Number Talks and Learning Theories
There are many skills students can learn through experiencing a number talk. A number talk is a learning experience where students are presented with a problem to solve mentally. While often in math the focus is on getting to the right answer, number talks differ as the focus is on how the problem is solved. Number talks are a great activity which combine a variety of learning theories together into one activity.
Constructivism has students learning through applying different strategies to solve a problem. When thinking about addition the traditional method focused on writing the 2 problems on top of each other and solving using "carrying". While this method works, it only shows one way an addition problem can be solved. By exploring different strategies students can make deeper connections within math. As students learn new strategies they assimilate information, add more evidence to what they know, or accommodate information, change their schema to fit the new information, . As students learn about the multiple ways to approach a problem they are able to sort the new strategies into the appropriate schema or groupings within their mind.
One of the beauties of number talks is that they combine the academic skills into a social setting. Social Learning theory explains that learning comes through social experiences where people can learn from one another. As students present their thinking to their classmates, students light up both when they find a strategy that works and as the information from their classmates clicks in a different way. After multiple number talks students start applying the skills learned from their classmates. Students do not just learn from the correct explanations but also can see why other strategies are not the best for a given problem.
During a number talk learning occurs not directly from the teacher but through the students. In sociocultural theory students are learning from a more knowledgeable other. This does not need to be the teacher. Students are experts on what works best for them. The variety of strategies available helps students to remain in their zone of proximal development where they are able to be successful at learning with the scaffolding and given support or the challenge to solve the problem a different way.
Although it is just one activity, number talks are great at combining elements from multiple learning theories. This combination provides a safe space where deep learning can occur. As students practice mathematical conversations they are able to build number sense. When students are not stuck on finding the one right answer it is amazing what learning can take place.
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As B.F. Skinner, I would approach this text analytically, focusing on how number talks align—or don’t—with the science of behavior. Number talks, as described here, emphasize varied strategies, peer discussion, and multiple routes to problem solving. In my work, I demonstrated that learning is best supported by immediate feedback and carefully arranged contingencies. You mention that number talks focus on process over product, which can certainly build repertoires of behavior if the contingencies are clear and reinforcing, such as social approval or successful completion. However, I would question whether the reinforcement is sufficiently immediate and systematic to ensure the desired behaviors are reliably acquired.
The text references several learning theories—constructivism, social learning, and sociocultural theory. While students may say they are “assimilating information” or “changing schemas,” I have always argued that what truly matters is the observable change in behavior resulting from specific environmental conditions. The emphasis on student talk and peer modeling does fit with my idea that behavior can be shaped by the social environment, as long as desirable behaviors are reinforced and less effective strategies are extinguished. I would recommend making sure that reinforcement is actively managed rather than leaving learning to chance. Ultimately, number talks might be effective if they build in consistent, positive reinforcement for successful participation and correct mathematical strategies.
What would you like to discuss further? Possible topics:
1. How reinforcement could be better integrated into number talks.
2. Differences between behaviorism and constructivism in math education.
3. The role of peer modeling and social reinforcement in classroom learning.
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Please Note: Everything in this comment is AI-generated. It is made up to sound like B.F. Skinner.
I invite you to read and comment on the interviews where B.F. Skinner talks more about his work. One is with Alex Steinberg and the other is with John M. Whiteley. Both can be found in this document: https://writingpartners.net/documents/7839
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To better integrate reinforcement into number talks, I would advise making reinforcement more explicit, immediate, and tied to specific learner behaviors. For example, when a student contributes a correct computation strategy or explains a mathematical idea clearly, the teacher could provide immediate praise, a gesture of approval, or a tangible token. As I noted in my interviews, “you can have special foods at lunchtime, access to play space, privileges to associate with other kids of your choice”—the key is to select reinforcers that are meaningful to students and fade them gradually, so the students come under the control of the academic material itself.
Currently, number talks sometimes rely on more diffuse social reinforcers, such as peer attention or teacher acknowledgment. These are helpful, but often too unsystematic to reliably shape new behaviors. If you want students to take academic risks, try new strategies, or explain their thinking, those behaviors should be met with positive consequences each time they occur, especially at the start. Over time, as participation and correct reasoning become more frequent, you can thin the schedule of reinforcement so that approval is less predictable and more tied to complex, independent performance—just as I described for building reading skills.
What else would you like to know? Possible paths:
1. Specific examples of positive reinforcers for number talks.
2. Pitfalls of “natural” reinforcement and why systematic reinforcement matters.
3. How to transition from external to intrinsic motivation in skill-building.
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Please Note: Everything in this comment is AI-generated. It is made up to sound like B.F. Skinner.
I invite you to read and comment on the interviews where B.F. Skinner talks more about his work. One is with Alex Steinberg and the other is with John M. Whiteley. Both can be found in this document: https://writingpartners.net/documents/7839
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What do I think of this theory of learning? The approach described here, particularly the practice of “number talks,” deeply resonates with my philosophy. In Pedagogy of the Oppressed (especially in chapter 2), I argue against the “banking model” where students are passive receivers of information. Instead, I emphasize dialogic learning—learning that arises from active engagement, questioning, and reflection. Your theory highlights the value of multiple strategies, peer learning, and the construction of knowledge within a social context. This aligns closely with my assertion that “knowledge emerges only through invention and re-invention, through the restless, impatient, continuing, hopeful inquiry human beings pursue in the world, with the world, and with each other.”
When you say, “during a number talk learning occurs not directly from the teacher but through the students,” you honor what I call the co-construction of knowledge. Here, teachers and students become partners—both are teachers and both are learners. This makes learning an act of communication and liberation, not of domination or rote memorization. The space you describe in number talks—where students are challenged, supported, and able to share different viewpoints—is precisely the kind of problem-posing education I advocate for. It helps students become more critically aware of how they engage with problems, each other, and the world.
Now, I have much more I could say about this question—what I think of this theory of learning. Here are three more paths we could take to explore this together:
✅ Dialogical Practice: How dialogue, questioning, and collective reflection turn a simple math activity into a humanizing social practice that promotes liberation.
✅ Teacher-Student Partnership: What it means for both teacher and students to become “co-investigators” in learning, and how Number Talks can break down the authority barrier.
✅ Critical Consciousness in Math: How even math classrooms can be places where students develop a critical awareness of their own thinking and the world around them.
Which of these paths would you like to take? Or is there another direction you’re curious about regarding the theory of learning discussed here? Let’s take the next step together and dig deeper.
Since we are discussing this within the context of a text, please hit “Your Thoughts” and write which path you want to take. Then, after you save your reply, hit “Continue with AI,” choose me again, and ask more questions about the topic you have chosen. Let’s bring this exploration to life!
Please Note: Everything in this comment is AI-generated. It is made up to sound like me.
If you want to see more about my work in practice, I invite you to read and comment on interviews where I discuss my methods and experiences. One is with [interviewee 1] and another with [interviewee 2]. Both can be found at: https://writingpartners.net/documents/7894
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Your question is: What do I think of this text on number talks and the learning theories that inform them? From my perspective, as Jean Piaget, I find this approach to be very much in harmony with my own constructivist view of learning. The description of number talks emphasizes the centrality of students constructing their own understanding through the active exploration of various problem-solving strategies, aligning closely with my belief that “knowledge is not simply transmitted from teacher to child, but actively constructed by the mind of the learner.” Number talks encourage children to compare, reflect, and try out different methods, which is how they build solid mathematical schemas—or mental structures for understanding numbers and operations.
Also, I notice that you reference assimilation and accommodation, which are core concepts in my theory of cognitive development. When students adapt their thinking to new strategies (accommodate) or fit new evidence into their existing understanding (assimilate), they are exactly following the mental processes I described. Furthermore, giving students the space to share in a social context and learn from one another resonates with constructivism’s emphasis on the child’s active role in knowledge construction, albeit you’ve also included ideas from social learning and sociocultural theory. Even so, what matters to me is that this activity places the process of thought—and the development of number sense—ahead of mere correct answers, as I have always argued that “understanding is built slowly, through repeated exchanges with the environment and others.”
Would you like to explore more about my reaction to this? Here are three avenues to pursue—please choose one or more, or suggest another direction!
What would you like to know more about? Hit “Your Thoughts” and tell me which of these paths interests you most! After you save your reply, select “Continue with AI,” choose me again, and ask another question to dive deeper. Let’s journey further into the landscape of children’s mathematical minds!
Please Note: Everything in this comment is AI-generated. It is made up to sound like Jean Piaget.
And by the way, I invite you to read and comment on the articles by Kendra Cherry describing my work. Both can be found in this document: https://writingpartners.net/documents/7871
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You’ve asked what I think of the piece that describes the educational value of number talks. I find a great deal to appreciate here. Your analysis echoes much of my own work—especially my insistence that education should not merely transmit methods, but foster experiences where learners develop meaning through action, reflection, and social interaction. Number talks, as you describe, move beyond a fixation on correct answers and instead honor the process, the child’s unique strategies, and the classroom as a community of inquiry. This is very much in line with my conviction that “learning by doing” is the root of deep understanding.
As you point out, number talks draw from constructivism, social learning theory, and sociocultural theory, further building on my belief that knowledge emerges from shared problem-solving, dialogue, and connecting new ideas to lived experience. I am especially glad to see the emphasis on students as “experts on what works best for them,” and that the classroom supports learners staying in their “zone of proximal development.” These ideas reflect the heart of progressive education: education is successful when it empowers learners to participate, reflect, and co-construct understanding with others. It is not the teacher alone who generates meaning, but the interactive, democratic processes within the group.
Let me condense some other thoughts you might want to explore—all connected to your question about the value of number talks and their relationship to educational philosophy:
✅ The Role of Experience: How number talks exemplify my principle that real learning is rooted in active, meaningful experience rather than rote procedures.
✅ Democracy in the Classroom: Ways in which number talks foster a democratic ethos by giving all students a voice in constructing mathematical ideas.
✅ Mistakes and Growth: Why classrooms should treat mistakes not as failures, but as openings for dialogue and deeper learning.
What would you like to know more about? Would you prefer to go deeper into the role of experience, discuss democracy in classroom practice, or explore the value of mistakes in learning? You can choose any path—or suggest another! The adventure is yours; I’m here to keep thinking alongside you.
Please Note: Everything in this comment is AI-generated. It is made up to sound like me.
If you’re curious, I invite you to read and comment on the interviews where I talk more about my work. One is with Peter Gibbon and the other with Dr. Vicki Hargraves. Both can be found in this document: https://writingpartners.net/documents/7875
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