CII
Council for Instructional Improvement
San Mateo County Office of Education
Friday, February 7, 2014
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Agenda
Welcome, Review Agenda
State/Federal Updates
California Mathematics Framework
Math Curriculum Evaluation Toolkit
Break
Common Core State Standards for
Mathematics and the Smarter Balanced
Assessments
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State and Federal Updates
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Mathematics
Framework
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Goals for the Mathematics Framework
• Guide the field in implementing the CA CCSSM
• Emphasize coherence across and within grade
levels
• Integrate the Standards for Mathematical
Practice and Standards for Mathematical Content
• Provide guidance on the higher mathematics
course progression
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Development of the Mathematics Framework
• Focus Group members—all educators in California
K–12 public schools, four regional meetings
• Mathematics Framework Committee members—a majority of
teachers, including teachers with experience teaching English
learners and students with disabilities, other educators, and
two content experts with Ph.Ds. in mathematics
• IQC—teachers, curriculum leaders, and administrators
• Staff of the Curriculum Frameworks and Instructional
Resources Division and mathematics expert Dr. Christopher
Yakes
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Development of the Mathematics Framework
• The field—provided comments on the draft Framework
during two 60-day review periods
• County Offices of Education—held discussion forums on the
first draft of the Mathematics Framework
• Common Core State Standards for Mathematics author and
expert Jason Zimba
• WestEd’s California Comprehensive Center, Neal Finkelstein
and Dona Meinders
• Staff of the California Department of Education’s Language
Policy and Leadership Office, STEM Office, and Assessment
Transition Office
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What is in the Mathematics Framework?
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Introduction
Overview of Standards Chapters
Grade-level chapters, TK8
Higher mathematics chapters by course:
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Traditional pathway (Algebra I, Geometry, Algebra II)
Integrated pathway (Mathematics I, II, and III)
Pre-calculus
Statistics and Probability
Advanced Placement Probability and Statistics
Calculus
Mathematical Modeling
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What is in the Mathematics Framework?
• Universal Access
• Instructional Strategies
• Supporting High-Quality Common Core Mathematics
Instruction
• Technology in the Teaching of Mathematics
• Assessment
• Instructional Materials to Support the CA CCSSM (including
the evaluation criteria for the mathematics adoption)
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What is in the Appendix?
A. Financial Literacy and Mathematics Education
B. Mathematical Modeling
C. Method Used for Solving Single-digit Addition and
Subtraction Problems
D. Course Placement and Sequences
E. Possible Adaptations for Students with Learning
Difficulties in Mathematics
F. Higher Mathematics Pathways Standards Chart
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K-8 Mathematics Framework Content
Focus Coherence Rigor
• A focus on understanding addition, subtraction,
multiplication, and division (the four operations) in
K5
• Building from whole numbers in K2 to fractions in
grades 35
• Expectations of fluency with whole numbers and
fractions in K5
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K-8 Mathematics Framework Content
Focus Coherence Rigor
• A focus on ratio, rates, percent, and statistics
and probability in 68
• Extending operations with fractions to rational
numbers in 68
• Expectations of fluency with expressions and
linear equations 68
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Structure of the Grade-Level Chapters
• Short discussion of learning in previous grade
• Four critical areas of instruction
• Standard or cluster of standards with a
narrative that provides additional explanation
• Sample problems that further illustrate the
standard
• Grade level explanations and examples for the
Standards for Mathematical Practice
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Higher Mathematics
Mathematics Framework Content
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Traditional Pathway (Algebra I, Geometry, Algebra II)
Integrated Pathway (Mathematics I, II, and III)
Precalculus
Statistics and Probability
Calculus
AP Probability and Statistics
Mathematical Modeling
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Higher Mathematics
Mathematics Framework Content
Focus
Coherence
Rigor
• A focus on the mathematics that students need for
success in college and careers
• Extending from algebraic concepts to calculus,
trigonometry, and advanced statistics
• Expectation that students are college and career
ready and able to utilize mathematics in their lives
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Universal Access
• California’s student diversity
• Planning and support for a range of leaners using
Universal Design for Learning (UDL) and Multi-Tiered
Systems of Supports (MTSS)
• Strategies to meet the increased language demands
of the California Common Core State Standards for
Mathematics
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Instructional Strategies
• Key Instructional Shifts in the
CA CCSSM
• Instructional Models
• Instructional Strategies for the Mathematics
Classroom
• Tools for Mathematics Instruction
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Technology in the Teaching of Mathematics
• Technology as a integral tool in the
mathematics classroom
• Illustrative examples by grade level
• Educational Technology (e.g. interactive
clickers, smart phones, tablets)
• Assistive Technology
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Assessment
• Purposes and types of assessments
– Formative assessment for learning
– Summative assessment of learning
• Methods and tools for assessment
• Sample rubrics
• Grading, homework, and the Smarter
Balanced Assessments
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Instructional Materials to Support CCSS
• Contains the “Criteria for Evaluating Mathematics
Instructional Materials for Kindergarten through
Grade Eight,” which was the basis for the January
2014 adoption
• Provides guidance to districts on adopting
instructional materials for higher mathematics,
including indicators of quality
• Outlines a process for local adoptions
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Supporting High-Quality Common Core
Mathematics Instruction
• Administrator Roles and Support
• Professional learning, including sources, research,
and critical content
• Leadership and professional collaboration
• Other programs of support (e.g., extended learning,
parents and families)
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Supporting High-Quality Common Core
Mathematics Instruction
Recommendations:
• Teacher Education
• Mentoring for Beginners
• Professional Learning Time
• Evaluation
• Leadership Pathways
From the “Greatness by
Design Report:
Supporting Outstanding
Teaching to Sustain a
Golden State. A report by
State Superintendent of
Public Instruction Tom
Torlakson’s Task Force on
Educator Excellence
September 2012
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Professional Learning for Teachers
Content
• Deepen mathematics teachers’ content knowledge
and provide effective instruction strategies.
• Engage in solving problems through using the
mathematical practices.
Pedagogy
• problem solving strategies
• Multiple representation
• Formative assessment strategies
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Forms of Professional Learning
• Sustained, content-embedded, collegial and
connected to practice
• Focused on student learning
• Models
– Summer
– Teacher collaboration
– Lesson Study
– Fostering teacher leaders
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Evaluation of Instruction
• Tie evaluation to useful feedback and to
profession learning opportunities
• Assess alignment to CCSS
• Include both formative and summative
assessments
• Differentiate support
• Build on successful peer assistance
• Value and promote collaboration
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What? How? When? Who?
Take a few minutes to reflect on the
recommendations from the Greatness by
Design report by filling in the Supporting
High-Quality Common Core Mathematics
Instruction template.
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View the Framework at
http://www.cde.ca.gov/ci/ma/cf/d
raft2mathfwchapters.asp
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Toolkit for Evaluating
CCSS Mathematics
Curriculum
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The Toolkit
• Evaluative
• Based on CDE
Framework
• Based on the Math
Progressions
• Based on CCSS
Standards
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Organization
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Section 1:
Alignment to standards and progressions
-Cluster, scope and sequence
Section 2:
Alignment to the (draft) Framework
-Alignment to standards
-Program Organization
-Assessment
-Universal Access
-Instructional Strategies
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Section 1
Alignment to standards and progressions
1. The need to build content knowledge.
2. The need to build pedagogy.
3. The scope of CCSS-math
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Alignment to standards / progressions
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3-5:
Approach to fractions (page 11)
· Use of number lines (Number and Operations- Fractions Progression)
· The textbook addresses fractions by using a number line diagram.
· The textbook compares two fractions with the same numerator or the
same denominator by reasoning about their size.
A
B C D
E
F
1/2
1
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Alignment to standards / progressions
• 3-5:
• Approach to multiplication (page 9)
• Students develop an understanding of the meanings
for multiplication and division of whole numbers
through activities and problems involving equal-sized
groups, arrays and area
models.
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Section 2
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Alignment to the (draft) Framework
-Alignment to standards
-Program Organization
-Assessment
-Universal Access
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Alignment to Standards
• Part 1: The mathematics content is correct, factually
accurate…
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-Review various lessons
-Is the content correct?
-Correct definitions
-Use of manipulatives
-No mnemonics or tricks
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Alignment to Standards
Part 2: The materials …include the standards for mathematical
practice at each grade level or course.
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Alignment to Standards
Part 3: In any single grade… students and teachers… spend the
large majority of their time, approximately three-quarters… on
major clusters
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Alignment to Standards
Part 4: Consistent Progressions: Materials are consistent with the
progressions in the Standards
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Program Organization
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How is the textbook set-up?
Standard/cluster
Organized by clusters within units
Intervention (RtI)
Acceleration Components
Support Materials
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Assessment
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General materials and SBAC Specific:
Variety of assessments (formative)
Summative
Content and Practice Standards
Concept, computation, fluency and
application
• Acceleration and compression aspects
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Assessment
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General materials and SBAC Specific:
Claim #1 – assessment of concept
Claim #2 – assessment problem solving strategies
Claim #3 – assessment provides opportunity to
construct a viable argument
• Claim #4 – assessment through complex, real-world
scenarios
• Technology enhanced problems
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Universal Access
• 2013 Math Framework, “Students with special needs must be
provided access to the same standards-based curriculum that
is provided to all students…”
• Differentiation
• Correction for common misconceptions
• Specialized teaching methods / materials for students with
special needs
• Strategies for English Learners
• Strategies for students with disabilities
• Alternate lessons for exceptional students (depth and
complexity
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Appendix A - Scoring
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Adoption Now?
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Download

Mathematics Framework Content