Supporting Rigorous Mathematics
Teaching and Learning
Shaping Talk in the Classroom:
Academically Productive Talk Features and
Indicators
Tennessee Department of Education
High School Mathematics
Algebra 2
© 2013 UNIVERSITY OF PITTSBURGH
Rationale
Teachers’ questions are crucial in helping students
make connections and learn important mathematics
and science concepts. Teachers need to know how
students typically think about particular concepts, how
to determine what a particular student or group of
students thinks about those ideas, and how to help
students deepen their understanding (Weiss & Pasley,
2004).
By analyzing a transcript of an Accountable Talk®
discussion, participants will consider the benefits to
student learning when the Accountable Talk features
and indicators are present in the Share, Discuss, and
Analyze Phase of the lesson.
Accountable Talk® is a registered trademark of the University of Pittsburgh.
Session Goals
Participants will:
• learn about Accountable Talk features and
indicators; and
• learn about the benefits of using indicators of all
three Accountable Talk features in a classroom
discussion.
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Overview of Activities
Participants will:
• analyze transcripts, identify Accountable Talk
features and indicators, and consider the benefits of
fostering this community; and
• plan for an Accountable Talk discussion.
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Accountable Talk Features and Indicators
• Read the list of Accountable Talk indicators related
to each of the features.
 Accountability to the Learning Community
 Accountability to Knowledge
 Accountability to Rigorous Thinking
• How do the features differ from one another?
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Accountable Talk Features and Indicators
Accountability to the Learning Community
• Actively participate in classroom talk.
• Listen attentively.
• Elaborate and build on each others’ ideas.
• Work to clarify or expand a proposition.
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Accountable Talk Features and Indicators
Accountability to Knowledge
• Specific and accurate knowledge
• Appropriate evidence for claims and arguments
• Commitment to getting it right
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Accountable Talk Features and Indicators
Accountability to Rigorous Thinking
• Synthesize several sources of information.
• Construct explanations and test understanding of
concepts.
• Formulate conjectures and hypotheses.
• Employ generally accepted standards of reasoning.
• Challenge the quality of evidence and reasoning.
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Accountable Talk Discussion
Turn and Talk with your partner about what you would
expect teachers and students to be saying during an
Accountable Talk discussion for each of the features.
− accountability to the learning community
− accountability to accurate, relevant knowledge
− accountability to discipline-specific standards
of rigorous thinking
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Accountable Talk Features and Indicators
Indicators of all three Accountable Talk features need to be
evident in a lesson. Lessons should be:
• accountable to the learning community;
• accountable to knowledge; and
• accountable to rigorous thinking.
Why might it be important to have Indicators of all three
features of Accountable Talk discussions in a conversation?
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Preparing for the Share, Discuss,
and Analyze (SDA) Phase of the
Lesson
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The Structures and Routines of a Lesson
Set Up of the Task
The Explore Phase/Private Work Time
Generate Solutions
The Explore Phase/Small Group Problem
Solving
1. Generate and Compare Solutions
2. Assess and Advance Student Learning
Share, Discuss, and Analyze Phase of the Lesson
1. Share and Model
2. Compare Solutions
3. Focus the Discussion on
Key Mathematical Ideas
4. Engage in a Quick Write
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MONITOR: Teacher selects
examples for the Share,
Discuss, and Analyze Phase
based on:
• Different solution paths to the
same task
• Different representations
• Errors
• Misconceptions
SHARE: Students explain their
methods, repeat others’ ideas,
put ideas into their own words,
add on to ideas and ask for
clarification.
REPEAT THE CYCLE FOR EACH
SOLUTION PATH
COMPARE: Students discuss
similarities and difference
between solution paths.
FOCUS: Discuss the meaning
of mathematical ideas in each
representation
REFLECT: By engaging
students in a quick write or a
discussion of the process.
Triple Trouble
Consider the two functions graphed below. Let ℎ 𝑥 = 𝑓(𝑥) ∙ 𝑔(𝑥)
1. David, Theresa, Manuel, and Joy are working in a
group together to determine the key
characteristics of h(x). They each make a
prediction. Decide whether you agree or disagree
with each student’s prediction. Use mathematics
to justify your position.
• David: h(x) will be a parabola.
• Theresa: h(x) will have a y-intercept at (0, 12).
• Manuel: h(x) will have negative y-values over
the interval −2 ≤ 𝑥 ≤ −1.
• Joy: h(x) will have three x-intercepts.
2. Sketch a graph of h(x) on the coordinate plane.
Then identify key characteristics of the graph
(zeros, y-intercept, max/min values, end behavior)
and explain how each key characteristics results
from key characteristics of f(x) and g(x).
3. Determine the equation of h(x). Justify your
answer in terms of f(x) and g(x).
© 2013 UNIVERSITY OF PITTSBURGH
The CCSS for Mathematical Content
CCSS Conceptual Category – Algebra 2
Building Functions
(F-BF)
Build a function that models a relationship between two quantities
F-BF.A.1
Write a function that describes a relationship between two
quantities.★
F-BF.A.1b
Combine standard function types using arithmetic operations. For
example, build a function that models the temperature of a cooling
body by adding a constant function to a decaying exponential, and
relate these functions to the model.
Arithmetic with Polynomials and Rational Expressions
(A-APR)
Understand the relationship between zeros and factors of polynomials
A-APR.B.3 Identify zeros of polynomials when suitable factorizations are
available, and use the zeros to construct a rough graph of the
function defined by the polynomial.
★Mathematical Modeling is a Standard for Mathematical Practice (MP4) and a Conceptual Category, and specific
modeling standards appear throughout the high school standards indicated with a star (★). Where an entire domain
is marked with a star, each standard in that domain is a modeling standard.
Common Core State Standards, 2010
The CCSS for Mathematical Practice
1.
Make sense of problems and persevere in solving
them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning
of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Common Core State Standards, 2010
Analyzing Student Work
Use the student work to further your understanding of
the task.
Consider:
• What do the students know?
• How did the students solve the task?
• How do their solution paths differ from each other?
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Group A
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Group B
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Group C
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Group D
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Group E
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21
Selecting Students’ Work
The teacher selected work from Groups B and C for the
Share, Discuss, and Analyze Phase of the lesson.
Consider the following:
• Why might the teacher have chosen these pieces of
student work for this lesson phase?
• What mathematical concepts can be targeted by the
teacher using the student work that s/he chose?
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Analyzing Teaching and Learning
Triple Trouble Task Vignettes:
Two classrooms are solving and discussing solution
paths to the Triple Trouble Task.
• Read a short transcript from Classroom A and
Classroom B.
• What are students learning in each classroom?
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Analyzing Teaching and Learning
What is similar and different between the opportunities
to learn in Classroom A and Classroom B?
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The Share, Discuss, and Analyze
Phase of the Lesson
What made it possible for this learning to occur?
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Accountable Talk Features and Indicators
Which of the Accountable Talk features and indicators
were illustrated in the transcript from Teacher A’s
classroom?
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The Share, Discuss, and Analyze
Phase of the Lesson
• In what ways did students engage in an
Accountable Talk discussion?
• What purpose did the Accountable Talk features
serve in the lesson?
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Your Turn
Consider the essential understanding below:
The product of two or more linear functions is a
polynomial function.The resulting function will have
the same x-intercepts as the original functions
because the original functions are factors of the
polynomial.
What would you need to hear from students to know that
they had this understanding?
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Your Turn
At your tables, plan questions and possible student
responses for a classroom discussion that will get at the
essential understanding.
How will you hold them accountable to the learning
community, knowledge, and rigorous thinking?
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Your Turn
• What did you notice about planning questions and
anticipating student responses?
• What are some things you said and did to hold students
accountable to the learning community, knowledge, and
rigorous thinking?
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Step Back: Reflecting on the Benefits
What are the benefits of using Accountable Talk
features and indicators as a tool for reflecting on the
classroom discussion?
For planning?
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