Transcript Common Core State Standards

Common Core State Standards
The Mathematics Standards
Anthony Quan—Consultant II, STEM
Belinda Lister—Math Consultant
Division of Curriculum and Instructional Services
commoncore.lacoe.edu
Agenda – Three Days
• Day 1
– Overview
– Content and Curriculum
• Day 2
– Instruction
• Day 3
– Assessment
– Instructional Materials
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Agenda - Today
• Introductions, Logistics
• Overview of the Mathematics CaCCSS
– Break
• Mathematical Practices
• Math Task
– Lunch
•
•
•
•
Domains
Formats
Comparisons of 1997 Standards
Closure
Common Core State Standards
The Mathematics Standards
Overview
commoncore.lacoe.edu
KWL
What I already KNOW
about the Common
Core State Standards
What I WOULD like to
learn about the
Common Core State
Standards
What I LEARNED about
the Common Core
State Standards
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© Copyright 2010. National Governors Association Center for Best
Practices and Council of Chief State School Officers. All rights reserved.
States that Adopted
Why?
To ensure that our students are…
• meeting college and career expectations
(Text Complexity needs to be increased K-12);
• provided a vision of what it means to be
an academically literate person in the
twenty-first century;
• prepared to succeed in our global economy
and society; and
• provided with rigorous content and applications of higher
knowledge through higher order thinking skills.
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2011 © CA County Superintendents Educational Services Association
Phil Daro
The CCSS for Mathematics
• are focused, coherent, and rigorous
• aim for clarity and specificity
• balance mathematical understanding
& procedural skills
• stress conceptual understanding
of key ideas
• are internationally benchmarked
• are research based
……are not a mile wide & an inch deep……
Fractions Domain (3-5)
Solve this problem on your own.
3 1
1 ¸
4 2
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History
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History
NCTM
o Curriculum and Evaluation Standards for
School Mathematics (1989)
o Professional Standards for Teaching
Mathematics (1991)
o Assessment Standards for School
Mathematics (1995)
o Principles and Standards for School
Mathematics (2000)
o Curriculum Focal Points (2006)
o High School Reasoning and Sense Making
(2009)
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Underlying Frameworks
National Council of Teachers of
Mathematics
5 Process Standards
•
•
•
•
•
Problem Solving
Reasoning and Proof
Communication
Connections
Representations
NCTM (2000). Principles and Standards for
School Mathematics. Reston, VA: Author.
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Underlying Frameworks
Strands of Mathematical Proficiency
Conceptual
Understanding
Strategic
Competence
Adaptive
Reasoning
Productive
Disposition
Procedural
Fluency
NRC (2001). Adding It Up. Washington, D.C.:
National Academies Press.
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2009
Common Core State Standard(CCSS)
Initiative was sponsored by:
•

NGA (National Governors Association)
and
CCSSO (Council of Chief State School Officers)
A committee was convened to develop…
1. CCSS
2. Nationwide assessment
3. Timeline for state adoption
Common Core State Standards
• Mathematics Standards
– Lead writers: Phil Daro, Bill McCallum, Jason
Zimba
– Writing teams
– Review teams
• Two rounds of public review and
feedback
• 85% of State Standards must be CCSS
– California Standards include 15% additional
Standards
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What’s different about CCSS?
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)
So What is Different?
o Focus on College & Career Pathways
o Emphasis on Mathematical Modeling
o Standards of Mathematical Practice
o Multiple Formats for Testing
o So far, there are no courses.
Think – Pair - Share
• What does it mean to be college
ready?
• What does it mean to be career
ready?
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College & Career Readiness
• ACT defines college & career readiness as the
acquisition of the knowledge & skills a student
needs to enroll & succeed in credit-bearing, first
year courses at a postsecondary institution without
the need for remediation.
• ACT’s definition of college & career readiness was
adopted by the Common Core State Standards
Initiative & provides a unifying goal upon which
educators & policymakers now must act.
www.act.org/commoncore/pdf/FirstL
ook.pdf
Common Core State Standards
Two types of mathematics
standards
• Standards for Content
• Standards for Practice
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Big Picture in Mathematics
CCSS
Standards of Mathematical Practice
Grade Level Standards
Grades K-5
Grades 6-8
High School Math
Grade 8
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California Grade 8
• Students who are ready for an Algebra course
in 8th grade could experience a revised 6th
and 7th grade instructional program
that embeds the CCSS for 8th grade into the
6th and 7th grade year.
• Standards for 8th grade
– 8th grade Common Core
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2011 © CA County Superintendents Educational Services Association
Standards for
Mathematical Practice
The Eight Standards for
Mathematical Practice place
an emphasis on student
demonstrations of learning
that describe the thinking
processes, habits of mind,
and dispositions that
students need to develop.
adapted from Briars & Mitchell (2010)
Getting Started with the Common Core State Standards
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Part 1: Standards for
Mathematical Practice
1. Make sense of problems and persevere in
solving them
…start by explaining the meaning of a problem and looking for entry
points to its solution
2. Reason abstractly and quantitatively
…make sense of quantities and their relationships to
problem situations
3. Construct viable arguments and critique the reasoning of
others
…understand and use stated assumptions, definitions, and previously
established results in constructing arguments
4. Model with mathematics
…can apply the mathematics they know to solve problems arising in
everyday life, society, and the workplace
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2011 © CA County Superintendents Educational Services Association
Part 2: Standards for
Mathematical Practice
5. Use appropriate tools strategically
…consider the available tools when solving a
mathematical problem
6. Attend to precision
…communicate precisely using clear definitions and calculate
accurately and efficiently
7. Look for and make use of structure
…look closely to discern a pattern or structure
8. Look for and express regularity in repeated
reasoning
…notice if calculations are repeated, and look for both general
methods and for shortcuts
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2011 © CA County Superintendents Educational Services Association
Standards for
Mathematical Practice
Locate the CCSS for Mathematics and read the first
three words for each mathematical practice and notice
the similarities.
Briars & Mitchell (2010)
Getting Started with the Common Core State Standards
What do they begin with?
Mathematically proficient students…
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Example of Mathematical Practice
Let’s look over some lessons.
How are these different from typical
lessons?
• Insidemathematics.org
• MARS Tasks
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CCSS Domains K-5
Domain
K
1
2
3
4
5
Counting and Cardinality
(CC)
✓
Operations and Algebraic
Thinking (OA)
Number and Operations in
Base 10 (NBT)
✓ ✓ ✓ ✓ ✓ ✓
Measurement and Data (MD)
✓ ✓ ✓ ✓ ✓ ✓
✓ ✓ ✓ ✓ ✓ ✓
✓ ✓ ✓
Geometry (G)
Number and Operation –
Fractions (NF)
✓ ✓ ✓ ✓ ✓ ✓
CCSS Domains 6-8
Domain
Ratio and Proportional
Relationships (RP)
The Number System (NS)
Expressions and Equations (EE)
Geometry (G)
Statistics and Probability (SP)
Functions (F)
6
7
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
8
✓
✓
✓
✓
✓
Domains and Conceptual Categories
Distribution
Findell & Foughty (2011)
College and Career-Readiness through the Common Core State Standards for Mathematics
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Focusing Attention Within
Number and Operations
K-5
Operations and Algebraic
Thinking
6-8
High School
Expressions and
Equations
Number and Operations Base Ten
Algebra
The Number
System
Number and
Operations Fractions
Briars & Mitchell (2010)
Getting Started with the Common Core State Standards
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Other Content Area Standards
• Common Core Standards for English
Language Arts have also been adopted.
• New Science standards are being
developed.
• Both are connected to the Math Standards
ELA Standards
• One of the main goals of the ELA
standards is to build “literacy across all
content areas.”
• More emphasis has been placed on more
complex types of reading: expository and
informational.
• Writing, Speaking and Listening apply to
all content areas.
More Instruction in
Expository Text Is Necessary
“To build a foundation for college and career
readiness, students must have ample opportunities
to take part in a variety of rich, structured
conversations—as part of a whole class, in small
groups, and with a partner.”
National Governors Association Center for Best Practices
and Council of Chief State School Officers (2010)
Common Core State Standards for ELA
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The Importance of
Informational Text
“…There is also evidence that current
standards, curriculum, and instructional practice have
not done enough to foster the independent reading of
complex texts so crucial for college and career
readiness, particularly in the case of informational
texts.”
National Governors Association Center for Best Practices
and Council of Chief State School Officers (2010)
Common Core State Standards for ELA
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NAEP Alignment in Reading
Grade
4
8
12
Literature
50%
45%
30%
Information
50%
55%
70%
Percentages do not imply that high school ELA
teachers must teach 70% informational text; they
demand instead that a great deal of reading should
occur in other disciplines.
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2011 © CA County Superintendents Educational Services Association
The 3 Big Buckets of Writing
Opinion/Argu
ment
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Narrative
Informative/Expl
anatory
5th Grade
Collaborative Conversations
• Engage effectively in collaborative discussions (one-on-one, in
groups, and teacher-led) with diverse partners, building on others’
ideas and expressing one’s own clearly.
• Come to discussions prepared, having read or studied required
material; explicitly draw on that preparation and
other information known about the topic to explore ideas
under discussion.
• Follow agreed-upon rules for discussions and carry out assigned
roles.
• Pose and respond to specific questions by making comments that
contribute to the discussion and elaborate on the remarks of others.
• Review the key ideas expressed and draw conclusions in light of
information and knowledge gained from discussions.
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2011 © CA County Superintendents Educational Services Association
Connections to the NGSS
• Each science standard is correlated to the
cognitive demands of both English
Language Arts standards and
mathematics standards.
• Specific correlation of the Common Core
standards are noted in the architecture of
each individual science standard.
Science Standards Connections
• Common Core State Standards Connections: [Note: these
connections will be made more explicit and complete in future
draft releases]
ELA
RI.1.2 Identify the main topic and retell key details of a text.
RI.1.10 With prompting and support, read informational texts
appropriately complex for grade.
W.1.2 Write informative/explanatory texts in which they name
a topic, supply some facts about the topic, and provide some
sense of closure. Mathematics
MP.1 Make sense of problems and persevere in solving them.
MP.3 Construct viable arguments and critique the reasoning
of others.
MP.7 Look for and make use of structure.
1.G.2 Reason with shapes and their attributes.
MATH
M6. Attend to precision
M7. Look for & make use
of structure
M8. Look for & express
regularity in repeated
reasoning
ELA
E2. Build strong content knowledge
E4. Comprehend as well as critique
E5. Value evidence
M2. Reason abstractly & quantitatively
M3. Construct viable argument & critique
reasoning of others
S7. Engage in argument from evidence
S6. Construct explanations & design solutions
S8. Obtain, evaluate & communicate information
E6. Use technology & digital media
M5. Use appropriate tools strategically
E1. Demonstrate independence
E7. Come to understand other perspectives &
cultures
Source: Working Draft, 12-6-11 by
Tina Cheuk, ell.stanford.edu
SCIENCE
S1. Ask questions &
S2. Develop
define problems
and use models
S5. Use mathematics &
S3. Plan & carry out
computational thinking
investigations
M4. Model with mathematics
S4. Analyze & interpret
data
M1. Make sense of
problems & persevere
in solving them
E3. Respond to the varying demands of
audience, talk, purpose, &
discipline
Challenges???
• In your group, discuss the challenges that
you foresee in implementing the Common
Core Standards.
• Be ready to share out in ten (10) minutes.
Implementing CCSS
• Challenge:
– CCSS assessments not available for
several years (2014-2015 deadline)
– Recognizing that CCSS are not “business
as usual”
– Providing assistance to teachers in the
Mathematical Practices
– Textbooks materials will not be available
before the first assessments.
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CCCS:
An Opportunity
• National dialogue about learning expectations
• Fewer, clearer standards
• Refocusing on college and career readiness that
begins earlier in standards
• Research-based, builds on strengths of best state
and international standards
• Equity
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Dr. Wu – UC Berkley
• The Common Core mathematics standards
succeed in being both mathematically
coherent and grade level appropriate.
Overall, they are the best standards I have
seen in the past twenty years. If we can
design a professional development
program of the same caliber to go with
these standards, then our nation will be
making a substantial first step towards
educational excellence in mathematics.
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