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 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?

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

- 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 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.

- 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' 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 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 look 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 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

- 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

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