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Let’s Talk – Promoting Mathematical Discourse in the Classroom

Using a Journal Article as a Professional Development Experience
Communication

Title:           Let’s Talk – Promoting Mathematical Discourse in the Classroom
Author:       Catherine C. Stein
Journal:      Mathematics Teacher
Issue:         November 2007, Volume 101, Issue 4, pp. 285-289

Rationale/Suggestions for Use

Communication in the mathematics classroom is vital to students sharing their understanding of concepts and skills, as well as benefiting from each others’ approaches to problem solving. This article provides participants with strategies to use to increase mathematical discourse for all students. This article may be used with pre-service teachers or by in-service teachers interested in exploring ways to increase discourse in their classroom.

Materials

Procedures/Discussion questions

Session One:

Goal: Participants will define student discourse and discussing strategies for increasing student discourse in the classroom.

1. Ask participants to brainstorm the types of mathematical communication their students engage in during class.
• How would you define student discourse?
• Make two lists (chart these) – title one list “IS considered student discourse” and the other list “IS NOT considered student discourse” Ask participants to brainstorm specific examples of classroom interactions for both lists.

Examples of what “IS considered student discourse”

• Students write in their journals about their mathematical reasoning or processes.
• A student states, “I see a pattern that I think will always work, because each number is 3 more than the one before it.”
• A group of students discuss the mathematical conditions in which an idea will or won’t always work.

Examples of what “IS NOT considered student discourse”

• The teacher provides instructions to the class about an activity they are about to engage in.
• The teacher provides a counter example to a method posed by a student.
• A student asks a question about nonmathematical procedures related to an assignment, such as when the assignment is due, whether students need to show their work, etc.
1. Extend the discussion with the following questions:
• What expectations and norms do you currently have related to classroom communication/discourse? How do you communicate those expectations and norms?
• How do you know if the communication/discourse is successful?
2. Have participants read the entire article and highlight 5 big ideas that are particularly interesting to them.
• In groups of four, ask participants to share one of the ideas they highlighted and why they think it is important. Continue with each participant sharing one of their ideas until all ideas are heard and/or until the facilitator calls time.
• Ask each table group to now discuss the ideas that came up at their table and come to consensus on the top five ideas they would like to share with the whole group and to write these on chart paper.
• Post the charts and facilitate a whole groups discussion about where they see similar ideas, something they have a question about, something that is unique, etc. (The goal here is to have a whole group discussion, but not have each group read their chart.)
• Discuss additional ideas for establishing expectations and norms in the classroom and for measuring the success of student discourse.
3. Using the chart on page 288, ask participants to assess the predominant level of discourse for each of their classes (0-3). With a partner, share your assessment and/or consider, “Where is it most difficult to make the move – from level 0 to 1, level 1 to 2, or level 2 to 3?” Then facilitate a whole group discussion beginning with asking for opinions about where it is most difficult to make the move, followed with questions such as: “What are some of the obstacles/issues that hinder a high level of discourse in your classes?” “What can you do to overcome these obstacles?”
4. Return to the lists created in #1 and revise/edit them as needed.
5. Now split the group into two jigsaw expert groups: give one group the article “Connecting Research to Teaching - Making the Right (Discourse) Moves: Facilitating Discussions in the Mathematics Classroom” and give the other group the article “Making the Most of Mathematical Discussions.”
6. Provide time for individuals to read their article. While reading they should reflect on the following:
• What strategies shared in the article will assist in increasing the level of discourse in the classroom? Be prepared to discuss how the strategy works and how it increases discourse.
• How does the implementation of that strategy impact my role in the classroom?
7. Have participants meet in expert groups and discuss their respective articles. They should be prepared to give a brief overview of the article and discuss their thinking about the reflection questions. Give each group a piece of chart paper and have them record all the strategies mentioned in the article that can assist in increasing the level of discourse in the classroom.
8. Reorganize the expert groups into groups of four with two members from each of the article expert groups. Provide 5-8 minutes for each pair to share the ideas from their article with the other pair.
9. After groups have finished their discussions, draw together the entire group and ask what questions still remain about the levels of student discourse and/or strategies to increase the level of student discourse. Ask participants to select 1-2 other participants with whom they will work between now and the next session. Pairs should select one strategy they would like to work on between now and the next session. (The purpose is to be able to support each other in the work by selecting the same strategy as their partner.) Explain the “assignment.”

Next Steps/Extensions

Have the participants select one of the strategies from the list and incorporate it into their classroom. Just before the next meeting, each partner should observe one class of the other partner.  During the observation, the partner should sit with a small group of students and scribe all student conversations that represent student discourse (refer back to the original list of what “is” considered student discourse.) Emphasize that the partner is not observing the teacher, but rather gathering data so the teacher can determine the effectiveness of the strategy they are implementing. Participants should bring two copies of their student data to the next meeting.

Session Two:

Goal: Participants will analyze student data to assess the level of student discourse observed and consider implications for their practice.
Note: You will need to make copies of the student discourse indicators (at the end of this document)

1. Open the session with some discussion about their experiences as observers scribing student discourse. “What did you learn as a result of listening to student discourse?” “Any strategies or suggestions to others as they scribe student discourse in the future?”
2. Working with their partner, provide about 10 minutes to “sort” through one person’s data (each partner should have a copy) and identify 3-5 examples of each level of student discourse. They can indicate the code (PF, J, or G – see chart below) beside the student data.
3. After a given amount of time, partners should switch and similarly analyze the other partner’s discourse data.
4. Ask each person to consider their own data and the strategy they were implementing to increase student discourse and to reflect on the following questions in writing.
• What mathematical ideas do students understand? What is your student discourse evidence of this understanding?
• What mathematical ideas are students struggling with? What is your student discourse evidence of this struggle?
• Based on this data sample, how would you classify the level of student discourse along the continuum from procedures/facts to generalization?
• What was surprising or unexpected about students’ thinking and what might be the reason for this?
• How did the implementation of the strategy you were working on effect the level of student discourse and how might you refine your work based on this student data sample?
5. In whole group, ask the participants to share (use a go-around so everyone has an opportunity to share) one professional learning from the experience of implementing a strategy and analyzing student discourse data.
6. Extend this conversation to include some discussion of the strategies and suggestions for each other around the implementation of the strategies.  Ask, “What changes do you plan to make in your classroom practice as a result of this experience?”

Discourse Level Indicators:

Procedures/Facts (P/F)

• Short answer to a direct question
• Restating facts/statements made by others
• Showing work/methods to others
• Explaining what and how
• Questioning to clarify
• Making observations/connections

Justification (J)

• Explaining why by providing mathematical reasoning
• Challenging the validity of an idea by providing mathematical reasoning
• Giving mathematical defense for an idea that was challenged

Generalization (G)
Using mathematical relationships as the basis for:

• Making conjectures/predictions about what might happen in the general case or in different contexts
• Explaining and justifying what will happen in the general case

Connections to Other NCTM Publications