Number & Math Talks

Part of Strengthening Number Sense

Math teachers often focus on having students complete problems in writing, rather than talking through their thought processes.

Often, students’ foundation, if based on memorization, crumbles when they are called to generalize arithmetic relationships in algebra courses.

Today’s information age requires students and adults to develop a deeper understanding of mathematics. Today’s mathematics curricula and instruction must not only focus on preparing students to be mathematically proficient and compute accurately, efficiently and flexibly but also enable them to communicate their ideas effectively to others.

For this “talking” about numbers & math with peers & teachers is an excellent strategy.

Number/ Math Talks & Discourses

These "talks" are also known as math discourses. We will use the term "talks" in this broader sense.

Number talks are a great way for teachers to begin a math lesson, supplement math instruction in small groups, or provide targeted intervention for students who struggle with math.

A typical number talk should not be longer than 15 minutes.

Talking with students about numbers & math while they are doing math provides a window into the way they are thinking about them. It is also an opportunity for them to explain what they are thinking and doing, to others, using mathematical vocabulary.

In this process, other students can also participate and their thinking process come out into the open for discussions.

It is an opportunity for teachers to point out the concepts underlying some of the rules that students use.

It gives an opportunity to teachers to correct their misconceptions and misunderstandings. It is a collective learning opportunity.

The introduction of number talks is a pivotal vehicle for developing efficient, flexible, and accurate computation strategies that build upon the key foundational ideas of mathematics such as composition and decomposition of numbers, our system of tens, and the application of properties.

Classroom conversations and discussions around purposefully crafted computation problems are at the very core of number talks.

Students are presented with problems in either a whole- or small-group setting and are expected to learn to mentally solve them accurately, efficiently, and flexibly.

By sharing and defending their solutions and strategies, students are provided with opportunities to collectively reason about numbers while building connections to key conceptual ideas in mathematics.

A problem is posed. Children are given an opportunity to record their answers. They are also asked to volunteer to defend their answers. If a child presents a particular strategy, others are asked if they have an alternate strategy.

Teacher tries to bring out the idea that math is about making sense of numerical relationships.

Necessary conditions for number-talks to succeed

1. An environment of learning and not competition

2. An environment which encourages discussion without a sense of fear. It also requires certain ground rules so that everyone can participate.

Advantages of discussions

1. Clarifies thinking

2. Communicate thinking to others

3. Listen to thinking of others

4. Evaluate other opinions

5. Investigate apply mathematical relations & concepts

6. Build a repertoire of strategies

In number talk classrooms, students have a sense of shared authority in determining whether an answer is accurate. The teacher is not the ultimate authority, and students are expected to think carefully about the solutions and strategies presented.

Wrong answers are also equally learning opportunities.

If a student understands why his/ her answer is wrong, it is both an opportunity to learn and develop a growth mindset that mistakes are stepping stones to learning.

Teachers’ role must shift from being the sole authority in imparting information and confirming correct answers to assuming the interrelated roles of facilitator, questioner, listener, and learner.

They need to change their question from “What answer did you get?” to “How did you solve this problem?”

Mental computation is a key component of number talks because it encourages students to build on number relationships to solve problems instead of relying on memorized procedures. When students approach problems without paper and pencil, they are encouraged to rely on what they know and understand about the numbers and how they are interrelated.

Mental computation forces students to be efficient with the numbers to avoid holding numerous quantities in their heads.

Mental computation is to help strengthen students’ understanding of place value, by looking at numbers as a whole rather than in terms of numerals.

Problems chosen for discussion should have possibilities to encourage certain ways of thinking. In early stages, it is better to avoid a random set of problems with different strategies.