# Dot Talks

• What are Dot Talks?

Dot Talks are short routines, approximately 15 minutes, in which students are asked to look at a collection of dots and think about how many dots there are without counting them one by one. There are multiple ways to see the dots and no one way is better than another. The focus of this routine is on students becoming comfortable with sharing their different ways of thinking with one another and developing an understanding that there are many ways to see (and do!) things in mathematics.

Jo Boaler, Professor of Mathematics Education at Stanford University,  writes that Dot Talks are “a powerful learning activity that shows students:

• creativity in math
• the visual nature of math and
• that there are many different ways people see math. [and]
• they also help to develop an important part of the brain called the Approximate Number System.”

Before a Dot Talk, it is very helpful to think about possible ways students might see the dot collection you will present, as well as how you might record their thinking. Below is an example of the recording of 3 different ways to “SEE” a collection of 7 dots.

There are many more ways to see this collection of dots. Try it for yourself: Find and record at least 3 additional ways of seeing this collection. Please note the use of color, which can be helpful for many students.

General Outline for a Dot Talk

1. Post the collection of dots for all students to see.
2. Provide wait time for students to mentally determine the number of dots, as well as to think about how they might explain their thinking.
3. Encourage students to think of more than way to see the dots.
4. Teacher records all the possible numbers of dots generated by the students, without judgment.
5. Select a student to share how they saw the dots.
6. Record the student's thinking geometrically.
7. Record the matching expression.
• Be sure to record the student's thinking as precisely as possible, both in your geometric representation and in the matching expression.
•  As you record, you might ask: Am I representing your thinking correctly? Is this how you saw the dots? Is this how you thought about how many dots there were?
8. Repeat, having multiple students share as time and interest allows.
9. To close, ask students to look across the various strategies, make connections between them, and reflect on new learning.

Some questions you might ask to help students describe their thinking:

• How many dots do you see?
• How did you SEE the dots?
• What’s another way to SEE the dots?
• Where do you see the ___ dots?
• Do you see the ___ dots on the left or the right? On the top or the bottom?
• How did you think about how many dots there are? What did you do first? next? last?