Number Talks are a wonderful way to see where our students are with their mathematical thinking. As a part of a daily routine, a Number Talk promotes number sense and mathematical reasoning. In this post, I revisit what a Number Talk can reveal about our students’ understanding of mathematics, and how they might be used to promote a fresh perspective. In addition, I examine a success criteria for Number Talks that is more expansive and recognises their true power.
"Number Talks" are 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. Number talks are all about mathematical reasoning. In place of an emphasis on right answers, we have an emphasis on the rationale for the response. Number talks are most effective when they become one of the routines of a classroom focused on mathematical reasoning and are a great fit with visible thinking strategies.
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)
In a number talk, I am inviting and requiring students to explain their thinking. Mathematical reasoning becomes more important than correct answers. Ask students to solve an addition like 68 + 95 in a number talk and you will know which students understand place value. While participating in the Number Talk students share numerous approaches to each question. They share and hear a range of strategies. Provide students with a whiteboard so they might make their thinking visible and you open new possibilities. Include the option of an extended Number Talk using concrete materials and you allow for diverse representations of mathematical thinking. In each instance, the students are revealing how they understand number and each response offers new insights to the teacher for future learning. Number Talks by design close the gap between student performance and teacher action to address and remediate misunderstandings.
Recently a colleague was engaging her class in a number talk. She had decided to use a “Which one doesn’t belong?” strategy with her class. In this, students are shown a collection of four related items and are asked to nominate one that they feel does not belong in this collection. Thinking is elicited through this strategy when students are asked to justify their choice. She had shared a collection of four numbers: 125, 135, 140, 145 and presented them as in the diagram below. The students were given thinking time and when ready, as indicated by a thumbs-up signal, the teacher invited suggestions. On this day, with this group of learners, suggestions were scarce. After some initial tentative offerings the class began to share with a little more confidence but they never truly picked up on the possibilities. Before the lesson, it had been discussed that the students might identify 140 as the one that did not belong. It was the only multiple of ten, the only odd number, the only number that did not end in a five. Maybe the students would notice that there would be a sequence of numbers increasing by ten from 125 and that the fourth number should be 145. With more mature and capable learners they might have noticed that only 135 is divisible by three. The teacher’s initial reaction was that the Number Talk had not gone well.
Looked at from the perspective of students demonstrating a high level of mathematical confidence, the session was not great. But this is not the key aim of a Number Talk. A dip into the world of Visible Thinking helps to better understand the value of a Number Talk. In “The Power of Making Thinking Visible”, Ron Ritchhart and Mark Church share the value that thinking routines have and offer the following advice:
Don't judge your success with how smoothly the lesson went. This improves with time. Judge your success by what is revealed about your students' thinking. The question we need to be asking ourselves as teachers after using a thinking routine is: “What have I learned about my students' thinking as a result of doing this routine?” (Ritchhart & Church)
In this instance, the Number Talk revealed much about where the students are with their number sense. Prime amongst the revelations was that they don’t yet have a full understanding of odds and evens and that they are yet to master either multiples of ten or five. The teacher came away with three pieces of useful information and can now develop a strategy to better address each concept. If success is measured by the quality of insights provided by the Number Talk then this was a clear success.
The success of the Number Talk was further increased by how the teacher reacted, or in this case, chose not to react, as the session revealed gaps in the students’ understanding. The teacher could easily have decided to offer her own suggestions. She might have shared with the students that 140 doesn’t belong because it is an even number or that it is the only one that is a multiple of ten. She could have explained her reasoning to the class, shared some illustrations, referenced a hundreds chart and hoped that the students would have learned the new content. Instead, she allowed the Number Talk to serve its purpose of illuminating for her the current state of her students’ thinking and closed the session. She knew now was not the time to push ahead into direct instruction. She valued the place that thinking plays in Number Talks and refrained from sending a message to the students that in a Number Talk, success is about correct answers. Again, Visible Thinking shines a light on the correctness of the teacher’s choices in this moment.
Here we must strive to identify when a student's challenge can lead to a productive struggle with the ideas and eventually yield new insights for that student versus when the challenge is overwhelming and likely to cause a student to shut down. (Ritchhart & Church)
In this case, the teacher recognised that the challenge here and the concepts involved were significant and she knows that there will be time in the future to redress these. Just as we create thinking time for our students, we must create thinking time for ourselves. When she does decide to address this content with her students, she will do so strategically.
The key here is to understand that our teaching can become more powerful when we use the time we have with our learners as opportunities for us to learn more about them as learners. If our singular focus is on teaching content, skills and dispositions we miss the chance to become students of our students, to observe them closely in the acts of thinking and learning and use what we notice to better meet their needs.
by Nigel Coutts with thanks to Stellina Sim
Cathy Humphreys & Ruth Parker (2015) Making Number Talks Matter: Developing mathematical practices and deepening understanding. Stenhouse Publishers
Nancy Hughes (2018) Classroom-Ready Number Talks for Third, Fourth and Fifth Grade Teachers. Ulysses Press
Ron Ritchhart & Mark Church. (2020) The Power of Making Thinking Visible: Practices to engage and empower all learners. Wiley.