Transcript Mathematical Tasks: The Study of Equivalence November 18

Supporting Rigorous Mathematics
Teaching and Learning
Using Academically Productive Talk Moves:
Orchestrating a Focused Discussion
Tennessee Department of Education
Middle School Mathematics
Grade 7
© 2013 UNIVERSITY OF PITTSBURGH
Rationale
Mathematics reform calls for teachers to engage students in
discussing, explaining, and justifying their ideas. Although
teachers are asked to use students’ ideas as the basis for
instruction, they must also keep in mind the mathematics
that the class is expected to explore (Sherin, 2000, p. 125).
By engaging in a high-level task and reflecting on ways in
which the facilitator structured and supported the discussion
of mathematical ideas, teachers will learn that they are
responsible for orchestrating discussions in ways that make
it possible for students to own their learning, as well as for
the teacher to assess and advance student understanding
of knowledge and mathematical reasoning.
Session Goals
Participants will:
• learn about Accountable Talk® features and indicators
and consider the benefit of all being present in a
lesson;
• learn that there are specific moves related to each of
the talk features that help to develop a discourse
culture; and
• consider the importance of the four key moves of
ensuring productive discussion (marking, recapping,
challenging, and revoicing).
© 2013 UNIVERSITY OF PITTSBURGH
Accountable Talk® is a registered trademark of the University of Pittsburgh
Overview of Activities
Participants will:
•
review the Accountable Talk features and
indicators;
•
identify and discuss Accountable Talk moves in a
video; and
•
align CCSS and essential understandings (EUs) to
a task and zoom in for a more specific look at key
moves for engaging in productive talk (marking,
recapping, challenging, and revoicing).
© 2013 UNIVERSITY OF PITTSBURGH
Linking to Research/Literature:
The QUASAR Project
The Mathematical Tasks Framework
TASKS
TASKS
TASKS
as they
appear in
curricular/
instructional
materials
as set up by
the teachers
as
implemented
by students
Student
Learning
Stein, Smith, Henningsen, & Silver, 2000
Linking to Research/Literature:
The QUASAR Project
The Mathematical Tasks Framework
TASKS
TASKS
TASKS
as they
appear in
curricular/
instructional
materials
as set up by
the teachers
as
implemented
by students
Student
Learning
Stein, Smith, Henningsen, & Silver, 2000
Setting Goals
Selecting Tasks
Anticipating Student Responses
Accountable Talk® is a registered trademark of the
University of Pittsburgh
Orchestrating Productive Discussion
• Monitoring students as they work
• Asking assessing and advancing questions
• Selecting solution paths
• Sequencing student responses
• Connecting student responses via Accountable
Talk® discussions
Accountable Talk
Features and Indicators
© 2013 UNIVERSITY OF PITTSBURGH
Accountable Talk Discussion
• Study the Accountable Talk features and indicators.
• Turn and Talk with your partner about what you
would expect teachers and students to be saying
during an Accountable Talk discussion so that the
discussion is accountable to:
− the learning community;
− accurate, relevant knowledge; and
− standards of rigorous thinking.
© 2013 UNIVERSITY OF PITTSBURGH
Accountable Talk Features and Indicators
Accountability to the Learning Community
• Active participation in classroom talk.
• Listen attentively.
• Elaborate and build on each others’ ideas.
• Work to clarify or expand a proposition.
Accountability to Knowledge
• Specific and accurate knowledge.
• Appropriate evidence for claims and arguments.
• Commitment to getting it right.
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.
© 2013 UNIVERSITY OF PITTSBURGH
Solving and Discussing the
Cognitive Demand of the
Light Bulb Task
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The Structure and Routines of a Lesson
Set Up
Up the
of the
Task
Set
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: Engage students
in a Quick Write or a discussion
of the process.
Engaging in a Lesson:
The Light Bulb Task
• Solve the task.
• Discuss your solutions with your peers.
• Attempt to engage in an Accountable Talk discussion
when discussing the solutions. Assign one person in
the group to be the observer. This person will be
responsible for reporting some of the ways in which
the group is accountable to:
− the learning community;
− accurate, relevant knowledge; and
− standards of rigorous thinking.
© 2013 UNIVERSITY OF PITTSBURGH
Engaging in a Lesson:
The Light Bulb Task
Alazar Electric Company sells light bulbs to big box stores –
the big chain stores that frequently buy large numbers of
bulbs in one sale. They sample their bulbs for defects
routinely.
A sample of 96 light bulbs consisted of 4 defective ones.
Assume that today’s batch of 6,000 light bulbs has the same
proportion of defective bulbs as the sample. Determine the
total number of defective bulbs made today.
The big businesses they sell to accept no larger than a 4%
rate of defective bulbs. Does today’s batch meet that
expectation? Explain how you made your decision.
© 2013 UNIVERSITY OF PITTSBURGH
Reflecting on Our Engagement in the
Lesson
The observer should share some observations about
the group’s engagement in an Accountable Talk
discussion.
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Reflecting on Our Engagement in the
Lesson
• In what ways did small groups engage in an
Accountable Talk discussion?
• In what ways did we engage in an Accountable Talk
discussion during the group discussion of the
solutions?
© 2013 UNIVERSITY OF PITTSBURGH
Aligning the CCSS to the Light Bulb
Task
• Study the Grade 7 CCSS for Mathematical Content
within the Ratio and Proportion domain.
Which standards are students expected to
demonstrate when solving the task?
• Identify the CCSS for Mathematical Practice required
by the written task.
© 2013 UNIVERSITY OF PITTSBURGH
The CCSS for Mathematical Content: Grade 7
Ratios and Proportional Relationships
7.RP
Analyze proportional relationships and use them to solve real-world and
mathematical problems.
7.RP.A.1
Compute unit rates associated with ratios of fractions, including
ratios of lengths, areas and other quantities measured in like or
different units. For example, if a person walks 1/2 mile in each 1/4
hour, compute the unit rate as the complex fraction ½ / ¼ miles per
hour, equivalently 2 miles per hour.
7.RP.A.2
Recognize and represent proportional relationships between
quantities.
7.RP.A.2a
Decide whether two quantities are in a proportional relationship,
e.g., by testing for equivalent ratios in a table or graphing on a
coordinate plane and observing whether the graph is a straight line
through the origin.
7.RP.A.2b
Identify the constant of proportionality (unit rate) in tables, graphs,
equations, diagrams, and verbal descriptions of proportional
relationships.
Common Core State Standards, 2010, p. 48, NGA Center/CCSSO
The CCSS for Mathematical Content: Grade 7
Ratios and Proportional Relationships
7.RP
Analyze proportional relationships and use them to solve real-world
and mathematical problems.
7.RP.A.2c
Represent proportional relationships by equations. For
example, if total cost t is proportional to the number n of items
purchased at a constant price p, the relationship between the
total cost and the number of items can be expressed as t = pn.
7.RP.A.2d
Explain what a point (x, y) on the graph of a proportional
relationship means in terms of the situation, with special
attention to the points (0, 0) and (1, r) where r is the unit rate.
7.RP.A.3
Use proportional relationships to solve multistep ratio and
percent problems. Examples: simple interest, tax, markups
and markdowns, gratuities and commissions, fees, percent
increase and decrease, percent error.
Common Core State Standards, 2010, p. 48, NGA Center/CCSSO
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, p. 6-8, NGA Center/CCSSO
Determining the Cognitive
Demand of the Task:
The Light Bulb Task
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Determining the Cognitive Demand
of the Task
Refer to the Mathematical Task Analysis Guide.
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A., 2000. Implementing standards-based mathematics
instruction: A casebook for professional development, p. 16. New York: Teachers College Press.
How would you characterize the Light Bulb Task in
terms of its cognitive demand? (Refer to the indicators
on the Task Analysis Guide.)
© 2013 UNIVERSITY OF PITTSBURGH
The Mathematical Task Analysis Guide
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000) Implementing standards-based mathematics instruction:
A casebook for professional development, p. 16. New York: Teachers College Press
.
The Light Bulb Task:
A Doing Mathematics Task
• Requires complex and non-algorithmic thinking (i.e., there is not a
predictable, well-rehearsed approach or pathway explicitly suggested by
the task, task instructions, or a worked-out example).
• Requires students to explore and to understand the nature of
mathematical concepts, processes, or relationships.
• Demands self-monitoring or self-regulation of one’s own cognitive
processes.
• Requires students to access relevant knowledge and experiences and
make appropriate use of them in working through the task.
• Requires students to analyze the task and actively examine task
constraints that may limit possible solution strategies and solutions.
• Requires considerable cognitive effort and may involve some level of
anxiety for the student due to the unpredictable nature of the solution
process required.
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Accountable Talk Moves
© 2013 UNIVERSITY OF PITTSBURGH
The Structure and Routines of a Lesson
Set Up
Up the
of the
Task
Set
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: Engage students
in a Quick Write or a discussion
of the process.
Accountable Talk Moves
Examine the ways in which the moves are grouped based on
how they:
• support accountability to the learning community;
• support accountability to knowledge; and
• support accountability to rigorous thinking.
Consider:
In what ways are the Accountable Talk categories
similar? Different?
Why do you think we need a category called “To Ensure
Purposeful, Coherent, and Productive Group Discussion”?
© 2013 UNIVERSITY OF PITTSBURGH
Accountable Talk: Features and Indicators
Accountability to the Learning Community
• Active participation in classroom talk.
• Listen attentively.
• Elaborate and build on each others’ ideas.
• Work to clarify or expand a proposition.
Accountability to Knowledge
• Specific and accurate knowledge.
• Appropriate evidence for claims and arguments.
• Commitment to getting it right.
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.
© 2013 UNIVERSITY OF PITTSBURGH
Accountable Talk Moves
Talk Move
Function
Example
To Ensure Purposeful, Coherent, and
Productive Group Discussion
Marking
Direct attention to the value and importance of
a student’s contribution.
That’s an important point.
Challenging
Redirect a question back to the students, or use
students’ contributions as a source for further
challenge or query.
Let me challenge you: Is that always true?
Revoicing
Align a student’s explanation with content or
connect two or more contributions with the goal
of advancing the discussion of the content.
S: 4 + 4 + 4.
Make public in a concise, coherent form, the
group’s achievement at creating a shared
understanding of the phenomenon under
discussion.
Let me put these ideas all together.
What have we discovered?
Recapping
You said three groups of four.
To Support Accountability to Community
Keeping the
Channels
Open
Ensure that students can hear each other, and
remind them that they must hear what others
have said.
Say that again and louder.
Can someone repeat what was just said?
Keeping
Everyone
Together
Ensure that everyone not only heard, but also
understood, what a speaker said.
Can someone add on to what was said?
Did everyone hear that?
Linking
Contributions
Make explicit the relationship between a new
contribution and what has gone before.
Does anyone have a similar idea?
Do you agree or disagree with what was
said?
Your idea sounds similar to his idea.
Verifying and
Clarifying
Revoice a student’s contribution, thereby
helping both speakers and listeners to engage
more profitably in the conversation.
So are you saying..?
Can you say more?
Who understood what was said?
Accountable Talk Moves
(continued)
To Support Accountability to Knowledge
Pressing for
Accuracy
Hold students accountable for the accuracy,
credibility, and clarity of their contributions.
Why does that happen?
Someone give me the term for that.
Building on
Prior
Knowledge
Tie a current contribution back to knowledge
accumulated by the class at a previous time.
What have we learned in the past that links
with this?
To Support Accountability to
Rigorous Thinking
Pressing for
Reasoning
Elicit evidence to establish what contribution a
student’s utterance is intended to make within
the group’s larger enterprise.
Say why this works.
What does this mean?
Who can make a claim and then tell us
what their claim means?
Expanding
Reasoning
Open up extra time and space in the
conversation for student reasoning.
Does the idea work if I change the
context? Use bigger numbers?
© 2013 UNIVERSITY OF PITTSBURGH
Reflection Question
As you watch the short video segment, consider what
students are learning and where you might focus the
discussion in order to discuss mathematical ideas listed
in the CCSS.
Identify:
• the specific Accountable Talk moves used by the
teacher; and
• the purpose that the moves served.
 Mark times during the lesson when you would call
the lesson academically rigorous.
© 2013 UNIVERSITY OF PITTSBURGH
The Light Bulb Lesson Context
• Visiting Teacher: Victoria Bill
• Teacher: Reginald Coleman
• School: Community Health Academy of the Heights
Middle School
• District: New York City Schools
• Principal: Ms. Vu
• Grade Level: 7th Grade
The students in the video episode are in a mainstream
mathematics classroom in the New York City Schools.
The students are solving the Light Bulb Task. This part
of the video captures the Share, Discuss, and Analyze
phase of the lesson.
© 2013 UNIVERSITY OF PITTSBURGH
Norms for Collaborative Study
The goal of all conversations about episodes of teaching (or
artifacts of practice in general) is to advance our own learning, not
to “fix” the practice of others.
In order to achieve this goal, the facilitator chooses a lens to frame
what you look at and to what you pay attention. Use the
Accountable Talk features and indicators when viewing the lesson.
During this work, we:
• agree to analyze the episode or artifact from the identified
perspective;
• cite specific examples during the discussion that provide
evidence of a particular claim;
• listen to and build on others’ ideas; and
• use language that is respectful of those in the video and in the
group.
© 2013 UNIVERSITY OF PITTSBURGH
The Light Bulb Task
Alazar Electric Company sells light bulbs to big box stores
– the big chain stores that frequently buy large numbers of
bulbs in one sale. They sample their bulbs for defects
routinely.
A sample of 96 light bulbs consisted of 4 defective ones.
Assume that today’s batch of 6,000 light bulbs has the
same proportion of defective bulbs as the sample.
Determine the total number of defective bulbs made today.
The big businesses they sell to accept no larger than a 4%
rate of defective bulbs. Does today’s batch meet that
expectation? Explain how you made your decision.
© 2013 UNIVERSITY OF PITTSBURGH
Reflecting on the Accountable Talk
Discussion
Step back from the discussion. What are some patterns
that you notice?
What mathematical ideas does the teacher want
students to discover and discuss?
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Essential Understandings
Study the essential understandings the teacher
considered in preparation for the Share, Discuss, and
Analyze phase of the lesson.
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Essential Understandings
Essential Understanding
CCSS
Comparing Quantities
Two quantities can be compared using addition/subtraction or
6.RP.A.1
multiplication/division. Forming a ratio is a way of comparing two quantities
multiplicatively. Reasoning with ratios involves attending to and coordinating two
quantities.
Unit Rate
When the ratio of a/b is scaled up or down to a/b/1, a/b to 1 is referred to as a
7.RP.A.1
unit rate. Two unit rates are associated with a multiplicative relationship a and b:
a/b to 1 and b/a to 1. Each unit rate reveals different information about realworld problems associated with the relationship.
Proportional Reasoning
A proportion is a statement that two ratios are equivalent, b/a = d/c. There are a
variety of ways a proportion can be organized to establish an equality
7.RP.A.2
relationship between two quantities.
Constant of Proportionality
Forming a ratio indicates that two quantities are being compared in such a way
that one of them is a constant multiple of the other, i.e., since the ratios a/b = c
implies a = bc, then a is a constant multiple, c, of b. A ratio can be scaled up
using multiplication because the two quantities vary in such a way that one of
them is a constant multiple of the other; a ratio can be scaled down using
division, since division by some number, q, is the equivalent of multiplication by
the
multiplicative
inverse of q, 1/q.
© 2013
UNIVERSITY OF PITTSBURGH
7.RP.A.2b
Characteristics of an Academically
Rigorous Lesson
This task is a cognitively demanding task; however, it
may not necessarily end up being an academically
rigorous task.
What do we mean by this?
© 2013 UNIVERSITY OF PITTSBURGH
Academic Rigor in a Thinking Curriculum
The principle of learning, Academic Rigor in a Thinking
Curriculum, consists of three features:
• A Knowledge Core
• High-Thinking Demand
• Active Use of Knowledge
In order to determine if a lesson has been academically
rigorous, we have to determine the degree to which
student learning is advanced by the lesson.
What do we have to hear and see in order to determine
if the lesson was academically rigorous?
© 2013 UNIVERSITY OF PITTSBURGH
Essential Understandings
Essential Understanding
CCSS
Comparing Quantities
Two quantities can be compared using addition/subtraction or
6.RP.A.1
multiplication/division. Forming a ratio is a way of comparing two quantities
multiplicatively. Reasoning with ratios involves attending to and coordinating two
quantities.
Unit Rate
When the ratio of a/b is scaled up or down to a/b/1, a/b to 1 is referred to as a
7.RP.A.1
unit rate. Two unit rates are associated with a multiplicative relationship a and b:
a/b to 1 and b/a to 1. Each unit rate reveals different information about real-world
problems associated with the relationship.
Proportional Reasoning
A proportion is a statement that two ratios are equivalent, b/a = d/c. There are a
variety of ways a proportion can be organized to establish an equality
7.RP.A.2
relationship between two quantities.
Constant of Proportionality
Forming a ratio indicates that two quantities are being compared in such a way
that one of them is a constant multiple of the other, i.e., since the ratios a/b = c
implies a = bc, then a is a constant multiple, c, of b. A ratio can be scaled up
using multiplication because the two quantities vary in such a way that one of
them is a constant multiple of the other; a ratio can be scaled down using
division, since division by some number, q, is the equivalent of multiplication by
the
multiplicative
inverse of q, 1/q.
© 2013
UNIVERSITY OF PITTSBURGH
7.RP.A.2b
Five Different Representations of a Function
Language
Context
Table
Graph
Equation
Van De Walle, 2004, p. 440
Focusing on Key
Accountable Talk Moves
The Light Bulb Task
© 2013 UNIVERSITY OF PITTSBURGH
Accountable Talk: Features and Indicators
Accountability to the Learning Community
• Active participation in classroom talk.
• Listen attentively.
• Elaborate and build on each others’ ideas.
• Work to clarify or expand a proposition.
Accountability to Knowledge
• Specific and accurate knowledge.
• Appropriate evidence for claims and arguments.
• Commitment to getting it right.
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.
• OF
Challenge
the quality of evidence and reasoning.
© 2013 UNIVERSITY
PITTSBURGH
Accountable Talk Moves
Talk Move
Function
Example
To Ensure Purposeful, Coherent, and
Productive Group Discussion
Marking
Direct attention to the value and importance of
a student’s contribution.
That’s an important point.
Challenging
Redirect a question back to the students, or use
students’ contributions as a source for further
challenge or query.
Let me challenge you: Is that always true?
Revoicing
Align a student’s explanation with content or
connect two or more contributions with the goal of
advancing the discussion of the content. .
S: 4 + 4 + 4.
Make public in a concise, coherent form, the group’s
achievement at creating a shared understanding of
the phenomenon under discussion.
Let me put these ideas all together.
What have we discovered?
Recapping
You said three groups of four.
To Support Accountability to Community
Keeping the
Channels
Open
Ensure that students can hear each other, and
remind them that they must hear what others
have said.
Say that again and louder.
Can someone repeat what was just said?
Keeping
Everyone
Together
Ensure that everyone not only heard, but also
understood, what a speaker said.
Can someone add on to what was said?
Did everyone hear that?
Linking
Contributions
Make explicit the relationship between a new
contribution and what has gone before.
Does anyone have a similar idea?
Do you agree or disagree with what was
said?
Your idea sounds similar to his idea.
Revoice a student’s contribution, thereby
helping both speakers and listeners to engage
more profitably in the conversation.
© 2013 UNIVERSITY OF PITTSBURGH
Verifying and
Clarifying
So are you saying..?
Can you say more?
Who understood what was said?
Accountable Talk Moves (continued)
To Support Accountability to Knowledge
Pressing for
Accuracy
Hold students accountable for the accuracy,
credibility, and clarity of their contributions.
Why does that happen?
Someone give me the term for that.
Building on
Prior
Knowledge
Tie a current contribution back to knowledge
accumulated by the class at a previous time.
What have we learned in the past that links
with this?
To Support Accountability to
Rigorous Thinking
Pressing for
Reasoning
Elicit evidence to establish what contribution a
student’s utterance is intended to make within
the group’s larger enterprise.
Say why this works.
What does this mean?
Who can make a claim and then tell us
what their claim means?
Expanding
Reasoning
Open up extra time and space in the
conversation for student reasoning.
Does the idea work if I change the
context? Use bigger numbers?
© 2013 UNIVERSITY OF PITTSBURGH
Focusing on Accountable Talk Moves
Read the description of each move and study the
example that has been provided for each move.
What is distinct about each of the moves?
• Revoice student contributions;
• mark significant contributions;
• challenge with a counter-example; or
• recap the components of the lesson.
© 2013 UNIVERSITY OF PITTSBURGH
Revoicing
• Extend a student’s contribution.
• Connect a student’s contribution to the text or to
other students’ contributions.
 Align content with an explanation.
 Add clarity to a contribution.
 Link student contributions to accurate
mathematical vocabulary.
 Connect two or more contributions to advance
the lesson.
© 2013 UNIVERSITY OF PITTSBURGH
An Example of Revoicing
S: —and it gives you 12 or you multiply 4 times 3
because there’s 3 boxes.
T: All right, he said you could do 4 times 3 and then—
how would you get from here to here, though? (Points
to other side of table, the total number of bulbs.)
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Marking
Explicitly talk about an idea.
• Highlight features that are unique to a situation.
• Draw attention to an idea or to alternative ideas.
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An Example of Marking
S: It looks like they wrote fractions. Like, broken bulbs
over total bulbs. 4 over 96 is equal to 250 over 6,000.
T: Hmm—did everyone hear what Selena just said? She
noticed that when we write the fraction of defective
bulbs out of total bulbs, they are both equivalent.
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Recapping
Summarize or retell.
• Make explicit the large idea.
• Provide students with a holistic view of the
concept.
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Challenging
Redirect a question back to the students, or use
students’ contributions as a source for further challenge
or query.
• Share a counter-example and ask students to
compare problems.
• Question the meaning of the math concept.
© 2013 UNIVERSITY OF PITTSBURGH
An Example of Recapping and
Challenge
S:
Multiply by – by 4 – 62 times 5 – no, 62.5 times 4.
5
10
T:
62 and
times 4, 4 defective?
S:
T:
Uhm, I get 250.
250! Clap your hands if everyone got that.
[Applause] So, why did you have to do – why did you
5
5
multiply 96 by 62 and and also 4 by 62 and ?
10
S:
T:
10
What?
Why did you have to do it on both sides? When we
worked up here, we did 92 x 2 and on the other side
we did 4 x 2. When we multiplied by 3 on this side we
multiplied by 3 on the other side. Why do we have to
do this in order for it to be proportional?
© 2013 UNIVERSITY OF PITTSBURGH
Appropriation
The process of appropriation is reciprocal and
sequential.
• If appropriation takes place, the child transforms
the new knowledge or skill into an action in a new
and gradually understood activity.
• What would this mean with respect to classroom
discourse? What should we expect to happen in
the classroom?
© 2013 UNIVERSITY OF PITTSBURGH
Orchestrating Discussions
Read the segments of transcript from the lesson.
Decide if examples 1 – 3 illustrate marking, recapping,
challenging, or revoicing.
Be prepared to share your rationale for identifying a
particular discussion move.
Write the next discussion move for examples 4 and 5
and be prepared to share your move and your rationale
for writing the move.
© 2013 UNIVERSITY OF PITTSBURGH
Reflecting on Talk Moves
What have you learned about:
• marking;
• recapping;
• challenging; and
• revoicing?
Why are these moves important in lessons?
© 2013 UNIVERSITY OF PITTSBURGH
Application to Practice
• What will you keep in mind when attempting to use
Accountable Talk moves during a lesson? What role
does talk play?
• What does it take to maintain the demands of a
cognitively demanding task during the lesson so that
you have a rigorous mathematics lesson?
© 2013 UNIVERSITY OF PITTSBURGH