CII
Council for Instructional Improvement
San Mateo County Office of Education
Friday, February 7, 2014
www.smcoe.org
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
www.smcoe.org
www.smcoe.org
State and Federal Updates
www.smcoe.org
Mathematics
Framework
5
www.smcoe.org
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
6
www.smcoe.org
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
7
www.smcoe.org
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
8
www.smcoe.org
What is in the Mathematics Framework?
•
•
•
•
Introduction
Overview of Standards Chapters
Grade-level chapters, TK8
Higher mathematics chapters by course:
–
–
–
–
–
–
–
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
9
www.smcoe.org
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)
10
www.smcoe.org
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
11
www.smcoe.org
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
12
www.smcoe.org
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
13
www.smcoe.org
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
14
www.smcoe.org
Higher Mathematics
Mathematics Framework Content
•
•
•
•
•
•
•
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
15
www.smcoe.org
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
16
www.smcoe.org
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
17
www.smcoe.org
Instructional Strategies
• Key Instructional Shifts in the
CA CCSSM
• Instructional Models
• Instructional Strategies for the Mathematics
Classroom
• Tools for Mathematics Instruction
18
www.smcoe.org
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
19
www.smcoe.org
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
20
www.smcoe.org
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
21
www.smcoe.org
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)
22
www.smcoe.org
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
www.smcoe.org
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
24
www.smcoe.org
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
www.smcoe.org
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
www.smcoe.org
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.
www.smcoe.org
View the Framework at
http://www.cde.ca.gov/ci/ma/cf/d
raft2mathfwchapters.asp
www.smcoe.org
Toolkit for Evaluating
CCSS Mathematics
Curriculum
www.smcoe.org
The Toolkit
• Evaluative
• Based on CDE
Framework
• Based on the Math
Progressions
• Based on CCSS
Standards
30
www.smcoe.org
Organization
•
•
•
•
•
•
•
•
•
•
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
31
www.smcoe.org
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
32
www.smcoe.org
Alignment to standards / progressions
•
•
•
•
•
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
33
www.smcoe.org
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.
•
34
www.smcoe.org
Section 2
•
•
•
•
•
Alignment to the (draft) Framework
-Alignment to standards
-Program Organization
-Assessment
-Universal Access
35
www.smcoe.org
Alignment to Standards
• Part 1: The mathematics content is correct, factually
accurate…
•
•
•
•
•
-Review various lessons
-Is the content correct?
-Correct definitions
-Use of manipulatives
-No mnemonics or tricks
36
www.smcoe.org
Alignment to Standards
Part 2: The materials …include the standards for mathematical
practice at each grade level or course.
37
www.smcoe.org
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
38
www.smcoe.org
Alignment to Standards
Part 4: Consistent Progressions: Materials are consistent with the
progressions in the Standards
39
www.smcoe.org
Program Organization
•
•
•
•
•
•
How is the textbook set-up?
Standard/cluster
Organized by clusters within units
Intervention (RtI)
Acceleration Components
Support Materials
40
www.smcoe.org
Assessment
•
•
•
•
•
General materials and SBAC Specific:
Variety of assessments (formative)
Summative
Content and Practice Standards
Concept, computation, fluency and
application
• Acceleration and compression aspects
41
www.smcoe.org
Assessment
•
•
•
•
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
42
www.smcoe.org
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
43
www.smcoe.org
Appendix A - Scoring
44
www.smcoe.org
Adoption Now?
www.smcoe.org