WELCOME TO THE MAISA
COMMON CORE STATE STANDARDS
INITIATIVE
MATHEMATICS CURRICULUM MATERIALS SESSION
August 8, 2013
Presented by:
Denise Brady
brady@sresd.org
Shiawassee RESD/Clinton County RESA
Mathematics Consultant
1
AGENDA
• Session Overview, Development and Current
Status of the Project
• CCSSI Mathematics Curriculum
Materials/Resources and Professional
Learning Models
– Exploring a Complete Unit of Study
– Teaching and Learning Trajectories Across Grades
– Curriculum Alignment Model
– Modified Lesson Study Model
• Planning for Transition
13-Apr-15
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MAISA CCSSI
Collaborative
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Allegan Area ESA
Berrien RESA
Clinton County RESA
Genesee ISD
Kalamazoo RESA
Kent ISD
Macomb ISD
Manistee ISD
Muskegon ISD
Oakland ISD
Ottawa ISD
Shiawassee RESD
Traverse Bay Area ISD
Wayne RESA
Wexford-Missaukee ISD
Collaborations
WITHIN MICHIGAN
•Glenda Lappan and Betty Phillips, MSU, Middle School Mathematics
Content
•Edward Silver, UM, Algebra Teaching and Learning 7 – 11
•Jack Smith, MSU, Elementary Measurement
BEYOND MICHIGAN
•Hugh Burkhardt, Shell Centre, Secondary Assessment
•National Council of Supervisors of Mathematics
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Phase 1
Common
Unit &
Lesson
Templates
Common
Focus Area
for Unit
Content
Materials
written and
revised
based on
reviews
from the
field
9 - 11 Units
on Transformations
app.gosoapbox.com
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Event Code: 769-052-273
Phase 2
Leadership
from ISDs
determine
content for
future units
4 additional Units,
units per gradeLessons,
provided in and
2012-2013Assessments
written
3 additional
units per grade
provided 20132014
TOTAL of 6 to
8 units per
grade level from
the project
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Pilot and
Review
Teams from
ISD provide
feedback for
Reviews
Three Year Implementation
PHASE 3
Year 1
One unit of study per
grade (K-11) for both ELA
and Math
Year 2
Four additional units of
study per grade (K-11) fro
both ELA and Math
Year 3
Full K-11 curriculum model
for both ELA and Math
aligned to CCSS
Proposed process for development of K-11 curriculum aligned to
Common Core State Standards for both ELA and Mathematics
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GRADE LEVEL
STRUCTURE
6-8 Units
Per Grade Level
1 Highlight Lesson
per Unit of Study
1 Formative
Assessment Task
Designed Around
Re-engagement
Instructional
Resources
Professional
Learning Resources
Professional
Learning Tasks
(Artifacts)
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CCSS Mathematics
Standards
Standards for Content
Standards for Practice
 Greater balance of concept and skill development
 Greater access for all students
 New focus on
• Mathematical Modeling
• Problem Solving
• Reasoning
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“To help young people learn the more
complex and analytical skills they need for
the 21st century, teachers must learn to
teach in ways that develop higher-order
thinking and performance. To develop the
sophisticated teaching required for this
mission, education systems must offer more
effective professional learning…”
Darling-Hammond and Richardson, 2009
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What do teachers or
administrators need to
consider as they
implement the CCSS
units ?
How might the
MAISA CCSSI
Curriculum
Materials be a
tool to support
CCSS
implementation?
What discussions
need to happen
locally to
implement the
CCSS units?
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FOCUS QUESTIONS
Implementation . . .
Common Core State
Standards MAISA Initiative
The goal of the Common Core State Standards Initiative
(CCSSI) is to provide support and direction for educators
as they move toward full implementation.
CCSS are organized into an aligned curriculum of
coherent units of study. The resources are particularly
designed to highlight needed shifts in content related and
pedagogical practices.
• Highlight Lesson
• Formative Assessment
• Resources (video, sample student work, rubrics, instructional
websites, etc.)
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Key Features of CCSS
addressed in CCSSI materials
• Emphasis on the use of student thinking within instruction
and assessment
• Attention to both content and practice standards to
support a balance of conceptual understanding and
procedural fluency
• Incorporation of mathematical explanations by students
• Use of multiple representations (technology)
• Integration of accessibility strategies including attention to
Title One support strategies
• Learning opportunities and assessments that include
inquiry and exploration
• Embedded research-based tools to support
implementation
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Connecting
Representations
Oral
Language
Verbal
(written and oral)
Pictures
Real-World
Situations
Written
Symbols
Contextual
Manipulative
Models
Symbolic
Geometric/
Graphical
Tabular
Adapted from Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations among
Representations in Mathematics Learning and Problem Solving. In C. Janvier, (Ed.), Problems
of Representations in the Teaching and Learning of Mathematics (pp. 33-40). Hillsdale, NJ:
Lawrence Erlbaum.
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Frequently Asked Questions
• Will this curriculum
replace my instructional
materials?
• No, these materials are
designed to support teachers’
use of their instructional
materials.
• They are intended to be tools
to guide instruction and
provide contexts for
professional learning as
teachers reorganize their
instruction and work to
implement the CCSS
• Not self-enacting
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Professional
Learning
Models
1.
2.
3.
4.
Exploring a Complete Unit of Study
Curriculum Alignment
Teaching & Learning Trajectories across Grades
Modified Lesson Study
MAISA COMMON CORE
STATE STANDARDS
INITIATIVE (CCSSI)
Model 1:
Exploring a Complete Unit of Study
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Key Characteristics of
Mathematics Standards
 Focus on key topics at each grade level so that students gain
strong foundations
 Coherence: Connections across grades AND link major
topics within grades
 Rigor: An increase in conceptual understanding, procedural
skill and fluency, and application with equal intensity
 Mathematical practices: Foster reasoning and sensemaking in mathematics
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UNIT TITLES
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Grade Level Unit Components
1. Unit Themes
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Graphic
Focus Questions
Intellectual Processes
Key Concepts
2. Content Standards
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Abstract
CCSS Standards
3. Instructional Resources
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Illuminations
Children’s Literature
Texas Instruments
References
Applets
4. Professional Resources
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NCTM Articles
Books
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Orientation to the Unit
Refer to the unit overview:
1. Where do you see opportunities for teachers to grow their
understanding of mathematics content and develop standards
for practice?
2. How might a single unit support teachers in making both
content related and pedagogical shifts in practice?
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Atlas Curriculum Mapping
Units, Highlight Lessons, Formative Assessments
and other resources available in Atlas by Rubicon
http://gomaisa-public.rubiconatlas.org/Atlas/Public
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Units of Study
Lesson resources
Assessment resources
Professional resources
• Video
• Sample student work
• And more
Highlight Lesson Components
1. Highlight Lesson Themes
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Graphic
Focus Questions
Intellectual Processes
Key Concepts
2. Highlight Lesson Content
Standards
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Abstract
CCSS Standards
Lesson Instructional
Resources
3. Sequence of Lesson
Activities
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Selecting and Setting up a
Mathematical Task
Launch
Supporting Students’
Exploration of the Task
Sharing and Discussing the
Task
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Thinking Through a Lesson Protocol
Smith, M.S., Bill, V., &
Hughes, E.K. (2008).
Thinking through a lesson:
Successfully implementing
high-level tasks. Mathematics
Teaching in the Middle School,
14, 132-138.
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TEACHERS & TASKS
MATTER
Tasks as
they appear
in curricular
materials
Tasks as
enacted by
teachers
and
students
Tasks as
set up by
teachers
Student
learning
The Mathematical Tasks Framework
Stein, Grover & Henningsen (1996)
Smith & Stein (1998)
Stein, Smith, Henningsen & Silver (2000)
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Reengagement
A Formative Assessment Strategy
Reengagement:
• is a formative assessment strategy by which teachers
use information from student work to design a
learning opportunity that is an evolution of the
original task and is focused on enhancing students’
current understandings;
• is grounded in the effective and intentional use of
student thinking to forward learning; and
• requires interactions between and among teachers,
students, and the content to be learned.
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Formative Assessment
Reengagement Framework
1. Give the assessment
task
2. Collect and analyze
student thinking
3. Reengage students
with an evolution of
the original task
4. Summarize
5. Provide independent
practice
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CCSSI Curriculum Resources
In groups: Individually consider
either the Unit, Highlight Lesson,
or Formative Assessment:
Where do you see opportunities
for students and teachers to grow
in their:
• understanding of
mathematics content AND
practices
• use of technology for
instruction?
How might your teachers use
these resources?
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Be prepared to share your
thinking with your group!
Professional
Learning
Models
1.
2.
3.
4.
Exploring a Complete Unit of Study
Curriculum Alignment
Teaching & Learning Trajectories across Grades
Modified Lesson Study
MAISA Common
Core State
Standards
Initiative (CCSSI)
Model 3:
Learning Trajectories across Grades
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Learning Trajectories
and the Common Core
State Standards
“A teacher or test designer seeing exclusively within the
grade level will miss the point [of the number line].
Multi-grade progression views of standards can avoid
many misuses of standards” (p.43).
How might understanding the CCSS learning
trajectories improve student learning?
UNIT TITLES
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Learning Trajectories Across
Grades
Professional Learning Model 3
Activity – Working with your table group, discuss the
development of the mathematical ideas across the grade
levels.
1. What do you notice about the
development of the mathematics
across the grades?
2. How might understanding this
mathematical trajectory impact
instruction, particularly issues of
accessibility and formative
assessment? Give one or two
specific examples of how this
might impact some aspect of
teaching.
Learning Trajectories and the
Common Core State Standards
RESOURCES:
www.turnonccmath.net
http://ime.math.arizona.edu/progressions
Slide
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Building Connections & Coherence
at Two Levels
Work at the systems level:
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Course curriculum design within and across grades/courses
Course offerings (tracking, acceleration, integrated content)
Instructional tasks
Collegial conversations within and across grades/courses (District
Dialogues)
Work at the classroom level:
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Task selection
Assessment for learning
Identifying misconceptions
Connecting to prior knowledge and future lessons (mathematical
language, tasks, strategies)
LUNCH
12:00-12:45
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Professional
Learning
Models
1.
2.
3.
4.
Exploring a Complete Unit of Study
Curriculum Alignment
Teaching & Learning Trajectories across Grades
Modified Lesson Study
MAISA Common Core
State Standards
Initiative (CCSSI)
Model 2:
Mathematics Curriculum Alignment:
Using the MAISA CCSS
Mathematics Curriculum Materials
to Guide Instruction
A Challenging Opportunity!
“These Standards are not
intended to be new names
for old ways of doing
business. They are a call to
take the next step. It is time
for states to work together
to build on lessons learned
from two decades of
standards based reforms. It
is time to recognize that
standards are not just
promises to our children, but
promises we intend to
keep.”
— CCSS (2010, p.5)
Planning for CCSS Implementation
What do we need to do to
implement both the pedagogy
and content of the CCSSI
units?
How can our textbooks be a
resource for us?
Curriculum Alignment
Professional Learning Model 2
1. Preliminary Analysis - Compare the list of CCSSI Curriculum Unit
Titles to the unit titles in your instructional materials and begin to
map corresponding units.
2. Concepts and Skills - Focused Analysis: Review the concepts and
skills in your instructional materials using a particular CCSSI Unit as
a curriculum guide. Make notes regarding your instructional
material’s inclusion/exclusion of the CCSS for mathematical
concepts and skills.
3. Practice-Focused Analysis: Repeat Step 2 with
a focus on the CCSS for Mathematical Practice.
Curriculum Alignment
Professional Learning Model 2
1. Preliminary Analysis
(about 20 minutes)
Compare the list of CCSSI
Curriculum Unit Titles to the
unit titles in your instructional
materials and begin to map
corresponding units.
•
Topic 1: Numeration
•
Topic 2: Number Sense: Addition and Subtraction
•
Topic 3: Using Place Value to Add and Subtract
•
Topic 4: Meaning of Multiplication
•
Topic 5: Multiplication Facts: Use Patterns
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Topic 6: Multiplication Fact: Use Known Facts
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Topic 7: Meanings of Division
•
Topic 8: Division Facts
•
Topic 9: Understanding Fractions
•
Topic 10: Fraction Comparison and Equivalence
•
Topic 11: Two-Dimensional Shapes and Their
Attributes
•
Topic 12: Time
•
Topic 13: Perimeter
•
Topic 14: Area
•
Topic 15: Liquid, Volume, and Mass
•
Topic 16: Data
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Curriculum Alignment
Professional Learning Model 2
2. Concepts and Skills-Focused
Analysis (about 50 min)
Review the concepts and
skills in your instructional
materials using a particular
CCSSI Unit as a curriculum
guide. Make notes regarding
your instructional material’s
inclusion/exclusion of the
CCSS-M concepts and skills.
Textbook Enactment Guide –
Annotated Template
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SAMPLe only
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Sample only
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Textbook Enactment Guide –
Blank Template
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Curriculum Alignment
Professional Learning Model 2
3. Practice-Focused Analysis
(about 30 minutes)
Repeat Step 2 with a focus
on the CCSS for
Mathematical Practice.
Reflections
1. What is your reaction to the work
we have done thus far?
What seems promising and/or
challenging at this point?
2. What work needs to be continued
to support mathematics teaching
and learning?
BREAK
1:45-2:00
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Professional
Learning
Models
1.
2.
3.
4.
Exploring a Complete Unit of Study
Curriculum Alignment
Teaching & Learning Trajectories across Grades
Modified Lesson Study
MAISA Common Core
State Standards
Initiative (CCSSI)
Model 4:
Modified Lesson Study:
Using the MAISA CCSS
Mathematics Curriculum
Materials to Guide
Instruction
A Challenging Opportunity!
“These Standards are not
intended to be new names
for old ways of doing
business. They are a call to
take the next step. It is time
for states to work together
to build on lessons learned
from two decades of
standards based reforms. It
is time to recognize that
standards are not just
promises to our children, but
promises we intend to
keep.”
— CCSS (2010, p.5)
Planning for CCSS Implementation
How can we use
collaborative planning and
debriefing opportunities to
support shifts in practice?
What might we learn from
collaborative planning and
debriefing opportunities to
support learning of
mathematics?
Modified Lesson Study:
Collaboratively Planning and Debriefing Lessons
Modified Lesson Study using the Highlight Lesson
1
Preview and Plan
a) the lesson
b) the post lesson discussion
2
3
Reflect and Learn
a) the lesson
b) instructional elements
Modified Lesson Study:
Collaboratively Planning and Debriefing Lessons
Modified Lesson Study using the Highlight Lesson
1
Preview and Plan
a) the lesson
b) the post lesson discussion
2
3
Reflect and Learn
a) the lesson
b) instructional elements
Modified Lesson Study:
Collaboratively Planning and Debriefing Lessons
Modified Lesson Study using the Highlight Lesson
1
Preview and Plan
a) the lesson
b) the post lesson discussion
2
3
Reflect and Learn
a) the lesson
b) instructional elements
Modified Lesson Study:
Collaboratively Planning and Debriefing Lessons
After experiencing the lesson discuss:
• What are the mathematical goals of the
lesson?
• What about this lesson highlights what is
“new” given the CCSS?
• What about this lesson might be
challenging for us and our students?
• What is apparent in the lesson that
could help make this lesson accessible
to all our students?
Modified Lesson Study:
Collaboratively Planning and Debriefing Lessons
Given the instructional focus we
are exploring:
• What artifacts might you collect from
this lesson that could be used as the
context for future learning given the
“new” and challenging lesson features
we identified?
Planning for 2013-14
•
•
Professional Development Focused
Around:
•
Possible Content:
•
•
•
Implementing the Practices and
Making Sense of Trajectories using
selected units to focus conversations
• Grade Level Meetings
• Grade Band Meetings
• Staff Meetings
• PD Days
• SI Days
• Common Planning
• Professional Learning Communities
•
•
Slide
62
Classroom Video to Identify Practices
Look For’s
Illustrating the Standards for
Mathematical Practice (NCSM)
Using 2-4 Units as Contexts for
Conversations
• Implement a Highlight Lesson and
Conduct Lesson Study
• Trajectory Conversations
Curriculum Alignment Model
• Grade Level Representative keep
notes on the extent to which the
resource (Text) aligns to each unit
in the grade level (Use tool to note:
Lessons in materials at CCSS grade
level, not at CCSS grade level,
evidence and attention to
mathematical practices, places
where needing to supplement, etc.)
• Develop a map to use the following
year (Spring/Summer 2014
Planning for 2014-15
•
•
Professional Development
Focused Around:
•
Possible Content:
•
Implementing the Practices and
Making Sense of Additional
Trajectories using selected units to
focus conversations
• Grade Level Meetings
• Grade Band Meetings
• Staff Meetings
• PD Days
• SI Days
• Common Planning
• Professional Learning
Communities
•
•
•
•
Slide
63
Classroom Video to Identify
Practices
Look For’s
Illustrating the Standards for
Mathematical Practice (NCSM)
Using Another 2-4 Units as Contexts
for Conversations
• Implement a Highlight Lesson and
Conduct Lesson Study
• Continue Trajectory
Conversations
Curriculum Alignment Model
• Develop a map to use the
following year (Spring/Summer
2014)
• Share the maps with staff
• Implement Lesson Study
• Continue Curriculum Alignment
Our Collaborative Work
School/District Implementation
Individually, write down your initial
thoughts given what we have started
today.
• What professional learning goals
might be productive for your grade
band, school, or district?
• How and when could you engage in
these conversations on a regular
basis?
• Which dialogues need to be
continued within your school/district
to support CCSS implementation?
Courses, Seminars, &
Resources
Website Resource Collections
•Turn on Common Core Math
http://turnonccmath.com/
•Progression Documents (Bill McCallum)
http://ime.math.arizona.edu/progressions
•National Council of Supervisors of Mathematics (NCSM)
•Illustrating the Standards for Mathematical Practice
http://www.mathedleadership.org/ccss/itp/index.html
•Inside Mathematics
http://insidemathematics.org/index.php/exemplary-lessonsintegrating-practice-standards
•Illustrative Mathematics
http://illustrativemathematics.org/
•Common Core Tools
www.nctm.org
Math Common Core Coalition
http://www.nctm.org/standards/mathcommoncore/
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