Common Core State Standards
Instruction (6-8)
Tere Hirsch
Cheryl Avalos
Math Consultants
Division of Curriculum and Instructional Services
commoncore.lacoe.edu
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Agenda
• Instruction and the CCSS/SMPs
• Cognitively Guided Instruction,
Mathematical Tasks , and the SMPs
• Rigor/Relevance Framework
• Dan Meyer Video
• Standards for Mathematical Practice
• English Language Learners
• Best Practices
• Closing
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CCSS for Mathematics
• Provide focus and coherence
• Organized around mathematical principles
• Stress conceptual understanding of key
ideas as well as skills
• Prepare students for college and career
What are the implications for instruction?
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Effective Instruction
“A long line of students has
established that the single most
important school influence on student
learning is the quality of the teacher.”
as presented by Linda Darling-Hammond (2007)
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Cognitively-Guided
Instruction Process
Start the study of a new
concept with a rich problem
or hypothesis
Use your understanding of
student thinking to guide
further instruction
Question, justify, and
critique thinking
Gendron (2011)
5 What’s New in the Common Core State Standards?
So,
Invite your students to
engage in the problem
Communicate multiple
representations of
solutions.
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Cognitively-Guided
Instruction Process
Start the study of a new
concept with a rich problem
or hypothesis
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Research Reveals
• Most math problems come from textbooks.
• The focus is on memorization and procedures
instead of reasoning and critical thinking.
• Understanding mathematics is directly connected
to the creation and exploration of questions.
• Ninety three percent of teacher questions
are knowledge based, focusing on recall of facts.
Adapted from a Margaret Smith presentation
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International Center for Leadership in Education (n.d.)
Rigor/Relevance Framework ®
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Students
gather and
store bits of
Application
knowledge/info
rmation and are Comprehension
expected to
Awareness
remember or
understand this
acquired
knowledge.
International Center for Leadership in Education (n.d.)
Quadrant A: Acquisition
A
3
2
Acquisition
1
1
2
Knowledge in
one discipline
Apply
knowledge in
discipline
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Students use
acquired
knowledge to
solve problems,
design
solutions, and
complete work.
Application
3
Comprehension
2
International Center for Leadership in Education (n.d.)
Quadrant B: Application
B
Application
Awareness 1
3
4
5
Apply
knowledge across
disciplines
Apply
to real-world
predictable
situation
Apply to
real-world
unpredictable
situation
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Evaluation
Students extend
Synthesis
and refine their
Analysis
knowledge so that
they can use it
Application
automatically and
routinely to analyze
and solve problems
and create
solutions.
6
5
4
C
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Assimilation
1
2
Knowledge in
one discipline
Apply
Knowledge in
one discipline
International Center for Leadership in Education (n.d.)
Quadrant C: Assimilation
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Students think in
complex ways and
apply acquired
knowledge
and skills, even
when confronted
with perplexing
unknowns,
to find creative
solutions and take
action that further
develops their
skills and
knowledge.
Evaluation
Synthesis
Analysis
Application
6
5
4
3
International Center for Leadership in Education (n.d.)
Quadrant D: Adaptation
D
Adaptation
3
4
5
Apply
knowledge across
disciplines
Apply
to real-world
predictable
situation
Apply to
real-world
unpredictable
situation
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Comparing Four Problems
• Work the problems/problem set.
• Determine the level of rigor in each
problem.
• What is the difference in the problems?
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Cognitively-Guided
Instruction Process
Invite your students
to engage in the
problem
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Learning Pyramid
Passive
Learning
Active
Learning
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adapted from Ntl Institute for Applied Behavioral Science (n.d.)
Dan Meyer
“Math Class Needs a Makeover”
http://blog.ted.com/2010/0513/math_cla
ss_needs/
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Over the Hill
• Cell tower
• Mountains
• Part I
• Part II
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BREAK
Begin the “Over the Hill” Activity and take
A 10 min break as needed, while you are
working
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Cognitively-Guided
Instruction Process
Question, justify, and
critique thinking
Communicate multiple
representations of
solutions.
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Cognitively-Guided
Instruction Process
Use your understanding of
student thinking to guide
further instruction
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• How do the standards of
mathematical practice fit in?
• Revisit the four Quadrants of Rigor
and Relevance and relate to what
students and teachers doing.
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Standards for
1. Make sense of problems and persevere
in solving them.
6. Attend to precision.
Mathematical Practice
2. Reason abstractly and quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
Reasoning and
explaining
Modeling and
using tools
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
adapted from McCallum (2011)
Standards for Mathematical Practice
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Overarching
habits of mind
of a productive
mathematical
thinker
Seeing structure
and generalizing
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Create a Frayer Model Poster
Essential
Characteristics
Examples
of What
Students Will
Be Doing
•
•
•
Teaching
Methods
Standard for
Mathematical
Practice
Non-examples
of What
Students Will
Be Doing
Each table or group will be assigned one of
the Standards for Mathematical Practice.
Create a Frayer Model Poster connecting
student actions and teacher actions.
Gallery walk or Carousel
Activity
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Frayer Model Poster Carousel
• Display your poster.
• Examine the posters to the right of your group’s
poster.
• Look for evidence of the “processes and
proficiencies.”
• Rotate to the right and continue until you have
finished examining all posters.
• Be ready to share out any questions or “ahas.”
Activity
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What about English Learners?
• AB 124 – Establishes ELD Advisory
Committee.
• ELD Standards are aligned to CCSS.
• Standards of Mathematical Practice and
ELLs.
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Mc Donald’s Claim:
Wikipedia reports that on any day an average
of 8% of all Americans eat at Mc Donald’s. In
the US there are approximately 310 million
Americans and 12,800 Mc Donald restaurants.
Do you believe the Wikipedia report to be
true? Create a mathematical argument to
justify your position.
Be prepared to present your argument.
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Best Practices for the
Common Core
1. Engage students with challenging tasks that
involve active meaning making
2. Quadrant B, C, and D learning opportunities
3. Cognitively-Guided Instruction with a focus on
the Standards for Mathematical Practice
4. Questioning to facilitate thinking and learning
5. Design instruction to support student success
6. Explicitly reinforce high effort and students’
use of effective strategies
7. Repackage content using real-world connections,
puzzles, and games
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8. Model a productive disposition
Reflection
• Think about what you learned today.
• Decide on one thing you will do
differently to start transitioning to the
Common Core State Standards.
• Share your ideas with a partner.
Activity
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For Next Time
March 5, 2013
• Try a CCSS based lesson in your
classroom.
• Bring a copy of the task to share.
• Be prepared to discuss how you and
your students fared in the
implementation of the task.
• Bring your textbook.
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Reflection and Evaluation
Please fill in the
Evaluation form for
Day 2 and leave it
on your table.
See you next
month.
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