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Academic!Talk!in!the!Math!Workshop!
WABE!2016!
Kristin'Percy'Calaff'&'Kaitlyn'Spore'
Highline'Public'Schools'
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Purpose:!!
To#serve#language#learners#effectively#by#supporting#mathematical#thinking#and#language#
skills#to#meet#Common#Core#State#Standards#(CCSS).#
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Objectives:!!
In!this!workshop,!participants!will!be!able!to…'
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Set'up'an'interactive'Math'Workshop'structure.'
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Use'technology'in'a'blended'learning'model.'
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Practice'accountable'“Math'Talk”'strategies.'
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Agenda:!
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Math!Workshop!
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Why'Use'a'Math'Workshop?'
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How'Does'It'Work?'
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Math'Workshop'Structure'
Blended!Learning!
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Framework'for'Blended'Learning'
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Management'Tools'and'Tips'
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Free'and'Paid'OnLline'Tools'
Math!Talk!Strategies!
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CCSS'Mathematical'Practices'
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Habits'of'Mind'and'Interaction'
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Math'Talk'Moves'
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Reflection:!
1. How'might'you'use'a'Math'Workshop'to'support'your'language'learners?'
2. Which'blended'learning'tools'have'you'used'or'will'you'try'out?'
3. How'will'you'use'“Math'Talk”'moves'to'build'more'intentional'academic'talk?'
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Entry!Tasks!
Academic'Talk'in'the'Math'Workshop'
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1) LISTEN!&!COMPARE:!Create'a'visual'justification'for'why'the'sum'of'two'odd'numbers'is'
always'an'even'number.'
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2) INTERPRET!&!COMPARE:!Use'the'numbers'5,'6,'7,'8,'and'9'and'put'one'digit'in'each'box.'
The'numbers'should'add'up'to'the'same'total'across'and'down.'
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3) REVOICE!&!COMPARE:!Maria'made'some'cookies.'1/3'of'the'cookies'were'chocolate'chip,'
3/4'of'the'remainder'were'oatmeal'raisin,'and'the'rest'were'peanut'butter.'If'Maria'made'4'
dozen'cookies,'how'many'peanut'butter'cookies'did'she'make?'
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Mathematically Productive Teaching Routine!
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Structuring) Student)Math/Talk!
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Purposes)
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Support the development of s t u d e n t -to-student interaction that is consistently equitable, status-free, and
mathematically productive. (For these purposes, mathematically productive means that student
interactions consistently include students' mathematical reasoning, sense making, representations,
justifications, and generalizations.)
Provide formative assessment information that drives instructional decisions
Student) Outcomes)
• Equitable, status-free, and mathematically
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productive student-to-student interaction
Increased metacognitive skills
Increased capacity to articulate and clarify
their math thinking
Productive socio-mathematical norms
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Increased math content knowledge
Improved Mathematical Habits of Mind/
Habits of Interaction
Increased accountability and engagement
Increased self-efficacy as mathematician
Groupings:))Affordances)and)Drawbacks) !
Mathematicians!Dyad!(2)!
Mathematicians!Triad!(3)!
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+ More strategies/modeling
+ Fewer groups to monitor
- Potential status issues for "third wheel"
- Discussion takes longer
Accountability for engagement
One-to-one modeling
Takes less time
Fewer strategies to compare
Less public
Nonproductive if one disengages
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Mathematicians!Quad!(4)!
+ Can flex between Dyads & Quads
+ Fewer groups to monitor
+ More strategies/modeling
- Discussion takes longer
- Can be easier for individuals to "ride"
on others’ ideas
- Comparing strategies could be complicated
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Logistics)
• Time: 4-15 minutes plus the ending plenary discussion; partners are always allocated equal "air-time."
• Who: All students either randomly mixed or purposely combined for differentiation, modeling, status treatment,
management, or specific content purposes. Partners may change regularly or be assigned for a set duration.
• Set-up: Referencing groupings by a name (e.g., Mathematicians Dyad/Triad/Quad) alerts s t u d e n t s t o m o v e
quickly into a known structure. When structuring student talk, it is helpful to demonstrate how partners should be
positioned (e.g., pairs in a knees-to-knees position, how to make eye contact, etc.). Movement provided by an
occasional Stand-up Mathematicians Dyad, Triad, or Quad in which all partners stand or a specified member of
each team stands to report, can boost energy, accountability, and attention.
• Task: The math task should: (1) always be central to the core mathematical purpose(s) of the lesson, and (2) always
require that the student mathematicians explain their math reasoning, sense making, representations,
justifications, and/or generalizations
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• Grouping and Structure: Determine whether the most mathematically productive grouping will be a Mathematicians
Dyad, Triad, or Quad and whether the most productive routine will be Listen & Compare, Revoice & Compare, or
Interpret & Compare.
Protocol)
• Introduce the task and implement the structure. Provide students the task - carefully worded to assure
emphasis on math reasoning, sense making, representations, justifications, and/or generalizations. Include
step- by-step-visual support for the structure process and deep math thinking.
• Monitor the math-talk. Listen for trends in student thinking. Select and sequence ideas for a plenary.
• Facilitate a plenary discussion of student ideas. Invite selected students to report about their thinking, their
partners' thinking, and/or their combined ideas. Sequence student reporting, interject information, and question
to focus, scaffold, and/ or advance student thinking about key concepts and connections.
• Reflect about the process. Ask the student mathematicians, "How was today's Mathematicians Dyad/Triad/Quad
process helpful for you?" A process debrief is not always necessary, but is important periodically. It fosters student
ownership and increases engagement and accountability.
Mathematically Productive Teaching Routine
Structuring) Student) Math/Talk!
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STRUCTURES FOR THE MATHEMATICIANS DYAD, TRIAD, AND QUAD
When students work in a Mathematicians Dyad, Triad, or Quad, the math-talk:
• Always begins with "Mathematicians Think Time" (i.e., time to think privately) about the task
• Always focuses on each group member's mathematical reasoning, sense making, representations,
justifications, and /or generalizations
• Always ends with a discussion of ways their ideas are mathematically the same and/or different.
• Always follows a prescribed structure that provides students "practice'' with status-free, and
mathematically productive student-to-student interaction
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LISTEN)&)
COMPARE
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A. Partner #1 explains her/his ideas while the other partner(s) silently listen to
understand Partner #1's thinking.
B. When the teacher announces, "Finish your thought and switch roles," repeat step A for
Partner #2. The teacher sets the timing according to the complexity of the
question/task and student backgrounds.
C. (for triads and quads) Repeat until all partners have reported.
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A. Partner #1 speaks while the other partner(s) silently listen to understand Partner #1's
mathematical thinking.
B. When the teacher announces, "Finish your thought and Partner #X revoice," Partner
#X carefully revoices Partner #l's ideas without judging, adapting, or commenting
about the correctness or sensibility of the ideas.
C. Partner #1 clarifies as needed.
D. When the teacher announces, "Rotate Partners," Partner #2 speaks while the other
partner(s) silently listen to understand.
E. When the teacher announces, "Finish your thought and Partner #Y revoice," Partner
#Y carefully revoices Partner #2's ideas.
F. Partner #2 clarifies as needed.
G. (for triads and quads) Repeat until all partners have revoiced and reported.
REVOICE))&)
COMPARE
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INTERPRET))) &)
COMPARE)
A. Two partners exchange their written work for a task. During Private Think Time, the
partners study each other's work and, without any discussion, try to understand each
other's reasoning.
B. Partner #1 reports her interpretation of Partner #2's reasoning.
C. Partner #2 clarifies.
D. Partner #2 reports his interpretation of Partner #1's reasoning.
E. Partner #1 clarifies.
COLLABORATION)
ROLE) PLAY)
A. The teacher arranges the students in teams (d y a d s , triads, or quads) and distributes a
role card to each student (all teams use the same roles). Student role assignments
may be purposeful or random.
B. Team members read their roles and sample role-talk to their partners.
C. The teacher poses a task and monitors while teams role play and complete the task.
D. The teacher periodically calls for "Role Huddles" in a corner of the room where the
Mathematical Habits of Interaction are posted. During a Role Huddle (e.g., all
Facilitators), the teacher gives additional directions related to the specific role and one
or more of the Mathematical Habits of Interaction and/or Mathematical Habits of
Mind. The Role Players return to their teams with information from the huddle.
E. Upon completion of the task and any required team reporting/presentations, the
teams debrief their effectiveness, challenges, and next steps as collaborative
mathematicians.
©2011 TEACHERS DEVELOPMENT GROUP V.3.2
HOW MATH TEACHING MATTERS
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