Let’s Talk – Promoting Mathematical Discourse in the
Classroom
Using a Journal Article as a Professional Development Experience
Communication
Title:
Author:
Journal:
Issue:
Let’s Talk – Promoting Mathematical Discourse in the Classroom
Catherine C. Stein
Mathematics Teacher
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
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Copies of each article for participants
Article, “Let’s Talk – Promoting Mathematical Discourse in the Classroom”
Connecting Research to Teaching - Making the Right (Discourse) Moves:
Facilitating Discussions in the Mathematics Classroom, G.T. Springer and
Thomas Dick, September 2006, Volume 100, Issue 2 pp. 105-109
Making the Most of Mathematical Discussions, Megan Staples and Melissa M.
Colonis, November 2007, Volume 101, Issue 4
Chart paper
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”
o
o
o
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”
o
o
o
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.
2. 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?
3. 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.
4. 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?”
5. Return to the lists created in #1 and revise/edit them as needed.
6. 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.”
7. 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?
8. 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.
9. 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.
10. 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)
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Short answer to a direct question
Restating facts/statements made by others
Showing work/methods to others
Explaining what and how
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Questioning to clarify
Making observations/connections
Justification (J)
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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:
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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
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Breyfogle, M. L., & Herbel, B. A. (2004, April). Focusing on students’
mathematical thinking. Mathematics Teacher, 97, 244-247.
Choppin, J. M. (2007, November). Teacher orchestrated classroom arguments.
Mathematics Teacher, 101, 306-310.
Fernsten, L. A. (2007, November). A writing workshop in mathematics:
Community practice of content discourse. Mathematics Teacher, 101, 273-278.
Himmelberger, K. S., & Schwartz, D. L. (2007, November). It’s a home run:
Using mathematical discourse to support the learning of statistics. Mathematics
Teacher, 101, 250-255.
Kitchen, R. S. (2004, January). Challenges associated with developing discursive
classrooms in high-poverty, rural schools. Mathematics Teacher, 97, 28-31.
Koellner-Clark, K., Stollings, L. L., & Hoover, S. A. (2002, December). Socratic
seminars for mathematics. Mathematics Teacher, 95, 682-687.
Kotsopoulos, D. (2007, November). Mathematics discourse: It’s like hearing a
foreign language. Mathematics Teacher, 101, 301-305.
Manouchehri, A. (2007, November). Inquiry-Discourse mathematics instruction.
Mathematics Teacher, 101, 290-300.
Manouchehri, A., & Lapp, D. A. (2003, November). Unveiling student
understanding: The role of questioning in instruction. Mathematics Teacher, 96,
562-566.
Manouchehri, A., & St. John, D. (2006, April). From classroom discussion to
group discourse. Mathematics Teacher, 99, 544-551.
Mason, R. T., & McFeetors, J. (2002, October). Interactive writing in
mathematics class: Getting started. Mathematics Teacher, 95, 532-536.
McIntosh, M. E., & Draper, R. J. (2001, October). Using learning logs in
mathematics: Writing to learn. Mathematics Teacher, 94, 554-557.
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Stein, M. K. (2001, October). Mathematical argumentation: Putting umph into
classroom discussions. Mathematics Teaching in the Middle School, 7, 110-112.
St. John, D., & Manouchehri, A. (2006, April). From classroom discussions to
group discourse. Mathematics Teacher, 99, 544-551.
Truxaw, M. P., & DeFranco, T. C. (2007, November). Lessons from Mr. Larson:
An inductive model of teaching for orchestrating discourse. Mathematics
Teacher, 101, 268-272.
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