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Mathematics in California
Sheri Willebrand Kathlan Latimer CMC President CMC President Elect
CaMSP April 4, 2011
WELCOME
Common
Core
California
Standards
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CaCCSSM
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Before 1997… What do you remember?
Before there were standards….
Rubrics
Replacement Units
O-E Problems
Mathematical Power
Writing in Math
Justify Thinking
Making Sense
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We had a VISION….
Math in Context
Programs were scripted, pacing guides drove instruction…
because of testing, testing, testing.
The 1997 CA standards gave teachers permission to teach skills and procedures.
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The right to ignore anything that doesn’t make sense is a crucial element
of any child’s learning--and the first right children are likely to lose when they
get to the controlled learningenvironment of school.
Frank Smith
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Unintended outcome….
° Research ° ° ° NAEP °
What number would you place in the box to make a true number sentence?
8 + 4 = [ ] + 5
What are possible student answers?
National Assessment Educational Progress
° Research ° ° ° From: Falkner, Levi & Carpenter, 1999°
Response / Percent Responding
Grade 7 12 17 12 and 17
1 & 2 5% 58% 13% 8%
3 & 4 9% 49% 25% 10%
5 & 6 2% 76% 21% 2%
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New California Standards
State Board of Education adopted new
mathematics standards.
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California Common Core State Standards
(CaCCSS)
TIME TO CELEBRATE!
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Where did the new mathematics standards
come from?
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Criteria for CCSS
• Fewer, clearer, and higher standards
• Aligned with college and work expectations
• Include rigorous content and application of knowledge through high-order skills
Criteria for CCSS
• Build upon strengths and lessons of current state standards
• Internationally benchmarked
• Based on evidence and research
COMMON CORE STATE STANDARDS (CCSS)
Adoption of CCSS is required for
Race to the Top funds.
California applied for Race to the Top
and adopted the CCSS.
COMMON CORE STATE STANDARDS (CCSS)
States that choose to align their standards to the common core standards must
accept 100% of the core.States may add additional standards.
California added about 15%.
Common Core State Standards:
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Focused
Coherent
Rigorous
Develops Concepts
Internationally Benchmarked
Prepare for College & Career
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Two Types of Standards• Mathematical Practice
recurring throughout the grades
• Mathematical Content
different at each grade level
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The Standards for Mathematical Practice
Define habits of mind of a Mathematically expert student.
A Place to Start
Adding it Up, 2001
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“ …describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high schools years.”
CCSS pg. 2
Standards for Mathematical Practice
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
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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
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The Standards for Mathematical Content
K - 5 ° 6 - 8 ° HS
A Quick Overview
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K – Grade 5 Domains
Domain K 1 2 3 4 5
Counting and Cardinality (CC) Operations and Algebraic Thinking (OA) Number and Operations in Base Ten (NBT)
Measurement and Data (MD)
Geometry (G) Number and Operations – Fractions (NF)
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Grades 6 – 8 Domains
Domain 6 7 8
Ratios and Proportional Relationships (RP)
The Number System (NS)
Expressions and Equations (EE) Geometry (G) Statistics and Probability (SP)
Functions (F)
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Grade Grade LevelLevel
DomainDomain
How the grade level standards are organized
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Format of K-8 Standards
ClusterCluster
ClusterCluster
StandardStandard
StandardStandard
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The added Standards from 1997 Standards (15%)
are bold, underlined and the source indicated.
CaCCSSM Added Standards
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CC Domains CA Strands Operations and Algebraic
Thinking Number and Operations
in Base Ten Number and Operations –
Fractions
Algebra and Functions Number Sense
Measurement and Data Measurement and Geometry
Geometry Statistics, Data Analysis, and Probability
Mathematical Practices Mathematical Reasoning
K – 5 CC Domains & CA Strands
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Mathematics Grade 8
“The California State Board of Education acknowledges that the goal for 8th grade students is Algebra I. However, they also recognize that not all 8th grade students have the necessary prerequisite skills for Algebra I. Consequently, the State Board of Education adopted two sets of standards for 8th grade.
“The first set describes standards for Algebra I.
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Mathematics Grade 8 (continued)
“The second set of standards is from the 8th grade Common Core document published June 2, 2010. These standards are for 8th grade students who do not have the necessary prerequisite skills for Algebra I. The goal of the 8th grade Common Core is to finalize the mathematics preparation for students in high school.
“There is some duplication of standards between grades and courses that will be resolved in the frameworks/instructional materials development process.”
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High School Mathematics
The high school standards are listed in conceptual categories:
Number and QuantityAlgebraFunctionsModeling GeometryStatistics and Probability
These are not courses.
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High School Standards
Conceptual Category
Standard
Cluster
Domain
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Available at http://www.corestandards.org/the-standards
The new standards have a greater expectation
for depth of understanding.
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CaCCSSM
What is important to know right now?
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Fractions on a
Number LinePrimary number
Next Steps
Mathematical Modeling
Transformational
Geometry
Number line in Quantity and measurement
Number line in Quantity and measurement
Equal PartitioningEqual Partitioning
FractionsFractions
Rational numberRational number
Properties of OperationsProperties of Operations
Rational ExpressionsRational Expressions
K - 2 3 - 6 7 - 12
Unitizing in base 10 and in
measurement
Unitizing in base 10 and in
measurement
Rates, proportional and linear relationships
Rates, proportional and linear relationships
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• Educators must be given resources, tools, and time to adjust classroom practice.
• Instructional materials needed that align to the standards.
• Assessments must be developed to measure student progress.
• Federal, state, and district policies will need to be reexamined to ensure they support alignment of the common core state standards with student achievement.
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Two Assessment Consortia Awarded Funds
States Distribution
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Next Steps
• Frameworks and instructional materials • Assessments • Professional development• Teacher Credentialing • Parent Education
Check out the
CMC website:
www.cmc-math.org
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To Learn More:
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–Implement a truly balanced math program as this will support the mathematical practices
–Continue to use quality assessments to inform and drive effective instruction
–Provide opportunities for teachers to collaborate and plan
Stay the Course…
People
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What will make the difference?
TeachersThat is US!!
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Sheri Willebrand
Kathlan Latimer