Number Talks have the power to transform students’ mathematical understanding. Yes, they are that powerful! During this 5 – 15-minute routine, students solve problems mentally, discuss strategies, and justify solutions. As I think about Number Talks, I’m reminded of a quote from Responsive Classroom, “The greatest cognitive growth occurs through social interaction.” Number Talks are students discussing with other students. They are students owning their understanding. They are mathematical thinking rather than memorization.

**Why Number Talks?**

Mathematical understanding is crucial for our students. According to Moss and Lamb (2001, p. 14), algebra is no longer just the gatekeeper for higher math. Now algebra is the gatekeeper for citizenship. “People who don’t have it are like the people who couldn’t read and write in the industrial age.”

Our students can no longer rely on a mathematical foundation that is built on memorization and procedures because this foundation falls apart when students must generalize arithmetic relationships in algebra courses. Too often, elementary teachers do not see the ramifications of a foundation built on memorization because the students have moved on to high school. Teachers do not see how the good memorizer in third grade math struggles during algebra because deeper understanding is needed for success.

Number talks are a great way to build conceptual understanding and to help students develop “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.” (Parrish, p. 4)

**What are Number Talks?**

Classroom discussions around carefully crafted computation problems are at the heart of number talks. They help build a community of learners and develop collective understanding of mathematical ideas. The focus is on connections between strategies rather than solely on correct solutions. Students are expected to solve problems mentally.

According to Parrish, five key components are necessary for successful implementation of number talks.

- Classroom Environment and Community
- Classroom Discussions
- The Teacher’s Role
- The Role of Mental Math
- Purposeful Computation Problems

**Key Components**

__Classroom Environment and Community__ – A safe, risk-free environment built on mutual respect is important. During number talks, students need to feel comfortable responding during discussions, questioning their own and other’s thinking, and thinking about new strategies. Time and space should be planned for, so students understand the importance of this routine. All students should be near the teacher. This helps build a sense of community and allows for better teacher observations of students’ thinking and better interactions between participants.

__Classroom Discussions__ – In a number talk, the teacher writes a problem on the board and gives students time to solve it mentally. Quiet signals are used so as not to interrupt thinking. Students start with a fist held against their chests. When students have a solution, they put their thumb up against their chests. Students are encouraged to continue finding efficient strategies, and as they find a new strategy, another finger is raised. Wait time is important so that most students can access the problem.

Once most students have a solution, the teacher records all answers on the board, both correct and incorrect, for students to consider. Then students share their strategies and justify their responses with the class. Students share the authority as they determine whether an answer is correct. Incorrect answers help to uncover misconceptions and enable students to investigate their own thinking and to learn from their errors (Parrish). As students become more flexible with strategies, the teacher encourages them to decide which strategy is the most efficient.

__The Teacher’s Role__ – The teacher facilitates, questions, listens, and learns. It is important that the teacher does not tell or explain. Remember the students share the authority. It is important that the teacher keeps the discussion focused on the important mathematics and helps students see the connections between strategies by asking open-ended questions, such as “How did you get your answer?” The teacher also helps students to “learn to structure their comments and wonderings to ensure that the conversation flows in a meaningful and natural way” (Parrish, p. 11).

__The Role of Mental Math__ – Teachers often ask if students can use whiteboards or notebooks as they solve the problems, but the answer is no they cannot. Mental math is a goal of number talks. “Mental computation is a key component of number talks because it encourages students to build on number relationships to solve problems rather than relying on memorized procedures” (Parrish, p. 13) Mental math also helps students to be efficient with numbers, so they avoid holding numerous quantities in their heads.

__Purposeful Computation Problems__ – The problems used for number talks should guide students to focus on mathematical relationships. The teacher’s goals and purposes should determine the numbers and operations used in the problems. While there are many examples available in books and online, the teacher needs to choose carefully and plan based on the needs of the class. The teacher should also plan how to record student thinking, so that it is accessible to the other students. Prior to the number talk, teachers should think about possible strategies students may use and how they might be recorded so that the mathematical ideas are clear.

One question that I’m often asked by both teachers and administrators is, “How do we hold students accountable for the mathematical work that is done during a number talk?” There is a fine line here. Too much accountability and it seems like just another solution-oriented task, but too little accountability enables many students to slide under the radar and not build mathematical understanding. Parrish offers a list of ideas to develop student accountability.

- Ask students to use finger signals to indicate the most efficient strategy.
- Keep records of problems posed and the corresponding student strategies. Write the student’s name next to the strategy he/she posed.
- Hold small group number talks throughout the week.
- Create and post class strategy charts.
- Require students to solve an exit problem using the discussed strategies. I love the idea of using an index card. On one side, students solve the problem using a strategy that was discussed, and on the other side, they use a strategy of their choice to solve the problem. These exit tickets are used for formative assessment, so they are not graded.
- Give a weekly computation assessment with problems like the ones in the week’s number talks.

**Conclusion** – My advice to teachers, especially those who want everything to be perfect the first time, is start small, but most importantly, just start. You will be amazed at the way students intuitively think about math. As students become familiar with the routine and the flow of discussions, the number talks will improve. As you become more comfortable in the role of facilitator, you will trust your students more, and your questioning will improve. Planning is key, especially as you begin number talks. Our students must build an understanding of math right from the beginning. Number talks help build flexible, efficient mathematicians who understand math.

This piece is was written by our team member, Denise Rawding.

References

Moses, Robert P., and Charles E. Cobb Jr 2001. *Radical Equations: Math Literacy and Civil*

* Rights*. Boston, MA: Beacon Press.

Parrish, Sherry 2014. *Number Talks: Helping Children Build Mental Math and Computation *

* Strategies*. Sausalito, CA: Math Solutions.