Using Productive Classroom Talk in
Mathematics Content Courses for Elementary
and Special Education Teachers
Suzanne H. Chapin
Boston University
Framingham State College
April 3, 2008
The Essential Questions??

What content should be in each course?

What methods do we want to emphasize?

How do we balance content and
methods?
BU Course Offerings

MA 107 Elementary Math I

Number and Operations
• 4 credits

MA 108 Elementary Math II

Geometry and Algebra
• 4 credits
To Little Time …….

How do we fit methods into content
courses?
Model the desired methodology
 Require students to practice the methodology
 Focus on teaching and learning with
understanding
 Use assignments that connect content to the
classroom

Extensive Use of Discourse

Discussions

Partner talk

Presentations

Written explanations
What is Productive Talk?

Productive talk is classroom talk by
students and teachers that supports
the development of students’
reasoning and students’ abilities to
express their thoughts clearly.
All academically productive talk is
talk about academically important
content.
Why Use Productive Talk?
To learn mathematics content
Why Use Productive Talk?

To strengthen and expand students’
reasoning in all subject areas
“I think there are an infinite number of
degrees possible [in a circle], because you
can think of the degrees like wedges that get
smaller and smaller, so more and more fit
in.”
Improve Reasoning Skills
Logical reasoning can be
strengthened and taught.
Claim

Evidence
or
Counterexample
Self Reflection About Knowledge
Getting students to talk about
academic ideas or procedures can
bring to the surface their gaps in
understanding: they may realize that
they don’t understand.
“I’m really confused by what you just said. Could you
repeat it?”
Address Misconceptions
Talk allows teachers to hear students’
misconceptions and identify what
students do and don’t understand.
Teacher: “So you are saying that one-sixth is larger
than one-third because six is bigger than 3?”
Student 1: “Yes, I just look at the bottom number in a
fraction and I can decide right away.”
Create a Community of Learners
Talking about ideas and procedures exposes
students to what other students think about
these same concepts.
Student 2: “I think that one-sixth is smaller than onethird. One-sixth means you cut a pizza into six
pieces. One of those pieces is smaller than if you cut
the pizza into three pieces.”
Student 1: “What if it isn’t pizza? Isn’t pizza special?
It seems like one-sixth should be more.”
Enhance Student Engagement
Allowing students to talk
about academic thinking
and problem solving gives
them more to observe,
more to listen to, and more
chances to participate.
Develop Students’ Language Skills
• the ability to produce precise and full
descriptions;
• the ability to understand and analyze complex
texts and problem situations;
• the ability to clearly externalize their thinking;
and
• the ability to acquire and use new vocabulary.
Provide Motivation to Learn
It is hard work to
communicate
clearly. Knowing
that others are
listening and
trying to make
sense of what
you say is a
source of
motivation to
make the effort.
Normative Practices
• Respectful discourse


Students set the rules
Consistency
• Equitable participation
Call on everyone
 Students practice with a partner or group

What do we talk about?






Concepts and relationships
Procedures
Representations
Strategies
Types of reasoning
Vocabulary, symbols, conventions
How Do We Talk —Productive Talk Moves

Revoicing

Repeating
Reasoning
 Do you agree or disagree? Why?
Further participation
 Who would like to add to this discussion?
Wait time



Talk Moves: Revoicing
Revoicing is a talk move that
enables teachers to deal with
the inevitable lack of clarity of
many student contributions.
“So you’re saying …….?
Is that right?”
Talk Moves: Repeating
Repeating is a talk move where students repeat
or paraphrase what others have said.
Repeating slows down the pace of the conversation,
providing more time to process the information.
Repeating provides evidence that other students
heard the contribution and can participate.
Repeating provides a student with evidence that
his or her thinking is taken seriously.
Talk Moves: Agree or Disagree?
This talk move focuses on students’
reasoning about another’s claim.
It is critical that the teacher ask for
justification.
“Do you agree or disagree
with Carlos? Why?”
Talk Moves: Further Participation
This talk move is used to bring students into a
discussion. It reinforces the idea that everyone’s
contribution is important and valued.
Students often state the same
information as their peers, illustrating
the need for each individual to make
sense of the ideas and procedures.
Fall Semester

Introduce productive talk methodology
including talk moves

Read and discuss “Teaching and Learning with
Understanding”





Tasks
Tools
Structuring and applying knowledge
Reflection and articulation
Making mathematical knowledge one’s own
Fall Semester — Students

Complete small math projects

Watch and discuss short video clips of
students solving problems (in class)

Students read and discuss articles about
learning with understanding

Solve problems and exercises
Spring Semester

Students study mathematics curriculum
materials to see if they support learning with
understanding

Students analyze video clips of student
thinking

Students continue talking about mathematics
and solving problems
Examples of Talk Topics

Which fractions can be represented as terminating
decimals? Why?

Is the sum of two odd numbers even or odd? Why?

Explain why the standard algorithm for multiplication of
2-digit by 2-digit numbers works.

Examine three different definitions of the term,
“function.” What do the definitions mean? Define a
function in your own words.
Examples of Methodology

Explain the mathematics that a child is using when she
solves 9 + 4 by changing the problem to 10 + 3. How
might you support this strategy?

What concrete models are used to teach base 10
concepts? What are the advantages and disadvantages
of each model?

What will you do when a child states that there are no
numbers between 5.7 and 5.8? Reflect on activities you
did in class and for homework.
Required Textbooks

A Problem Solving Approach to Mathematics for Elementary
School Teachers
Billstein, Libeskind, and Lott

Math Matters: Understanding the Math You Teach
Chapin and Johnson

Classroom Discussions: Using Math Talk to Help Students Learn
Chapin, O’Connor, and Anderson

Thinking Mathematically: Integrating Arithmetic & Algebra in
Elementary School
Carpenter, Franke, and Levi
For More Information

Contact Suzanne Chapin at schapin@bu.edu

Resources:

How Students Learn: Mathematics in the Classroom (2005). Donovan
& Bransford (Eds.). National Academy Press.

Making Sense: Teaching and Learning Mathematics with
Understanding (1997). Hiebert et.al. Heinemann.

Adding It Up: Helping Children Learn Mathematics. (2001).Kilpatrick,
Swafford & Findell (Eds.). National Academy Press.

Mathematics Classrooms that Promote Understanding. (1999).
Fennema & Romberg (Eds). Erlbaum.