Overview

Session Focus

This session focuses on facilitating discussions, which are a key aspect of students’ mathematics learning. You will watch videos of discussions, complete activities, and read about ways to foster whole-class discussions in which each and every student has opportunities to:

• Articulate mathematical ideas and develop mathematical language
• Share different approaches to solving a problem and analyze why they work (or don't)
• Pose conjectures and identify evidence to support them
• Use representations to describe mathematical relationships
• Compare and connect ideas, representations, and solutions
• Consider and question each other's ideas

Reflect on your own experience facilitating math discussions with students. Share your thoughts about the following questions on the Overview Forum: What do you believe makes discussions successful? What are some of the challenges?

Activity 1: Establishing a Mathematics Community that Supports Discussion

This activity focuses on ways to support equitable participation in whole class discussions. You will watch a video about the connections between student participation in discussions and students’ sense of agency and ownership in the math learning community. You will also consider ways to gather data about student participation in discussions and take action to promote equitable participation based on this data.

What is Equitable Participation?

We believe that equitable participation means that:

• Every student has the opportunity to express their ideas, to revise and build on them.
• Every student has the opportunity to have others respectfully listen to and engage with their ideas, and to be seen as a mathematical thinker who makes meaningful contributions to classroom conversations.

All students' ideas should be a part of the public discourse, including those who do not feel confident about their math or communication skills and those who opt to stay on the periphery.

Supporting Equitable Participation in Math Discussions

Listen as author Kassia Omohundro Wedekind, author of the book Hands Down, Speak Out: Listening and Talking Across Literacy and Math K-5, talks about the connections between participation in discussions and students’ sense of agency and ownership within the learning community.

To access the video, click on the link below.

https://www.youtube.com/watch?v=ZNSYWdCDJo0

Which of the ideas offered in this video might you try out in your classroom?

Gathering and Reflecting on Data About Student Participation in Math Discussions

As Kassia Omohundro Wedekind comments, regularly gathering data about who is and is not participating in discussions, and the different forms of participation students use, can be extremely informative. Reflecting on the patterns this data reveals and using this information to assess one’s own practice and take action is a powerful way to encourage and support equitable participation.

Read more about ways to gather and use data about student participation in math discussions in this blog post.

What new ideas does this blog raise for you? How will you learn more about student participation in your math classroom?

Activity 2: Preparing for Productive Mathematical Discussions

In this activity, you will consider ways to prepare for mathematical discussions that are rooted in student thinking. You will move through a set of steps for planning and structuring discussions that focus on developing knowledge of the mathematical content and examining student thinking about that content. This set of steps is adapted from the book 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret Smith and Mary Kay Stein. If you are interested in learning more about the 5 practices, you can listen to this interview with one of the authors, from the podcast Kids Talk Math.

Establishing Student Learning Goals

Establishing a clear mathematical goal (or goals) is a critical first step when planning discussions. Considering the key mathematical ideas and relationships that students have been exploring and how to highlight them in the discussion informs every other step of the planning process.

Select ONE of the following lessons from the Investigations 3 curriculum. Review the lesson, taking note of the Math Focus Points that appear at the top of the first page, and Math Focus Points for Discussion that appear at the beginning of the discussion section.

Kindergarten lesson about subtraction	3rd grade lesson about division

What are the math focus points for the session and for the discussion that you reviewed?

Doing the Mathematics and Anticipating Student Strategies

Actively envisioning how students might solve a problem and anticipating student strategies, supports mathematical discussions. It is important to solve the problem(s) that will be discussed in as many ways as possible. Some teachers also find it useful to work with colleagues to identify a range of possible student strategies.

Solve the problem that is featured in the discussion in the lesson that you reviewed, in more than one way. Record your solutions on a separate sheet of paper.

Click on the image of the problems to enlarge them.

Kindergarten problem	3rd grade problem

How do you envision students might approach the problem you solved? What misconceptions might arise as students work on this problem?

Observing Students at Work and Selecting Student Work for Discussion

Observing what students do and say as they solve problems, asking questions to uncover their thinking, and helping students clarify and articulate their ideas can help teachers determine what or whose work to focus on during the discussion. When selecting student work to share during a discussion, teachers should consider student work that will advance the mathematical ideas under investigation. This work should represent the range of understanding in the class and allow for a range of learners to share and comment.

Consider the math focus points for the discussion you reviewed.

Look through the set of student work that corresponds with the problem you solved and the lesson you reviewed. As you look through the work, consider the following questions:

• What are the basic approaches to solving this problem that students are using?
• Is there a difficulty or misconception that many students are having? If so, what is it?
• Which students have ideas or approaches that you think should be shared?
• Which pieces of student work could help the teacher address the math focus point(s) for discussion?

Select 2-3 pieces of work that you might want to share during the discussion outlined in the lesson you reviewed and decide how you might sequence the work if you were facilitating a discussion about this work.

Grade K Student Work

Grade 3 Student Work

Please share which pieces of student work you selected and why on the Student Work Forum. Also share how you would sequence this work in a discussion and why.

Watch as this Grade 2 teacher observes his students at work and selects work for the upcoming discussion, which you will see in Activity 3. As you watch, pay particular attention to the teacher's moves and jot down some notes in response to the following questions:

• What kinds of questions does he pose to elicit how students solved the problem?
• What considerations do you think he is making as he moves about the classroom and selects students to check in with?

Activity 3: Facilitating Productive Mathematical Discussions

This activity focuses on facilitating discussions that focus on students’ mathematical ideas. You will watch videos and read about different ways to support students as they share their solutions, and to help students make connections and build on each other’s mathematical ideas.

Watch the following clip of a mathematics discussion in this 2nd grade class.

How did this teacher choose to sequence student work in this discussion? How does he help students draw connections between their solutions and others’ solutions?

Supporting Meaningful Student Participation

There are several ways that teachers can support meaningful student participation in discussions. Depending on the learning goals, a teacher may choose to structure the discussion in a variety of ways, to highlight and build upon students’ ideas.

Read the following article by Allison Hintz and Elham Kazemi about how open and targeted sharing can be used to foster discussions that build on students’ understandings of key mathematical content. As you read, consider the following question: What are some of the ways that teachers can support students as sharers and as listeners during classroom discussions?

Watch the following video in which Judy Storeygard discusses different strategies for making the mathematics accessible to all students during discussions.

Consider the activities and resources you engaged with during this session. What new ideas have been raised for you regarding including all learners in discussions?

Forums

• Return to the Facilitating Math Discussions Forum and read posts from other participants. Respond to at least one post that is of interest to you.
• Look through the Student Work Forum for the grade band you selected. Read the posts and comment on at least one post that is of interest to you.

Key Takeaways

• Equitable participation in discussions means that each and every student has the opportunity to  express their ideas and to revise and build on them. In equitable discussions, every student has the opportunity to have others respectfully listen to and engage with their ideas, and to be seen as a mathematical thinker who makes meaningful contributions to classroom conversations. One way teachers can promote equitable participation is by gathering data about who is participating in discussions, reflecting on that data, and incorporating what they learn into their teaching..
• Math discussions that support and engage the range of learners are structured around 1-2 targeted math ideas that relate to the mathematics students worked on during the session.
• Anticipating how students might solve a problem, observing students at work, selecting and sequencing specific pieces of work or students’ strategies to share, and considering how to facilitate connections between and among these examples, are all part of the planning process for facilitating math discussions that focus on student thinking and help move student thinking forward.