Challenging All Teachers to Engage in Number Talks
By Amy Smith and Mercedes Tichenor
Number Talks have been a proven mathematical practice for over three decades. However, not all teachers may know about Number Talks or understand how powerful they can be to promote student engagement and mathematical reasoning. More importantly, though, some teachers may not see Number Talks as a quick, easy tool to recenter math around student understanding. In this article, we describe ways teachers can embrace Number Talks and provide ideas that target a range of mathematical concepts. Specifically, we share simple solutions for common challenges to using Number Talks in today’s classrooms.
What are Number Talks?
Number Talks are brief instructional routines designed to engage students in mathematical discussions where they can listen to and share their unique ways of reasoning. Because the focus of Number Talks is not solely on the answer, but rather on mathematical reasoning, Number Talks allow students to think and reason at their individual levels (Bieda and Staples, 2020), which can provide a more equitable mathematical experience for students. Moreover, Number Talks can build number sense, promote mental math, encourage mathematical conversation, develop computational fluency, and increase conceptual understanding (Boaler, 2022; Parker and Humphreys, 2015).
Challenges of Number Talks
If Number Talks have been around for decades and have been proven to benefit children’s computational and conceptual understanding of math, are teachers using them in their classrooms? If not, why? To answer these questions, we surveyed practicing teachers to understand their knowledge of and feelings about Number Talks. Over one hundred kindergarten through sixth grade teachers from twelve schools responded to our survey. Interestingly, but not surprisingly, almost half of the respondents do not use Number Talks in their classrooms. After reviewing responses as to why they do not use Number Talks, the following common challenges were identified.
Simple Solutions to Overcoming Challenges
To support each potential challenge, we offer some simple solutions—beginning with time. We recognize that teachers have a lot of math content to cover in a short amount of time and appreciate that “adding one more thing” might feel overwhelming. A great thing about Number Talks is their versatility. A Number Talk can be completed in as little as five minutes, does not require any prepared materials, and does not have to directly relate to the content being taught during whole-group math time. This means that teachers can essentially “plug in” a Number Talk at any point during their day.
As stated, Number Talks can cover any math content. This means they can, but do not have to, align with curricular scope and sequences. If, for example, a fourth-grade class were studying the standard “Build fractions from unit fractions” (CCSS.MATH.CONTENT.4.NF.B.3), they could still use 197+384 as a perfectly appropriate Number Talk (which aligns with CCSS.MATH.CONTENT.4.NBT.B.4). Or, they could support the current standard and have a Number Talk on different ways to create six-eighths. Teachers could use Number Talks as support for current content or a review of past concepts—both would make great opportunities for learning.
The final, and most critical, challenge our survey revealed is that teachers are unsure of how to do Number Talks. During a typical Number Talk, the teacher presents students with a math task that is accessible to them. Students are then given wait time to mentally solve the problem using any method that makes sense to them. Once they have an answer, they indicate their readiness with a discreet thumbs-up at their chest, allowing the teacher to gauge the class's progress without disrupting others' thinking. When most students indicate a solution, the teacher selects a few to share their answer. Strategically choosing different voices can support a more equitable classroom environment. After recording these responses, the teacher invites volunteers to explain their reasoning and problem-solving process, which is the most important component of a Number Talk. This initial discussion can be followed up with additional, related tasks. We now present some sample Number Talk prompts across the elementary spectrum.
Number Talk Ideas
To promote subitizing (recognizing groups of objects as a single quantity), teachers can present a quick image (see below) and ask, “How many dots do you see?” These types of tasks can be used across grades, from “Counting to tell the number of objects” (CCSS.MATH.CONTENT.K.CC.B.4) to “Representing and solving problems involving multiplication and division” (CCSS.MATH.CONTENT.3.OA.A.1) and are a great way to introduce the Number Talk process and focus on justification.
Straightforward equations can focus students on a particular type of problem. For example, presenting the additive problems shown below in sequence could support combinations of ten, place value reasoning, and inverse operations. While the values presented might be appropriate for second grade (CCSS.MATH.CONTENT.2.NBT.B.5), teachers in lower or higher grades could modify the numbers to make the task more appropriate for their students.
Word problems can provide context to numbers through any operation. A multiplicative problem might be: “Jack and Jill are throwing a party. Jack has three, six-packs of Sprite and Jill has nine, six-packs of Dr. Pepper. How many cans of soda will Jack and Jill bring together?” This type of question (CCSS.MATH.CONTENT.4.OA.A.3) promotes problem-solving and has numerous entry points for students to engage in. Again, although this problem might be appropriate for fourth grade, by changing the six-packs to twelve-packs or increasing the number of packs could easily make this a fifth-grade level Number Talk.
After using tasks such as these, the most important part of a Number Talk is the discussion (“Construct viable arguments and critique the reasoning of others” CCSS.MATH.PRACTICE.MP3). This is where students can share their reasoning and learn from one another. To promote such discussions, the teacher needs to listen and question to understand the student, not to assess. Here are some questions teachers can ask to foster discussion: “How did you get your answer? “Why did that strategy work?” “What do you mean by that?” or “Can you explain that in a different way?” Asking open-ended questions aimed at listening to students’ thinking is another equitable opportunity that Number Talks provides.
Conclusion
Number Talks are a proven practice in math classrooms that can offer many benefits to student learning, and despite the challenges posed by Number Talks, the results can be long-lasting and well worth the effort. We encourage all teachers to begin Number Talks today.
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● Classroom-Ready Number Talks for Kindergarten, First and Second Grade Teachers: 1000 Interactive Activities and Strategies that Teach Number Sense and Math Facts by Nancy Hughes.
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● Classroom-Ready Number Talks for Third, Fourth and Fifth Grade Teachers: 1000 Interactive Math Activities that Promote Conceptual Understanding and Computational Fluency by Nancy Hughes.
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References
Bieda, Kristen, and Megan Staples. “Justification as an Equity Practice.” Mathematics Teachers: Learning and Teaching PK-12, 113, no.2 (2020): 102-108.
Boaler, Jo. Mathematical Mindset: Unleashing Students’ Potential through Creative Mathematics, Inspiring Messages and Innovative Teaching 2nd ed. New Jersey: Jossey-Bass, 2022.
Parker, Ruth, and Cathy Humphreys. Making Number Talks Matters. Portland, MA: Stenhouse Publishers, 2015.
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Dr. Amy Smith is an Assistant Professor of Elementary Mathematics Education and Faculty Fellow for Inclusive Pedagogy at Stetson University in DeLand, Florida. Her research focuses on advancing pedagogical practices and improving elementary mathematics. |
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Dr. Mercedes Tichenor is a Professor of Education at Stetson University in DeLand, Florida. |