Transcript Document

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 1
© 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.
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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
© 2013 UNIVERSITY OF PITTSBURGH
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.
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No Place Like Home
Two sisters, Janet and Sandy, each represented their
travels from home by sketching their paths on the graph
shown below. The x-axis represents the time of their
journeys in minutes and the y-axis represents the distance
from home in miles.
Sandy
miles
Janet
minutes
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No Place Like Home
1. Decide whether you agree or disagree with each of the
following statements. Support your answer
mathematically, using specific points or time intervals
where appropriate.
a. Janet traveled mostly uphill while Sandy traveled
mostly downhill.
b. Sandy traveled at a faster rate than Janet.
c. Sandy and Janet were at the same place at the
same time once during their journeys.
d. Each girl always traveled at a constant rate.
e. Both girls were at home at some point during their
journeys.
f. Sandy stopped walking at 14 minutes.
g. Each girl’s journey represents a function.
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No Place Like Home Task
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The CCSS for Mathematical Content
CCSS Conceptual Category – Algebra 1
Interpreting Functions
(F-IF)
Interpret functions that arise in applications in terms of the context
F-IF.B.4
For a function that models a relationship between two quantities, interpret key
features of graphs and tables in terms of the quantities, and sketch graphs showing
key features given a verbal description of the relationship. Key features include:
intercepts; intervals where the function is increasing, decreasing, positive, or
negative; relative maximums and minimums; symmetries; end behavior; and
periodicity.★.
F-IF.B.5
Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes. For example, if the function h(n) gives the
number of person-hours it takes to assemble n engines in a factory, then the
positive integers would be an appropriate domain for the function.★
Reasoning with Equations and Inequalities
(A-REI)
Represent and solve equations and inequalities graphically
A.-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y =
f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the
solutions approximately, e.g., using technology to graph the functions, make tables
of values, or find successive approximations. Include cases where f(x) and/or g(x)
are linear, polynomial, rational, absolute value, exponential, and logarithmic
functions.★
★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
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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
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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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Selecting Students’ Work
The teacher selected work from Groups E, 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
No Place Like Home Task Vignettes:
Two classrooms are solving and discussing solution
paths to the No Place Like Home 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 language of change and rate of change (increasing,
decreasing, constant, relative maximum or minimum) can
be used to describe how two quantities vary together
over a range of possible values
What would you need to hear from students to know that
they had this understanding?
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Your Turn continued
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 continued
• 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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