Download Final CCSS Overview K-12 Math

CALIFORNIA
COMMON
CORE
STATE
STANDARDS
(CCSS)
MATHEMATICS
OVERVIEW
Walter Lewis
[email protected]
760.312.6176
WHAT IS THE TIMELINE
AGENDA
Welcome /Outcomes /Agenda
 Overview-What is the direction of Math Education?
 Math CCSS
 Standards for Mathematical Practice
 Content Standards
 Assessment/Consideration/Reflection

BUT FIRST A PROBLEM…
SALE!
Max bought 2 items in a sale.
One item was 10% off.
One item was 20% off.
Max says he saved 15% altogether. Is he right?
Explain.
SALE! (SEVENTH GRADE-SBAC)
Max bought 2 items in a sale.
One item was 10% off.
One item was 20% off.
Max says he saved 15% altogether. Is he right?
Explain.
WRAP THE MUMMY
Pam is thirteen today. She is holding a party
at which she plans to play the game 'Wrap the
mummy'. In this game, players try to
completely cover themselves with toilet paper.
A roll of toilet paper contains 100 feet of paper,
4 inches wide.
Will one toilet roll be enough to wrap a
person?
Describe your reasoning as fully as possible.
(You will need to estimate the average size of
an adult person)
WRAP THE MUMMY (SEVENTH GRADE-SBAC)
Pam is thirteen today. She is holding a party
at which she plans to play the game 'Wrap the
mummy'. In this game, players try to
completely cover themselves with toilet paper.
A roll of toilet paper contains 100 feet of paper,
4 inches wide.
Will one toilet roll be enough to wrap a
person?
Describe your reasoning as fully as possible.
(You will need to estimate the average size of
an adult person)
WHAT SHOULD MATHEMATICS INSTRUCTION
LOOK LIKE NOW…MARZANO’S ANALYSIS
The
Perils
and
Promises
of
Discovery
Learning
Quality instruction
Checking for Understanding
2
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California Common Core State Standards
Common Core State Standards
What I already know
about the Common Core
State Standards.
What I would like to
What I learned today
learn about the Common about the Common Core
Core State Standards.
State Standards.
WHY THE COMMON CORE STATE STANDARDS?
Ensure that our students are…
 meeting college and career expectations with text
complexity 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.
BENEFITS OF THE CCSS
 Internationally benchmarked
 Evidence and research-based
 Expectations clear to students, parents,
teachers, and the general public
 Costs to the state reduced
 Consistent expectations for all—not
dependent on a zip code
HEART & SOUL OF CCSS
Math
ELA
Standards for
Mathematical
Practice
College and
Career
Readiness
Standards
MATHEMATICS INCLUDES TWO
SETS OF STANDARDS:
Standards for Mathematical Practice AND
Content Standards
AUTHORS FOR THE STANDARDS…
Professor
William
McCallum
Jason
Zimba
Ph.D.
Phil
Daro
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.
STANDARDS FOR MATHEMATICAL PRACTICES
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
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
1.
Make sense of problems
and persevere in solving
them.
6. Attend to precision
Common Core State Standards
Mathematical Practices
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.
THE STANDARDS FOR
MATHEMATICAL PRACTICE
Take a moment to examine the first
three words of each of the 8
mathematical practices…what do
you notice?
Mathematically Proficient
Students…
Briars, Diane. “Getting Started with the Common Core State Standards.”
Power Point Presentation. NCSM Winter Conference, 2011.
THE STANDARDS FOR [STUDENT]
MATHEMATICAL PRACTICE
SMP1: Explain and make conjectures…
SMP2: Make sense of…
SMP3: Understand and use…
SMP4: Apply and interpret…
SMP5: Consider and detect…
SMP6: Communicate precisely to others…
SMP7: Discern and recognize…
SMP8: Notice and pay attention to…
Briars, Diane. “Getting Started with the Common Core State Standards.”
Power Point Presentation. NCSM Winter Conference, 2011.
THE STANDARDS FOR [STUDENT]
MATHEMATICAL PRACTICE
The 8 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.
that describe mathematical content students
need to learn.
Adapted from Briars, Diane. “Getting Started with the Common Core
State Standards.” Power Point Presentation. NCSM Winter
Conference, 2011.
CCSS DOMAINS AND CONCEPTUAL CATEGORIES
K
1
2
3
4
5
6
7
8
HS
Counting &
Cardinality
Number and Operations in Base Ten
Number and Operations –
Fractions
Ratios and Proportional
Relationships
Number &
Quantity
The Number System
Expressions and Equations
Algebra
Operations and Algebraic Thinking
Functions
Geometry
Measurement and Data
Functions
Geometry
Statistics and Probability
Statistics &
Probability
Findwell, Bradford & Foughty, Zachary. “”Preparing to Implement the Common Core State Standards for Mathematics. Indiana
Department of Education and Ohio Department of Education. March 30, 2011
CCSS DOMAINS K-8
Domain
K1 2 3 4 5
Counting and Cardinality
(CC)

Operations and Algebraic
Thinking (OA)
Domain
678
Ratios and Proportional
Relationships (RP)


The Number System (NS)

Number and Operations in
Base Ten (NBT)

Expressions and Equations (EE)

Measurement and Data
(MD)

Geometry (G)

Geometry (G)

Statistics and Probability (SP)

Number and Operations –
Fractions (NF)

Functions (F)

GRADE SHIFTS
EXAMPLES 6-8
1997
Standards
CCSS
Dividing fractions by fractions
Grade
5
Grade
6
Concepts of mean and median to
summarize data sets
Grade
5
Grade
6
Operations with numbers in
scientific notation
Grade
7
Grade
8
Pythagorean Theorem
Grade
7
Grade
8
Concept
CALIFORNIA GRADE 8 OPTIONS
The Goal for 8th grade students is Algebra 1.
However, there are two sets of standards for
grade 8
 Standards for Algebra 1-Taken from 8th
grade Common Core, high school Algebra
content cluster and CA Algebra standards
 8th grade Common Core-Finalize
preparation for students in high school.
HIGH SCHOOL MATHEMATICS
The CCSS high school standards are organized in 6 conceptual
categories:
 Number and Quantity
 Algebra
 Functions
 Modeling (*)
 Geometry
 Statistics and Probability
California additions:
 Advanced Placement Probability and Statistics
 Calculus
Modeling standards are indicated by a (*) symbol.
Standards necessary to prepare for advanced courses in mathematics are indicated by a (+) symbol.
Two Mathematics Pathways
Two Regular Sequences:
Traditional Pathway
2 Algebra courses,1
Geometry course, with
Probability and Statistics
interwoven
Courses in higher level mathematics: Precalculus,
Calculus*, Advanced Statistics, Discrete Mathematics,
Advanced Quantitative Reasoning, or courses designed
for career technical programs of study.
Algebra II
Mathematics III
Geometry
Mathematics II
High School
Algebra I
Mathematics I
Integrated Pathway
3 courses that attend to
Algebra, Geometry, and
Probability and Statistics
each year
Traditional Pathway
Typical in U.S.
Integrated Pathway
Typical outside of U.S.
GETTING TO CALCULUS SOONER:
TWO COMPACTED PATHWAYS
Accelerated Pathway
Two additional pathways (one traditional and one integrated) that compact the
curriculum and require a faster pace
The traditional compacted pathway has students completing the content of
7th grade, 8th grade, and High School Algebra I in grades 7 (Compacted 7th
Grade) and 8 (8th Grade Algebra I), enabling students to finish Algebra II by
the end of the sophomore year.
The integrated compacted pathway has students completing the content of
7th grade, 8th grade, and Mathematics I in grades 7 (Compacted 7th Grade)
and 8 (8th Grade Mathematics I), enabling them to complete Math III by the
end of the sophomore year.
Both prepare students for Precalculus in their junior year and Calculus in
their senior year
CCSS AND CALIFORNIA STANDARDS
CROSSWALKS
OVERVIEW
PAGE
HOW TO READ THE STANDARDS
Briars, Diane. “Getting Started with the Common
Core State Standards.” Power Point
Presentation. NCSM Winter Conference, 2011
How to Read the Standards
Geometry Conceptual Category Example
ASSESSMENT: WHAT WE KNOW



Assessments will begin in 2014
California has recently signed on with SMARTER
Balanced Assessment Consortium
Assessments will include:


Computer Adaptive Assessments (interim & summative)
Performance Assessments (interim & summative)



Selected Response
Constructed Response
Both Two-hour and Extended Performance Assessments
SMARTER APPROACH

3 Assessments Each Year
 Reading
 Writing,
Listening and Speaking, Language
 Math

Optional Interim Assessments in ELA and Math
SMARTER END OF YEAR
Computer-adaptive
 2 ELA and 2 Math “performance events” for
Grades 3-8
 Up to six math and ELA “events” for Grade 11
 Grades 9 & 10 Optional
 Combination of computer and human scoring

SMARTER INTERIMS





Computer-adaptive
To be implemented based on state and district policy
Teacher-administered “performance-events”
Combination of human and computer scoring within 2
weeks
Items will be non-secure for teacher and principal
analysis
SMARTER ITEM TYPES
Writing Prompts
 Constructed Responses
 Technology-Enhanced Items
 Standardized Performance Events
 Single Session; administered within 12 weeks
of end of the school year

KEY TAKEAWAYS FROM THE
DRAFT K‐12 CCSS INITIATIVE IN MATHEMATICS
The K‐5 standards provide students with a
solid foundation in whole numbers, addition,
subtraction, multiplication, division, fractions
and decimals‐‐which help young students
build the foundation to successfully apply
more demanding math concepts and
procedures, and move into applications.

In kindergarten, the standards follow
successful international models and
recommendations from the National Research
Council’s Early Math Panel report, by focusing
kindergarten work on the number core:
learning how numbers correspond to
quantities, and learning how to put numbers
together and take them apart (the beginnings
of addition and subtraction).

The standards stress not only procedural skill
but also conceptual understanding, to make
sure students are learning and absorbing the
critical information they need to succeed at
higher levels ‐ rather than the current practices
by which many students learn enough to get by
on the next test, but forget it shortly thereafter,
only to review again the following year.

Having built a strong foundation K‐5, students
can do hands on learning in geometry, algebra
and probability and statistics. Students who
have completed 7th grade and mastered the
content and skills through the 7th grade will be
well‐ prepared for algebra in grade 8.

The K‐5 standards build on the best state
standards to provide detailed guidance to
teachers on how to navigate their way through
knotty topics such as fractions, negative
numbers, and geometry, and do so by
maintaining a continuous progression from
grade to grade.

The middle school standards are robust and
provide a coherent and rich preparation for
high school mathematics.

The high school standards call on students to
practice applying mathematical ways of
thinking to real world issues and challenges;
they prepare students to think and reason
mathematically.

The high school standards set a rigorous
definition of college and career readiness, by
helping students develop a depth of
understanding and ability to apply mathematics
to novel situations, as college students and
employees regularly do.

The high school standards emphasize mathematical
modeling, the use of mathematics and statistics to analyze
empirical situations, understand them better, and improve
decisions. For example, the draft standards state: “Modeling
links classroom mathematics and statistics to everyday life,
work, and decision‐making. It is the process of choosing and
using appropriate mathematics and statistics to analyze
empirical situations, to understand them better, and to
improve decisions. Quantities and their relationships in
physical, economic, public policy, social and everyday
situations can be modeled using mathematical and
statistical methods. When making mathematical models,
technology is valuable for varying assumptions, exploring
consequences, and comparing predictions with data
COMMON CORE RESOURCES
California Department of Education Resources
Hunt Institute CCSS Video Library
SMARTER BALANCED ASSESSMENT CONSORTIUM
ICOE Math BoE Page
[email protected]