"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?*

This commonly shared example shows a student who has rote learned the vertical algorithm for subtraction but with little understanding. 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)

**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)

**Questions to Ask when facilitating Number Talks**

Carefully selected questions are used to focus the students 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?

Let’s try to visualise that?

What makes you say that?

Is there a pattern here?

Can you build on that idea?

Can we find a new way of looking at this?

What if . . .? & How might . . .?

The language of a number talk is very deliberate and designed to invite participation and alternate perspectives. We ask ‘Who has an idea for a solution?’ rather than ‘Who knows the answer?”. All responses are valued and no response is dismissed. Each time a student is told their thinking is wrong, they learn that in mathematics there is a right answer and the goal is to guess what that answer is. Number talks work best within a culture that values mathematical thinking more than calculation. Students should be encouraged to share their ideas, debate responses, look for other solutions and demonstrate their thinking in multiple ways.

**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.

By Nigel Coutts

Adapted from http://globalcognition.net/index.html

**Resources that Support 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