## Wednesday, February 6, 2019

### Buzzwords Decoded: Number Talks and Mental Math

One challenging thing about teaching is that terminology and popular buzzwords change all the time. For example, “math talks” or “number talks” used to commonly refer to a conversation about math in the classroom. These days, though, “number talks” usually refer to a specific protocol for a structured conversation about mental math, as outlined in the book Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4-10, by Cathy Humphreys and Ruth Parker (2015).

Why has this protocol taken over this terminology? One reason is that the protocol is effective at reaching all students and achieving multiple goals in developing mathematical thinking.

The protocol begins with students being presented a mental math problem. Students place their fist over their heart. When they have solved it using one strategy, they open one finger. Two strategies, another. And so on. The teacher gives a set amount of time, and students find as many strategies as they can.

After one or a series of problems are solved, a class discussion of strategies ensues. Students share the strategies they used to find the solution.

Why is this effective?

Wait time. In many traditional math classrooms, teachers respond to raised hands, often among the first ones up. This creates several problems:

• Boys have been shown to raise their hands even if they aren’t sure of the answer, or even if they don’t have an answer, while girls are more reluctant to do so. This can lead to an imbalance of learning and to girls feeling less confident in class.
• Some students process more slowly than others. If the fastest students are consistently providing the answers, those are the ones seen as “smart,” while other students may have more creative or innovative solutions. This can lead to slower/deeper students checking out mentally in class.
• When one student is called on at a time, this leads to one student learning at a time when it’s a simple problem. If it’s a question of sharing strategies or ideas, it works to have students share one at a time, because that’s interesting! But for numerical or simple solutions, other strategies, such as choral response, white boards, or Plickers, can be more effective to collect responses and retain student engagement.

Differentiation. The activity is naturally differentiated.

• Students who know the answer by rote can find other ways to find the same solution.
• Students who are still learning the concept have more time to come up with one strategy.
• Everyone has a chance to feel successful. Even the teacher can participate and learn something.

Rich learning possibilities. When students share their strategies with each other, they may learn much more than with traditional approaches to teaching mental math.

• Students who have made errors can correct themselves and understand why they made that error, possibly preventing the same error in the future.
• Students who did not understand a strategy when it was taught in class might understand it when another student presents it.
• Spending time on multiple strategies can help create stronger neural networks around the concept, making reconnection to the pattern easier in the future.

The Matholia tools can be useful to present a situation for students to consider, or for students to represent their thinking. For example, students who have learned how to add fractions without common denominators might be asked to find the sum of these two fractions.
Alternatively, they could be presented with 3 ÷ 4 and asked to use these tools to represent this fraction as a sum of two or more fractions.

One example of how a number talk might look in a classroom can be seen here. Note that the fist and fingers response is not shown, but the solution strategy sharing is.

Have you tried this approach? Share your experiences with us!
Susan Midlarsky is a Math Consultant, a Curriculum Writer, and is keenly interested in questions related to learning math. You can find out more about her at susanmidlarsky.com.