Transcript Day 2 PPT Math PLC Actual

Mapping to the Core
Professional Learning
Community
Math
1 CCSS, 2010, p. 5
2 PARCC – Draft Content Framework - 2011
Housekeeping
On your
own-1 hour
Math PLC Norms
Practice the “P” word (Perseverance)
Think, Talk, and Write about mathematics
Manage your electronic devices respectfully
Track your progress toward learning targets
Establishing Team Norms
What will it take for you to be
able to participate to your
fullest?
Listen to understand
Set aside preconceived notions
Speak openly and honestly
Pay attention to your “feathers”
Day 2
Phase 2 of Curriculum Mapping
• Establishing Expectations
• Firm up SMP, Critical Areas of Focus, and
Use look at Learning Progressions
• Lunch 11:30-12:30 on your own
• Draft a 10 month pacing guide Domain,
Clusters and Standards
• Next Steps-Unit Planning
Big/Ideas for this course
Day 1-Laying the Foundation- Phase 1
Day 2-Consensus Mapping-Phase 2
Day 3- Draft Unit/Lesson Plan Development
and align assessments- Phase 3
Day 4-Training on Mapping Software and
entering units/plans in the system.
Day 5-Read-throughs for SMP’s, Critical Areas
of Focus and upgrading with web 2.0 toolsPhase 4
Wikispace…
What does literacy look like in the
mathematics classroom?
• Learning to read mathematical text
• Communicating using correct mathematical terminology
• Reading, discussing and applying the mathematics
found in literature
• Researching mathematics topics or related problems
• Reading appropriate text providing explanations for
mathematical concepts, reasoning or procedures
• Applying readings as citing for mathematical reasoning
• Listening and critiquing peer explanations
• Justifying orally and in writing mathematical reasoning
• Representing and interpreting data
21st Century Skills
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Creativity and innovation
Critical thinking and problem solving
Communication and collaboration
Information, media and technology literacy
Personal management
Productivity and accountability
Leadership and responsibility
Interdisciplinary and project-based learning
MP + CAF + Standards = Instruction
In order to design instruction that meets the
rigor and expectations of the CCSSM,
understanding the Mathematical Practices
and Critical Areas of Focus are essential.
CCSS Mathematical Practices
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
Which SMP is illustrated below?
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and
persevere in solving them
Reason abstractly and
quantitatively
Construct viable arguments
and critique the reasoning of
others
Model with mathematics
Use appropriate tools
strategically
Attend to precision
Look for and make use of
structure
Look for and express
regularity in repeated
reasoning
Which SMP is illustrated below?
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and
persevere in solving them
Reason abstractly and
quantitatively
Construct viable arguments
and critique the reasoning of
others
Model with mathematics
Use appropriate tools
strategically
Attend to precision
Look for and make use of
structure
Look for and express
regularity in repeated
reasoning
Which SMP is illustrated below?
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and
persevere in solving them
Reason abstractly and
quantitatively
Construct viable arguments
and critique the reasoning of
others
Model with mathematics
Use appropriate tools
strategically
Attend to precision
Look for and make use of
structure
Look for and express
regularity in repeated
reasoning
Which SMP is illustrated below?
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and
persevere in solving them
Reason abstractly and
quantitatively
Construct viable arguments
and critique the reasoning of
others
Model with mathematics
Use appropriate tools
strategically
Attend to precision
Look for and make use of
structure
Look for and express
regularity in repeated
reasoning
Which SMP is illustrated below?
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and
persevere in solving them
Reason abstractly and
quantitatively
Construct viable arguments
and critique the reasoning of
others
Model with mathematics
Use appropriate tools
strategically
Attend to precision
Look for and make use of
structure
Look for and express
regularity in repeated
reasoning
Which SMP is illustrated below?
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and
persevere in solving them
Reason abstractly and
quantitatively
Construct viable arguments
and critique the reasoning of
others
Model with mathematics
Use appropriate tools
strategically
Attend to precision
Look for and make use of
structure
Look for and express
regularity in repeated
reasoning
Which SMP is illustrated below?
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and
persevere in solving them
Reason abstractly and
quantitatively
Construct viable arguments
and critique the reasoning of
others
Model with mathematics
Use appropriate tools
strategically
Attend to precision
Look for and make use of
structure
Look for and express
regularity in repeated
reasoning
Which SMP is illustrated below?
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and
persevere in solving them
Reason abstractly and
quantitatively
Construct viable arguments
and critique the reasoning of
others
Model with mathematics
Use appropriate tools
strategically
Attend to precision
Look for and make use of
structure
Look for and express
regularity in repeated
reasoning
Grade Level Introduction
Cross-cutting
themes
Critical Area of
Focus
• Progressions
– Describe a sequence of increasing
sophistication in understanding and
skill within an area of study
• Three types of progressions
– Learning progressions
– Standards progressions
– Task progressions
Learning Progressions Document for
CCSSM
http://ime.math.arizona.edu/progressions/
• Narratives
• Typical learning progression of a topic
• Children's cognitive development
• The logical structure of mathematics
• Math Common Core Writing Team with
Bill McCallum as Creator/Lead Author
CCSS Domain Progression
K
1
2
3
4
5
6
7
8
HS
Counting &
Cardinality
Number and Operations in Base Ten
Number and Operations –
Fractions
Ratios and Proportional
Relationships
The Number System
Expressions and Equations
Number &
Quantity
Algebra
Operations and Algebraic Thinking
Functions
Geometry
Measurement and Data
Functions
Geometry
Statistics and Probability
Statistics &
Probability
Use Place Value Understanding
Grade 1
Grade 2
Grade 3
Use place value understanding
and properties of operations to
add and subtract.
4. Add within 100, including adding a
two-digit number and a one-digit
number, and adding a two-digit
number and a multiple of 10, using
concrete models or drawings and
strategies based on place value,
properties of operations, and/or the
relationship between addition and
subtraction; relate the strategy to a
written method and explain the
reasoning used.
Understand that in adding two-digit
numbers, one adds tens and tens,
ones and ones; and sometimes it is
necessary to compose a ten.
5. Given a two-digit number, mentally
find 10 more or 10 less than the
number, without having to count;
explain the reasoning used.
6. Subtract multiples of 10 in the
range 10-90 from multiples of 10 in
the range 10-90 (positive or zero
differences), using concrete models
or drawings and strategies based on
place value, properties of operations,
Use place value understanding
and properties of operations to
add and subtract.
5. Fluently add and subtract within
100 using strategies based on place
value, properties of operations,
and/or the relationship between
addition and subtraction.
6. Add up to four two-digit numbers
using strategies based on place
value and properties of operations.
7. Add and subtract within 1000,
using concrete models or drawings
and strategies based on place value,
properties of operations, and/or the
relationship between addition and
subtraction; relate the strategy to a
written method. Understand that in
adding or subtracting three digit
numbers, one adds or subtracts
hundreds and hundreds, tens and
tens, ones and ones; and sometimes
it is necessary to compose or
decompose tens or hundreds.
8. Mentally add 10 or 100 to a given
number 100–900, and mentally
subtract 10 or 100 from a given
number 100–900.
Use place value understanding
and properties of operations to
perform multi-digit arithmetic.
1. Use place value understanding to
round whole numbers to the nearest
10 or 100.
2. Fluently add and subtract within
1000 using strategies and algorithms
based on place value, properties of
operations, and/or the relationship
between addition and subtraction.
3. Multiply one-digit whole numbers
by multiples of 10 in the range 10–90
(e.g., 9 × 80, 5 × 60) using strategies
based on place value and properties
of operations.
Gallery Walk
Count off by 5’s
Go to assigned chart and discuss
Move clockwise to the next chart when cued
Listen to the docent’s overview
Knowing what you know about your grade level,
what are some critical points you can share.
Move to the next chart when cued
Break- 10 minutes
Grade Level Comparative Analysis
Content that is new to Grade 8
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The Number System Know that
there are numbers that are not
rational, and approximate them by
rational numbers. (8.NS.1-2)
Functions Define, evaluate, and
compare functions. (8.F.1-3)
Functions Use functions to model
relationships between quantities.
(8.F.4-5)
Geometry Understand congruence
and similarity using physical
models, transparencies, or
geometry software.[initial
introduction] (8.G.1-2)
Geometry Understand and apply
the Pythagorean Theorem. [initial
introduction] (8.G.6-8)
Statistics and Probability
Investigate patterns of association
in bivariate data. (8.SP.4)
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Content that is still included at Grade 8, but
may be modified or at a greater depth
Expressions and Equations Work with
radicals and integer exponents.
(8.EE.1-4)
Expressions and Equations Understand
the connections between proportional
relationships, lines, and linear equations.
[derive y=mx] (8.EE.5-6)
Expressions and Equations Analyze and
solve linear equations and pairs of
simultaneous linear equations.
(8.EE.7-8)
Geometry Understand congruence and
similarity using physical models,
transparencies, or geometry software.
(8.G.3-5)
Geometry Solve real-world and
mathematical problems involving volume
of cylinders, cones, and spheres. (8.G.9)
Statistics and Probability Draw informal
comparative inferences about two
populations. (7.SP.3-4)
Statistics and Probability Investigate
patterns of association in bivariate data.
(8.SP.1-3)
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Content that is no longer a focus at
Grade 8
Number, Number Sense and
Operations Ratio, proportion percent
problems (See Grade 7.RP)
Measurement Order and conversion
of units of measure (See Grade 6.G)
Measurement Rates (See Grade
7.RP)
Geometry Geometric figures on
coordinate plane (See Grades 6-7.G)
Geometry Nets (See 6.G.4)
Patterns, Functions and Algebra
Algebraic expressions
(See Grades 6-7.EE)
Patterns, Functions and Algebra
Grade 8 learning is limited to linear
equations
Patterns, Functions and Algebra
Quadratic equations (See HS)
Data Analysis Graphical
representation analysis
(See Grade 6.SP)
Data Analysis Measures of center
and spread; sampling
(See Grade 7.SP)
Probability (See Grade 7.SP)
Digging Deeper into the CCSS
1. Get into Grade Level Groups
2. Read and Discuss Progressions
& Comparative Analysis
Documents
3. List the MUST DO’s and No
Longer at grade level as a “T”
Chart
45 min
Share out your discoveries
Listen for the Essential Understandings
Skills
Concepts
And note any potential gaps
Lunch-on your own
1 HOUR
Pirate Ship
Imagine you are a pirate ship captain who has
just discovered a treasure chest full of jewels.
You are greedy and do not really want to share
them. You easily outwit your crew by unfairly
distributing the jewels. You count yourself first
and last so that every time your crewmembers
get 1 jewel, you get 2. How many jewels would
you end up with if you were sharing 120 jewels
with 4 mates? Describe any patterns you see.
What Makes a Problem Rich?
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Significant mathematics
Mathematical Practices
Multiple layers of complexity
Multiple entry points
Multiple solutions and/or strategies
Leads to discussion or other questions
Students are the workers and the decision
makers
Rich Task Sources
Ohio Resource Center
• www.OhioRC.org
Inside Mathematics
• http://www.insidemathematics.org
Balanced Assessment (MARS tasks)
• http://balancedassessment.concord.org
NCTM Illuminations
• http://illuminations.nctm.org/
Research shows that a wellarticulated curriculum, aligned
to standards, is critical for
student achievement.
(Marzano 2003, 2006)
From... To… 21st Century Mapping
Textbook as
Curriculum
Assessments
Aligned to a
Program
Instruction
Focused on a
Program
Essential
Curriculum
Assessments
Aligned to
Essential
Curriculum?
Instruction
Focused on
Teaching
Strategies
Curriculum Maps
Benchmark Skills
Critical Skills
Instruction
Assessments
Focused on
Aligned to
Benchmark and learning through
an enacted
Critical Skills in
Curriculum Map Curriculum Map:
K-12
Consistent
and
Standardized
Professional
Development
Customized
and
Responsive
Professional
Development:
Training,
Coaching,
Leadership,
Through data
analysis
Making Sense of Mapping
OLD Curriculum Terms New Curriculum Terms
1. Goal
2. Lesson Plan
3. Scope & Sequence
Resource Guide
4. “Understands…”
5. Materials
6. Objective
7. Collaboration
8. Test/Quiz
1. Essential Questions
2. Activities
3. Curriculum Map-Living doc
4. Higher Order Thinking Verbs
5. Resources
6. Benchmark and Critical Skills,
Learning Targets
7. Collaboration
8. Formative and Summative
Assessments aligned to skills
Potential Roles of Administrators
in the
Mapping Process
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Include the mapping process in policies and procedures
Communicate with staff, board, parents, community
Make connections and hooks with current initiatives
Work toward clarity in expectations/goals
Deal with resistors
Support staff
Training
Staff development plan
Time
Accountability
Read-throughs
Addressing gaps, repetitions, etc
Leadership team
Deal with obstacles
Serve as a coach in the process
Use data to make decisions
Potential Roles and Responsibilities of
Curriculum Teacher Leaders
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Communicate Goals and progress towards goals regularly with, Staff, Principals,
Building Leadership Team, District Leadership Team, Central Office
As a team, determine who will gather reports using the mapping technology and how
you will provide feedback
Assist with the development of a Professional Development Plan to provide needed
skill training the areas of curriculum, instruction and assessment.
Consider Peer Observations to ‘coach’ each other on the use of new instructional
strategies
Plan and collaborate with other building teams to help make connections
Work with staff to revise and update Building Improvement Plan
Help facilitate discussions about data with staff
Keep focused on the “Big Picture” and help staff make the connection
Be aware and sensitive to different adult learning styles
Be a coach and cheerleader: clarify, guide, nudge, and support
Model good facilitation skills
Provide support to new staff, teach them the initial processes
Understand the curriculum software and provide support or request formal training if
needed
What is the depth of knowledge?
What Should Districts Do Now?
• Deepen your understanding of the CCSSM in
Professional Learning Communities through:
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the Standards for Mathematical Practice
the Critical Areas
the Model Curriculum
the Standards Progressions
the Comparative Analysis
• Begin focusing instruction around:
– the Mathematical Practices
– The Critical Areas
• Develop support structures for reaching all students
– Use previous mathematics in service of new ideas
– Provide all students access to the regular curriculum; RtI
Grade Level Groups-Draft 10 Month
Pacing Guide
Include DOMAINS, Clusters, and Standards
20 minutes at grade level groups, then back to district for details.
One hour with district.
Select a…
LEADER- to keep everyone on task, no side bar conversations
RECORDER-To chart or word process your information
TIME KEEPER-Give group a heads up at 20 minutes and 50 minutes.
Break- 10 minutes
Ohio’s Decision
Ohio had been a participating
member of two consortia.
On November 15, the Ohio State
Board of Education voted for Ohio
to join PARCC as a governing
member.
Ohio’s New Assessments
PARCC developed
assessments
English language arts
grades 3 – 8 and high
school
Mathematics
grades 3 – 8 and high
school
Assess the Common
Core Standards
Operational school year
2014-15
State developed
assessments
Science
grades 5 and 8 and
high school
Social Studies
grade 5 and 8 and high
school
Assess the revised Ohio
standards
Operational school year
2014-15
• K-3 Diagnostics (Mathematics K-2 only)
– Realigned to CCSS
– Minor modifications to fill gaps
– Ready for use in 2012-13
• OAA (Mathematics Grades 3-8)
– Continue to be administered through 2013-14
– Assessing the 2001 Ohio Academic Content
Standards
• OGT
– Continues after 2014 for additional opportunities for
passage
Resource
Mathematics: Show What You Know
• http://illustrativemathematics.org
• http://www.kindergartenkindergarten.co
m/math-problem-solving/
External Resources for CCSSM
• CCSSO
– www.ccsso.org/
• Achieve
– www.achieve.org
• NCTM
– www.Nctm.org
• Center for K-12 Assessment & Performance
Management at ETS
– www.k12center.org
• YouTube Video Vignettes explaining the CCSS
– http://www.Youtube.com/user/TheHuntInstitute#P/a
ODE Mathematics Consultants
• Brian Roget [email protected]
• Ann Carlson
[email protected]
• Yelena Palayeva
[email protected]
Next Steps
Next STEPS
1. Think about your Unit ideas and how
you can differentiate instruction for
diverse learners.
2. Review the Model Curriculum
Model Curriculum
Check your individual progress toward the
Learning targets for this course on your
BLUE SHEET
Change always comes bearing gifts.
–
~Price Pritchett
– Continuity gives us roots;
– Change gives us branches,
letting us stretch and grow and
reach new heights.
~ Pauline R. Kezer