## What is a Number Talk?

In order to build numerical reasoning in our students, Number Talk is an essential part of the math block, which Parrish (2010) explains is anywhere from 5 to 15 minutes. In my first year of teaching, I struggled to understand why so many of my students did not understand or remember how to use operations. Specifically, many of them, for example, would forget how to approach multiplication or division. It also reminded me of working with at-risk youth a few years back and having the same experience with them around number sense and numeration. As a result, I went on a mission to find something that allowed me to teach the curriculum and move towards other topics, while also being able to remediate and reinforce numbers. Fortunately, I first read about Number Talks on The Brown Bag Teacher and fell in love with the idea. While there are several ways to alternate this so it suits the dynamics of the classroom, The Brown Bag Teacher is still quite useful to get an understanding of Number Talk and how to start them in your own classroom.

Then, what exactly is a Number Talk? I read an explanation written by Kathy Richardson that sums it up best, "Number Talk comes from inspiring each child to think and make sense of mathematics they are presented." It essentially provides a space for students to have an ongoing practice of computation. The teacher's role is to guide the conversation rather than to dictate the conversation. Number Talk also keeps the students on their toes because it is a structured, yet unpredictable process. There are so many ways to approach a concept or problem that students learn from each other. For example, when I first started teaching, some students I worked with could spew the answer in a second regardless of what numbers were in front of them. Others took time to use their tables to sort through their answer. A few used a concept similar to how a teacher from Sparkles Online School teaches multiplication. The problem is the same, but the approaches are vastly different. According to Sun, Baldinger, & Humphreys (2018), "The focus of a Number Talk is primarily on supporting students as they explain their ideas and why their strategies make sense, rather than focusing only on the correct answer" (p. 49). Thus, this research reiterates the fact that math can be approached from different angles.

Chapin, O'Connor, & Anderson (2003) suggest that there are several formats for Number Talks. Traditionally, Number Talks occur in a whole class discussion. Here, the teacher focuses on student thinking and reasoning, encouraging students to become comfortable with discussing different approaches and strategies. Number Talks can also occur in small groups, where the teacher circulates around the classroom rather than acting as a facilitator. However, the teacher can participate and support the small groups, as a way to keep students on task. Partner Talk is another format, where students share their ideas with a partner similar to the talk-and-turn strategy.

Clearly, there are several benefits to Number Talks. Sun, Baldinger, & Humphreys (2018) suggest that Number Talks make sense of quantity and mathematical relationships. Parrish (2010) identifies five major benefits of sharing and discussing computation strategies. These include students having the opportunity to clarify thinking, considering several strategies, investigating mathematical relationships, building a foundation of strategies, and thinking about the most efficient strategy.

Planning for a number talk should not take too long either. I suggest using a data driven approach to plan for a number talk. Scan throw the data and focus on the major concepts/theories that students struggle with or where a majority of them show signs of misconception. Then build the rigour of the question as students grasp the concept or theory better through a series of number talks. In addition to the two examples provided below, the Elementary Math website has two resources that I really find useful; one on addition/subtraction strategies and another on multiplication/division strategies.

Now, with that basic understanding of a Number Talk, what does it look like through an example? Let's take a look.

Then, what exactly is a Number Talk? I read an explanation written by Kathy Richardson that sums it up best, "Number Talk comes from inspiring each child to think and make sense of mathematics they are presented." It essentially provides a space for students to have an ongoing practice of computation. The teacher's role is to guide the conversation rather than to dictate the conversation. Number Talk also keeps the students on their toes because it is a structured, yet unpredictable process. There are so many ways to approach a concept or problem that students learn from each other. For example, when I first started teaching, some students I worked with could spew the answer in a second regardless of what numbers were in front of them. Others took time to use their tables to sort through their answer. A few used a concept similar to how a teacher from Sparkles Online School teaches multiplication. The problem is the same, but the approaches are vastly different. According to Sun, Baldinger, & Humphreys (2018), "The focus of a Number Talk is primarily on supporting students as they explain their ideas and why their strategies make sense, rather than focusing only on the correct answer" (p. 49). Thus, this research reiterates the fact that math can be approached from different angles.

Chapin, O'Connor, & Anderson (2003) suggest that there are several formats for Number Talks. Traditionally, Number Talks occur in a whole class discussion. Here, the teacher focuses on student thinking and reasoning, encouraging students to become comfortable with discussing different approaches and strategies. Number Talks can also occur in small groups, where the teacher circulates around the classroom rather than acting as a facilitator. However, the teacher can participate and support the small groups, as a way to keep students on task. Partner Talk is another format, where students share their ideas with a partner similar to the talk-and-turn strategy.

Clearly, there are several benefits to Number Talks. Sun, Baldinger, & Humphreys (2018) suggest that Number Talks make sense of quantity and mathematical relationships. Parrish (2010) identifies five major benefits of sharing and discussing computation strategies. These include students having the opportunity to clarify thinking, considering several strategies, investigating mathematical relationships, building a foundation of strategies, and thinking about the most efficient strategy.

Planning for a number talk should not take too long either. I suggest using a data driven approach to plan for a number talk. Scan throw the data and focus on the major concepts/theories that students struggle with or where a majority of them show signs of misconception. Then build the rigour of the question as students grasp the concept or theory better through a series of number talks. In addition to the two examples provided below, the Elementary Math website has two resources that I really find useful; one on addition/subtraction strategies and another on multiplication/division strategies.

Now, with that basic understanding of a Number Talk, what does it look like through an example? Let's take a look.

## Example 1: Apples & Pears

Using the above image taken from Math is Visual, show the students an image with a visual representation of fruits for a total of three seconds. Then, ask students to guess how many fruits they saw in the image. As students share their guesses, write them down on the board or on a flip chart. Reveal the visual representation and tape it alongside the guesses. Now, the Number Talk commences. Ask students to share their thoughts on how they were able to guess the number 10, pointing out the strategies they used as well.

The following are a few strategies that students might consider:

The following are a few strategies that students might consider:

- Counting by 1s
- Counting by 2s
- Joining (4+6 or 6+4)
- Joining (5+5)
- Removing (10-6 or 10-4)
- Subitizing

## Example 2: Find the Sum

Show students an addition number sentence like the one in the image below. Ask students to take a minute to think about the answer, thinking of different ways they can solve this problem using different strategies.

Here, some students may solve 18 + 5 by counting on or joining. Other students may use the number chart or the number line to find 23. The notion behind a number talk is to have students discuss and share their approaches, providing their thought processes with their peers.

## What are Number Strings?

In a Number Talk, the focus is on one specific problem whereas Number Strings focus on a series of related problems, where one leads into another using a specific strategy. In the Number Talk, the facilitation allows for students to discuss and think about a range of strategies (e.g. 9 + 9 is solved using doubles or a ten frame). Conversely, in the Number Strings, the facilitation focuses on guiding students through a series of problems using a particular strategy.

The Teaching Channel provides a wonderful video of a Grade 4 classroom engaged in a Number Strings session, where the teachers uses one division problem (e.g. 300/3) using place values to divide a larger number. Another one is an example of a Grade 3 classroom, using number strings to explore multiplication strategies.

The Teaching Channel provides a wonderful video of a Grade 4 classroom engaged in a Number Strings session, where the teachers uses one division problem (e.g. 300/3) using place values to divide a larger number. Another one is an example of a Grade 3 classroom, using number strings to explore multiplication strategies.

## Talk Moves

Through both examples of the Number Talks above and an understanding of Number Talks in general, it is also important to think about ways to encourage students to actually participate (i.e. talk) during the session. Chapin, O'Connor, & Anderson (2003) suggest using talk moves to strengthen Number Talks. Talk Moves include revoicing, restating, applying own reasoning, prompting for participation, and wait time.

Revoicing |
This talk move is used to paraphrase what a student has said about their approach to solving the Math Talk problem. This helps students clarify their own thoughts and helps other students build clarify as well. |

Restating |
Here, another student is asked to restate the student's thinking in their own words. This ensures that the listeners are processing the information while also providing reassurance to the student who has shared the idea. |

Applying own Reasoning |
In order to build critical thinking in math, students are asked to apply their own reasoning to another student's approach. For example, you can ask, "Do you agree or disagree with that? What evidence do you have or how can you show that?" |

Prompting for Participation |
The teacher should actively prompt students to share their ideas. In addition, it can also be useful to encourage students to add on to other ideas. |

Wait Time |
This is the time provided to students to think about the question. Chapin, O'Connor, & Anderson (2003) suggest giving at least 10 seconds for the wait time. |

## References

- Chapin, S., O'Connor, C., & Anderson, N. (2003). Classroom discussion using math talk to help students learn. Math Solutions Publication. Sausalito, California.
- Parrish, S, (2010). Number talks: helping children build mental math and computation strategies. Math Solutions Publication. Sausalito, California.
- Sun, K.L., Baldinger, E.E. & Humphreys, C. (2018). Number talks: gateway to sense making. Mathematics Teacher, 112(1). The National Council of Teachers of Mathematics.

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