explanations are what matters.
• Taking a few minutes ahead of time to plan out a sequence of questions can be helpful. (i.e., I’ll start with 9 + 7, since everyone can do that, then we’ll do 9 + 17, then 19 + 17.)
• Make sure you emphasize the Number Talk protocol—hands at chests rather than waving in the air, for example. This will pay off, and you can use it in other places.
• Give students constructive language to use in the discussion, like, “I respectfully disagree, because…” and “I agree with _____, because…”
• Always keep the environment safe and positive.
• Don’t worry if you don’t reach total consensus on every problem. Sometimes a student will need more time to process. You can move on when it feels like it is time.
• Number Talks can sprawl if you’re not careful. Doing short (5 minute) Number Talks regularly is more powerful than long ones infrequently.

Number Talks by Grade Level

• Number Talks for Kindergarten
• Number Talks for 1st & 2nd Grade
• Number Talks for 3rd & 4th Grade

Other Resources

http://onceuponateachingblog.blogspot.com/2011/06/number-talks.html

More ideas are at http://www.cobbk12.org/bullard/NumberTalksK-2.pdf and http://www.mathperspectives.com/num_talks.html

Join Our Mailing List

Get tons of free content, like our Games to Play at Home packet, puzzles, lessons, and more!

When I think back over my memories of mathematics in school one of the most prevalent was of sitting in grade six class frantically trying to complete a worksheet full of arithmetic questions while the teacher timed us to see how many we could complete in the given time. I still remember that feeling of panic as I tried my hardest to get through those questions. To say it was traumatic may be overstretching but given what we know today about maths anxiety or as Stanford University Professor Jo Boaler puts it ‘maths trauma’, I am safe in saying that it definitely helped shape my relationship with maths for years to come.

Thankfully today, that focus on rote memorisation is, or should be, a thing of the past. What many mathematics educators know about maths learning is that it can no longer be looked at as a set of rules and procedures to be memorised, but rather a system of meaningful relationships to be investigated and explored.

Luckily for me, I also had some amazing maths teachers and lecturers who both encouraged and fostered my love of the subject in later years. Sadly however, for many kids and adults, this type of rule based learning and memorisation has caused long term damage and has played a large role in creating maths anxious and disaffected maths learners (Boaler, 2015).

Developing ‘Number Sense’

The good news is however, that there are ways that we as educators can help our students by building in them something called Number Sense .

Number sense is a relatively new term in maths education. It refers to the ability for students to work flexibly and conceptually with numbers. Research has shown that students who experience the greatest success in maths generally have a deeper, more intuitive understanding of numbers and how they relate to each other. They are able to view them conceptually and have developed strategies to adapt them to solve various situations. Simply put, they have good number sense.

Number sense is referred to in a range of mathematics literature. Books such as Number Sense Routines by Jessica F. Shumway and Jo Boaler’s Mathematical Mindsets talk extensively about how developing a strong ability to work flexibly with number is crucial in maintaining a deeper connection with maths concepts in later years. However, if I was to choose one book that encompasses this idea of developing strong number sense it would have to be Sherry Parrish’s Number Talks .

According to Parrish (2010), “Number talks are short ongoing daily routines that provide students with meaningful practice in mental computation”. They are designed to be introduced as both short, 5 – 15 minute warm ups at the beginning of a lesson or as stand-alone sessions that are used to extend and engage students in arithmetic strategies. Number talks are intended to encourage the development of students’ mental maths skills , an important facility for the reduction of the cognitive load when tackling heavy maths problems. During a number talk, students are encourage to justify their thinking while communicating the solutions to the problems solved mentally.

Here’s how a number talk works

• Students sit either on the floor or at their tables generally facing the front of the room.
• There is no calling out or hands up during a number talk. Instead, students make a fist and place it on the front of their chest.
• As the teacher, you present them with a question. You can say something like “Today we will be discussing the solution to 16 x 25”.
• Give the students time to come up with an answer and to think of a way to communicate the solution to the class.
• When students have a solution to the question they put a thumb up. This allows you, the teacher, to see who has an answer and who has not. The aim of the thumbs up instead of hands up concept is to give everyone an opportunity to solve the problem in their own time without the distraction of who has solved it the fastest.
• While they are waiting, encourage the students to find more than one way to get to the result. Once they have discovered another way they can now also put a finger up. The more ways, the more fingers they hold up to their chest.
• Once you are confident that most students have at least one solution, post them on the board for consideration. Incorrect solutions provide a great opportunity for conversations surrounding common misconceptions, so encourage these as well.
• At this stage, you can ask students to share their strategies for arriving at their answer. Place each strategy on the board along with the students name in order to recognise the individual child and identify their strategy.

In her book, Sherry also encourages the use of open arrays when communicating solutions in order to provide a visual understanding of each strategy used. There has been much literature on the importance of arrays in developing multiplicative thinking in students and they are a vital concept in learning multiplication and division. Their repeated use in a number talk helps to consolidate these important skills.

For the junior primary level, number talks can be done in the form of a dot talk. Helping students recognise quantity at an early level through subitising is a vital skill and this is encouraged through a dot talk. The basic rules are the same, but instead of presenting students with a numerical problem, a dot card is held up and students are asked ‘how many dots?’, as well as stating the different ways that they saw the collection. Again, these are all presented on the board and open for discussion and communication.

By immediately recognising a collection of numbers or subitising, students start to understand how a number is made up. This understanding of part-whole relationships helps children to separate and combine numbers and accelerates learning in addition and subtraction. An example of a dot talk is shown below.

Key components of a number talk

Five key components to doing a successful number talk are discussed in the book. These are:

• Classroom environment and community
• Classroom discussions
• The teacher’s role
• Role of mental health
• Purposeful computation problems.

In short, when doing a number talk, it is important to foster a cohesive classroom community where students feel safe enough to offer responses for discussion, question themselves and investigate new strategies. Communication is key and this should be encouraged and supported. Once students have practiced a few number talks, they will soon start to discover new experiences in mathematics and so many different ways of solving the same problem. In fact, I have not done a number talk where a student did not make the comment “I never thought of doing it that way” or, “I’m going to try that next time”. Over time, you will find that with regular use, number talks will dramatically improve their ability to access the mental maths strategies necessary to become facile maths learners. They also provide teachers with a great opportunity to establish the level of numerical understanding of each student.

Bibliography

Boaler, Jo   Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts. 2015

https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/2017/03/FluencyWithoutFear-2015-1.pdf

Flick Michael and Kuchey Debbie . “Contest Corner: Increasing Classroom Discourse and Computational Fluency through Number Talks”. Ohio Journal of School Mathematics, Spring 2015, Vol. 71. Pp. 38-41

https://eds-a-ebscohost-com.ezp.lib.unimelb.edu.au/eds/pdfviewer/pdfviewer?vid=3&sid=c7d38fd4-4c32-4081-a0e1-cda184663775%40sessionmgr4006

Shumway, Jessica F. 2011. Number Sense Routines

Boaler, Jo 2016. Mathematical Mindsets

Parrish, Sherry 2010. Number Talks: Helping children build mental math and computation strategies.

Number Sense – Jo Boaler: https://www.youcubed.org/resource/number-sense/

https://www.nesacenter.org/uploaded/conferences/SEC/2013/teacher_handouts/CairaFranklin.pdf

https://nrich.maths.org/2477

Number Talks: How and Why?

Subitising and Early Number Sense in Early Years Children

http://www.mathcoachscorner.com/2013/07/using-dot-cards-to-build-number-sense/

https://books.google.com.au/books/about/Number_Talks.html?id=p4B9F1u2T4kC&source=kp_cover&redir_esc=y

We acknowledge and pay respect to the Traditional Owners of the land upon which we operate

Planning  ICE-EM Textbooks Teacher PD Maths Education Research PD Handouts Teacher Content Modules

Middle Years (SAMS) Senior Years (SAMS)

Number and Algebra Measurement and Geometry Units of Work Games

Maths Videos Podcasts Careers 

PEDAGOGY NON GRATA

NUMBER TALKS

A number talk is a short classroom exercise that involves discussing and brainstorming processes to solve a given math question. This strategy has primarily been used to develop mental math and number sense skills by allowing students to work out the steps needed to solve math problems for themselves, rather than having a teacher outline the procedures for them. As such, number talks may be considered a metacognition strategy, since the ultimate goal of these exercises is to help students view math as a learning process. 

Recently, many educational professionals have begun to advocate for the use of number talks as the best way to teach mathematics. That said, as much as this strategy has become popular in classroom teaching, there are currently no meta studies examining the efficacy of this method or its impact size on student learning. In 2016, Angela Mader-Stewart of Lakehead University did, however, make a preliminary foray into quantifying the effects of number talks in mathematical instruction, ultimately concluding that “number talks is the very best strategy to teach both number sense and math facts at the same time” (Stewart, 115). 

This study was a case study and therefore, it did not, in fact, make use of a control group nor did it compare the impact size of results to any other method of teaching math. Indeed all this paper demonstrated was that the students showed an improvement between their pre intervention assessments and their post intervention assessments for the curriculum she covered with number talks. Although these results may appear statistically relevant, the students’ math test results, axiomatically, should have improved after being taught the assessessed curriculum materials, regardless of the strategy actually used to teach them. 

In 2017, Mark Duffy performed another quantitative study on a number talks intervention using secondary students. However, his study, like Mader-Stewart’s, had a small sample size and no control group (Duffy 66). The measured increases in math scores were also low, with the majority of students failing the post intervention assessment on two thirds of the sections and only 60% passing the final third section. Despite the veritable litany of voices now endorsing the methods outlined in these texts, Mark Duffy’s 2017 paper, which sought to establish a summative resource for ascertaining the efficacy of number talks, was only able to conclude that the extant data provided insufficient evidence for making such a determination. (Duffy, 73). 

A 2020 randomnized control trial, conducted by P, May, examined the efficacy of number talks for grade 5 students. The results showed an effect size of .63 for application skills, an effect size of .65 for accuracy, and a negative effect size of 1.6 for speed. That being said, the author wrote the speed results were positive, but the statistical data was negative, this leads me to believe that there may have been a typo here within the paper. Ultimately, as of this moment there exists little to no experimental evidence that Number Talks is an evidence-based strategy. However, it is a research based strategy. 

As previously stated, number talks are essentially a metacognition-strategy, which, according to John Hattie’s meta study on teaching factors, are high yield teaching tools that shows a mean effect size of .60. Number talks can be an effective tool for diagnosing specific inaccuracies in student understanding, promoting a growth mindset for math, and for increasing student awareness of some fundamental mathematical concepts. However, while there are benefits to the use of number talks, the practice is not without drawbacks, and, as with all educational strategies, there is an appropriate time and place for their best implementation in the classroom. Perhaps most importantly, number talks are a departure from direct instruction (another high yield strategy), and therefore they lower the amount of curriculum that can be covered in a limited timeframe. Ultimately, while it may be possible to incorporate number talks as an addendum to regular math instruction, their use should be limited to enrichment and should not supplant teaching methods, like direct instruction and individual practice time, which have been shown in meta analysis to produce the higher increases in math understanding.

Why You Should be Skeptical of Number Talks

References: S, Parish. (2014). Number Talks. Math Solutions. 

J, Hattie. (2018). Hattie Ranking: 252 Influences And Effect Sizes Related To Student Achievement Visible Learning. Retrieved from < https://visible-learning.org/hattie-ranking-influences-effect-sizes-learning-achievement/>. 

A, Stewarts. (2016). The Impact of Daily Number Talks on the Development of Mental Math Abilities of Second Graders within a Reform-Based Classroom. Lakehead University. Retrieved from < https://knowledgecommons.lakeheadu.ca/bitstream/handle/2453/4235/StewartA2018m-1b.pdf?sequence=1&isAllowed=y>.

Gersten, Chard, Jayanthi, Baker, Morphy, Flojo. (2009). A Meta-analysis of Mathematics Instructional Interventions for Students with Learning Disabilities: Technical Report. Instructional Research Institute. Retrieved from < http://3evoie.org/telechargementpublic/usa/gersten2009a.pdf?fbclid=IwAR0c-XjNJoSNy2dDvfWEwOqBl5EqtuFpU5GkW6s4QM7-jpuY90-I85Q5dyI>.

M, Duffy. (2017). Can Frequent Use Of Number Talks Increase The

Comprehension, Understanding, And Fluency Of Fractions, Decimals, And Percentages In Alternative High School Students? Hamline University. Retrieved from < https://digitalcommons.hamline.edu/cgi/viewcontent.cgi?article=5349&context=hse_all>. 

May, P. L. (2020). Number Talks Benefit Fifth Graders’ Numeracy. International Journal of Instruction, 13(4), 361–374. https://doi-org.ezproxy.lakeheadu.ca/10.29333/iji.2020.13423a

Back to Home - Number Sense - Principles for Number Talks - What does a Number Talk Look Like - Questions to Ask - Resources

"Number Talks" is an approach to the teaching and learning of Number Sense. Rather than relying on the rote-memorisation of isolated number facts achieved through drills of "table-facts", Number Talks aim to build confident, number fluency, where learners recognise patterns within and between numbers and understand the properties of numbers and operations. Number Talks are a "mind on" learning task that engages students in an active learning process as they search for patterns, decompose and recompose numbers and develop a flexible understanding. It is achieved through direct instruction methods and facilitative dialogue with the teacher or between groups of peers who have had experience with the number talks methodology. It becomes one of the routines of a classroom focused on mathematical reasoning.

Number talks are a valuable classroom routine for developing efficient computational strategies, making sense of math, and communicating mathematical reasoning. A number talk is structured to help students conceptually understand math without memorizing a set of rules and procedures. (Nancy Hughes) Number talks are: a brief daily practice where students mentally solve computation problems and talk about their strategies, as a way to dramatically transform teaching and learning in the mathematics classroom. Something wonderful happens when students learn they can make sense of mathematics in their own ways, make mathematically convincing arguments, and critique and build on the ideas of their peers. (Humphreys & Parker) Number Talks should be a regular routine within the Mathematics Programme; a tool for building the Mathematical Fluency that underpins an understanding of the "Big Ideas"

Number Sense or "Making Friends with Numbers"

Number Sense is fundamental to success in mathematics and involves developing an understanding of number, patterns inside numbers, patterns throughout sets of numbers and the effect that operations have on numbers. It is much more than memorisation of table facts and unlike learning by memorisation develops a deep and flexible understanding that promotes mathematical confidence and is a solid foundation for reasoning and problem solving.

Number sense is important because it encourages students to think flexibly and promotes confidence with numbers. . . . The fact is, students who lack a strong number sense have trouble developing the foundation needed for even simple arithmetic, let alone more complex mathematics. A large body of research has shown that number sense develops gradually, over time, as a result of exploration of numbers, visualizing numbers in a variety of contexts, and relating to numbers in different ways. ( Keith Devlin )

Research shows that students who are taught to rely on memorisation of number facts and mathematical processes do not perform as well as students who learn in an environment that emphasises number sense. Memorisation may help with less challenging questions, but is of little use as the questions become more challenging.

Students who avoid making an effort to understand mathematics concepts may succeed in some school environments; but a lack of deep, critical and creative thinking may seriously penalise these students later in life when confronted with real, non-routine problems. PISA results show that, across OECD countries, perseverant students, students with positive attitudes towards problem solving and mathematics, including high instrumental motivation to learn mathematics, interest in mathematics, high self-efficacy and self-concept, and low mathematics anxiety are less likely to use memorisation strategies. - OECD PISA Analysis - Is Memorisation a good strategy for learning mathematics?

Image: This commonly shared example shows a student who has rote learned the vertical algorithm for subtraction but with little understanding. (Source - Humphreys & Parker)

Rote practice is fraught with danger. Left unchecked, it can reduce rich mathematical concepts to a slew of rules and procedures that feel arbitrary and confusing to students. - Junaid Mubeen

Number sense is well supported by Number Talks as these inherently include opportunities for students to engage with the key strategies for number sense identified by Burns :

• Model different methods for computing
• Ask students regularly to calculate mentally
• Have class discussions about strategies for computing
• Make estimation an integral part of computing
• Encourage students to verify solutions for themselves
• Question students about how they reason numerically - their approaches and results - What makes you say that?
• Pose numerical problems that have more than one possible answer
• Value errors as opportunities for learning

10 Guiding Principles for Number Talks

• All students have mathematical ideas worth listening to, and our job as teachers is to help students learn to develop and express these ideas clearly.
• Through our questions, we seek to understand students' thinking.
• We encourage students to explain their thinking conceptually rather than procedurally.
• Mistakes provide opportunities to look at ideas that might not otherwise be considered.
• While efficiency is a goal, we recognise that whether or not a strategy is efficient lies in the thinking and understanding of each individual learner.
• We seek to create a learning environment where all students feel safe sharing their mathematical ideas.
• One of our most important goals is to help students develop social and mathematical agency.
• Mathematical understandings develop over time.
• Confusion and struggle are natural, necessary, and even desirable parts of learning mathematics.
• We value and encourage a diversity of ideas. (Source - Humphreys & Parker )

Number Talks are an ideal strategy for the "Number and Algebra" strand of K-10 Mathematics, but can be used in other strands to build fluency.

Making number talks routine.

Number Talks are most effective when they are a routine part of the students mathematical thinking and learning. A Number Talk is an ideal warm-up activity before other mathematical learning. A daily number talk can take between ten and fifteen minutes and this routine engagement with mathematical thinking builds number sense and fluency.

A ten to fifteen minute Number Talk should be a routine part of every learner's day.

What does a number talk look like.

• The teacher (or a student) presents a strategic computational problem. These are typically problems which focus on aspects of Number and Algebra (particularly Whole Number, Addition & Subtraction, Multiplication & Division).
• Students are given sufficient time to determine a solution; when they have an answer, they signal with a thumbs-up. This subtle messaging avoids the idea that speed is important. Fluency is not related to Speed.
• Students have access to resources that support multiple representations of their thinking (Concrete Materials, Pen & Paper). Multiple Representation is a a strategy that supports mathematical thinking.
• Teacher brings the class into a circle to share and discuss possible solutions - Begin by reminding the class of expectations for Circle Time .
• Teacher facilitates sharing of student solutions and methods and assists in making their thinking visible.
• Students share and explain their solution as the teacher records student strategies.
• Teacher asks key questions to elicit discussion and promote understanding e.g. What makes you say that?, How did you arrive at that method?, How does this connect with . . ?.
• Teacher is prepared to offer a strategy if needed. Students are encouraged to critique the teacher strategy.
• Class agrees on possible solutions and evaluates the methods offered. Solutions should be correct, elegant (not overly complex), well-understood, build on prior knowledge and creative. The class might agree on a criteria for solutions and use this to evaluate those offered. The purpose of evaluating solutions is to extend understanding and offer positive critique.
• The class might decide to select a 'favourite no'; a solution that while not correct, helped them to understand the problem in a new way.

Adapted from " Classroom-Ready Number Talks for Third, Fourth and Fifth Grade Teachers "

Wathc Jo Boaler Teaching A Dot Card NumberTalk from YouCubed .

My Favourite No

'My Favourite No' is a strategy shared in this video by Leah Alcala. Here the students are from a Middle School class and are discussing an age appropriate algebra question. The video models many of the fundamental aspects of a Number Talk, although in a typical Number Talk the students do most of the talking and questioning. It demonstrates the learning that can occur from mistakes and has a focus on 'growth' rather than only valuing correct responses and methods. It shows the effective use of a Number Talk like strategy as a learning tool and an Assessment For Learning method as the teacher is gaining valuable information about her student's learning and is able to use this to adjust her instruction.

Questions to Ask when facilitating Number Talks

Questions to focus on sense making at the beginning of the problem:

• What's going on here?
• What are you noticing?
• What do you wonder?
• Tell me something about the problem.
• Forget about the question for a second. What's going on in this situation?
• What do you estimate the answer might be?
• What do you predict the solution might lo ok like?

Questions to redirect students to the problem while solving:

• Can you read the problem aloud again?
• Let's go back to the question for a second. Is everything still making sense?
• Let's refresh our memories about what each of these numbers represents. What does "this" mean?
• Let's put numbers aside for a second and think about the units. Do they check out?
• Let's try to visualise what's going on in this problem. Does that seem possible?
• Can we visualise this in another way? What do you notice now?
• What do we know? What don't we know?
• What is not the answer? Why?
• What makes you say that?
• Is there a pattern here? What is it? Can you describe it, draw it or make it?

100 Questions that promote Mathematical Discourse - PDF Download

Circle Time

Circle Time is a pedagogical strategy developed to support student well-being, social & emotional learning, building of safe classroom environments and encouraging open discussion with respect for all members of the learning community. Circle Time strategies support Number Talks by ensuring students feel safe when offering their solutions and are therefore more likely to take risks with their thinking and share solutions even if they are not entirely confident with the methods they have chosen.

"Circle Solutions is a philosophy for healthy relationships and a pedagogy for teaching them. It is based in the principles of agency, safety, positivity, inclusion, respect and equality." ( Sue Roffey )

Each Circle Time begins with a review of the fundamental principles:

• Everyone gets a turn
• There are no put-downs, only personal positives
• When one person is speaking everyone will listen
• We will listen to you because what you say is important – this means that you also need to listen to others

Resources that Support Number Talks

• YouCubed - Number Talks
• Fluency without fear: Research evidence on the best ways to learn Math Facts - Read Online
• Sherry Parrish: Number Talks - Building numerical reasoning - 1hour 15 minutes - YouTube Video
• Making Number Talks Matter - by Cathy Humphreys & Ruth Parker - Amazon Australia Link
• In the Moment: Conferring in the Elementary Classroom - by Jen Munson - Amazon Australia Link
• Number Sense Routines: Building mathematical understanding every day in grades 3-5 by Jessica Shumway - Amazon Australia Link
• Classroom-Ready Number Talks for Third, Fourth and Fifth Grade Teachers - by Nancy Hughes. Ulysses Press. - Amazon Australia Link

Learn More:

• YouCubed - by Jo Boaler - Visit
• Mathematical Mindset Teaching Guide, Video and Resources - Visit
• Misconceptions of Mathematics - Back to Front Maths - Read
• Manu Kapur - Productive Failure in Learning Math - Read
• Paul Lockhart - A Mathematician’s Lament - Read
• Innovate My School - Innovating Mathematics Education - Read
• Rethinking Mathematics Education - Read
• Does Mathematics Education need a Re-think? - Read

  This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .

• >> Return to Heinemann.com

Dedicated to Teachers

• Sherry D. Parrish
• Ann Dominick
• Middle School
• Education Policy
• Language Arts
• Lucy Calkins
• View All Topics

Create Confident Problem Solvers with Number Talks

Number talks create confident student problem solvers Classrooms (at all grade levels) are filled with students and teachers who think of mathematics as primarily rules and procedures to memorize. This often happens without understanding the numerical relationships that provide the foundation for these rules. At times, the teaching of mathematics has focused on speed and accuracy without understanding the mathematical logic behind an idea or answer. For some people, thinking about math as strictly procedural has been successful. But for many of us, memorizing a set of rules has not led to greater mathematical confidence in our daily lives.

Number talks are a great way for teachers to help students share their mathematical thinking and grow their confidence as mathematicians. Number talks are needed now more than ever While a procedure-based version of math teaching may have seemed to work in the past, students today must develop a deeper understanding of mathematics. Today, students must learn to:

• reason numerically
• develop number sense
• evaluate the reasonableness of an answer

Students must choose strategies that are applicable to specific situations and figure out whether an answer makes sense. They also need to engage in math conversations and communicate their ideas about their solutions.

• composition and decomposition of numbers
• our system of tens
• properties of numbers

Conversations around purposefully crafted number problems are at the very core of number talks. These are opportunities for the class to come together to share their mathematical thinking.

Number talks are purposefully designed The problems in number talks are designed to elicit specific strategies that focus on number relationships and number theory. Students are presented with problems in either a whole- or small-group setting and are expected to learn to mentally solve them accurately, efficiently, and flexibly. By sharing and defending their solutions and strategies, students are provided with opportunities to collectively reason about numbers while building connections to key conceptual ideas in mathematics.

5 key components of number talks There are several key components to teaching with numbers talks: 1. Classroom environment and community 2. Classroom discussions 3. The teacher's role 4. The role of mental math 5. Purposeful computation problems

Topics: Math , Sherry D. Parrish , Ann Dominick

Recent Posts

Popular posts, related posts, let's talk math purposeful math with kent haines and steve leinwand, 8 reinvigorating and equitable mathematics teaching practices, 7 math workshop characteristics, matific's adaptive learning engine: a personalized path for every student.

© 2023 Heinemann, a division of Houghton Mifflin Harcourt