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
Geometry
© 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.
© 2013 UNIVERSITY OF PITTSBURGH
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.
Midsegments Task
A midsegment is a
segment that connects the
midpoints of two sides of a
triangle.
1. Draw a triangle on the
coordinate plane and
label the coordinates of
the vertices. Draw and
label the coordinates of
the midpoints of the
sides and then draw the
three midsegments.
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Midsegments Task (continued)
2. Analyze the relationship between the midsegments and the sides of the
triangles. What conjectures can you make? Support your conjectures
with mathematical evidence and compare your findings with the findings
of partners.
3. Marco’s group made the five conjectures listed below.
• The three midsegments of a triangle always have the same
length.
• A midsegment is parallel to the side of the triangle that it does not
intersect.
• The three midsegments of a triangle form an acute triangle.
• The length of the midsegment is half the length of the side of the
triangle that it does not intersect.
• The three midsegments create four congruent triangles.
a. Determine which conjectures are incorrect. For these conjectures,
describe a triangle that Marco may have drawn for which this
statement holds true. Then describe a counterexample for which the
statement is false.
b. Determine which conjectures are true. Describe using words,
diagrams, or symbols why the conjecture is a true statement.
© 2013 UNIVERSITY OF PITTSBURGH
The CCSS for Mathematical Content
CCSS Conceptual Category – Geometry
Expressing Geometric Properties with Equations
(G-GPE)
Use coordinates to prove simple geometric theorems
algebraically
G-GPE.B.4 Use coordinates to prove simple geometric theorems
algebraically. For example, prove or disprove that a figure
defined by four given points in the coordinate plane is a
rectangle; prove or disprove that the point (1, √3) lies on the
circle centered at the origin and containing the point (0, 2).
G-GPE.B.6 Find the point on a directed line segment between two given
points that partitions the segment in a given ratio.
G-GPE.B.7 Use coordinates to compute perimeters of polygons and
areas of triangles and rectangles, e.g., using the distance
formula.★
★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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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?
© 2013 UNIVERSITY OF PITTSBURGH
Analyzing Teaching and Learning
Midsegments Task Vignettes:
Two classrooms are solving and discussing solution
paths to the Midsegments 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?
© 2013 UNIVERSITY OF PITTSBURGH
Your Turn
Consider the essential understanding below:
Using coordinates of a midsegment of a triangle
justifies that the midsegment is parallel to the side
that it does not intersect because the slope of the
segment containing the midpoints is the same as the
slope of the segment connecting the endpoints of the
third side of the triangle.
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?
© 2013 UNIVERSITY OF PITTSBURGH
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?
© 2013 UNIVERSITY OF PITTSBURGH
Step Back: Reflecting on the Benefits
What are the benefits of using Accountable Talk
features and indicators as a tool for reflecting on
classroom discussion?
For planning?
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