Common Core State
Standards for Mathematics
Continued Progress or a
Continuum of Controversy?
Outline for the next hour
• What is the Common Core?
• What are the Goals of the CCSSM ?
• What is the Controversy About?
• What is the Basis for the CCSSM?
• How are our students doing now?
The Common Core State
Standards ARE:
• A listing of what K-12 students should know
and be able to do in mathematics at the
conclusion of each of the K-12 grades.
• A set of objectives that should constitute
85% of the math programs in all states and
jurisdictions that have adopted them.
• An accepted basis for building curricula.
The Common Core State
Standards ARE NOT:
•
•
•
•
A FEDERAL PROGRAM
A CURRICULUM
An ASSESSMENT SYSTEM
A SPECIFICATION OF TEACHING
METHODS
ALTHOUGH THEY COULD BE
COMPONENTS OF EACH ONE OF
THESE!
LET’S LOOK AT THE STANDARDS
Who Created the CCSSM?
• NATIONAL GOVERNORS’ ASSOCIATION
• COUNCIL OF CHIEF STATE SCHOOL
OFFICERS (CCSSO)
Funding came from the STATES, and the:
• Bill & Melinda Gates Foundation, National
Education Association, & American Federation
of Teachers
Who Wrote the CCSSM?
• A Committee of 20+ individuals from
mathematics and mathematics education.
• Supported by a Feedback Group of 20+ with
long histories in mathematics & mathematics
education.
• Bill McCallum, Distinguished Professor of
Mathematics at U of AZ chaired the writing.
CCSSM Development Timeline
• 1991 Time for Results: The Governors Report on
Education, followed the release of NCTM
Standards, the Governors called for better report
cards of results about what student know & can do.
• 2007 the Chiefs discuss developing common
standards for the states.
• 2008 the Chiefs, NGA, and Achieve release
Benchmarking for Success: Ensuring U.S. Students
Receive a 1st Class Education which focused being
globally competitive.
• 2009 Chiefs moved to CCSSO initiative and
invited states to indicate interest—48 states
did—and writing began in earnest with 3 rounds
of feedback and state reviews. In mid-summer a
draft of College and Career Readiness standards
was circulated and work began on K-12
standards. Soon after this the DoEd announced
its Race to the Top program.
• Sept. 2009—Release Draft C&CR Standards to
States and Feedback Group. October 2009
Feedback Round.
Nov. 2009—Release Draft K-12 Standards to
states and Feedback Groups, as well as to several
selected independent reviewers for in-depth
reviews.
Feb. 2010—Distributed revised version of K-12
Standards and College and Career Readiness
Standards to states, educators, public, and
validators. Third Feedback Round.
June, 2010—CCSSO and NGA release CCSS
• Sept. 2011-13—States & jurisdictions review the
CCSS, adapting, adopting, and ratifying CCSSM.
• By Dec. 2013, 45 states, D.C., DoDEA, Guam,
North Mariana Islands, and U.S. Virgin Islands
had adopted the CCSSM. Alaska, Minnesota,
Nebraska, Texas, & Virginia opted out.
• By Feb. 2015, political backlash led to three
adopting states rescinding adoptions: Indiana,
Oklahoma, and South Carolina. This leaves 42
states as of this morning having supporting the
CCSSM.
Looking at the parts of CCSSM:
Standards for Mathematical Practice
• Make sense of problems & persevere in solving them.
• Reason abstractly & quantitatively.
• Construct viable arguments & critique the reasoning of
others.
• Model with mathematics.
• Use appropriate tools strategically.
• Attend to precision.
• Look for & make use of structure.
• Look for & express regularity in repeated reasoning.
Looking at the Parts of CCSSM:
Standards for Mathematical Content—
Kindergarten
•
•
•
•
•
Counting and Cardinality
– Know number names and the count sequence.
– Count to tell the number of objects.
– Compare numbers.
Operations and Algebraic Thinking
– Understand addition as putting together and adding to, and understand
subtraction as taking apart and taking from.
Number and Operations in Base Ten
– Work with numbers 11–19 to gain foundations for place value.
Measurement and Data
– Describe and compare measurable attributes.
– Classify objects and count the number of objects in categories.
Geometry
– Identify and describe shapes.
– Analyze, compare, create, and compose shapes.
Where Did We Get Our Standards?
Commission on Post War Plans
1944-1947
• First major mathematics report in our times on
school mathematics was the Commission on Post
War Plans that responded to Adm. Nimitz’s
concerns over mathematical readiness and was
done by the NCTM
• Three Commission Reports
– 1st General recommendations
– 2nd Specific Recommendations Kind.—C.C.
– 3rd Guidance counselors, parents, administrator
First Thesis of the Commission
• The first thesis of the Post-War Commission was an
overarching statement for teachers at all grade
levels. It stated that “the school should guarantee
functional competence in mathematics to all who
can possibly achieve it” by outlining “the
mathematics of the core curriculum”. The
commission listed 28 different mathematical topics
describing “the essentials for functional competence
in mathematics”, including topics from number and
operation, algebra, geometry, & business
mathematics.
Standards for Mathematical Content—
Grade 4
• Operations and Algebraic Thinking
– Use the four operations with whole numbers to solve problems.
– Gain familiarity with factors and multiples.
– Generate and analyze patterns.
• Number and Operations in Base Ten
– Generalize place value understanding for multidigit whole numbers.
– Use place value understanding and properties of operations to perform
multi-digit arithmetic.
• Number and Operations—Fractions
– Extend understanding of fraction equivalence and ordering.
– Build fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers.
– Understand decimal notation for fractions, and compare decimal
fractions.
Standards for Mathematical
Content—Grade 4(cont.)
• Measurement and Data
– Solve problems involving measurement and conversion of measurements
from a larger unit to a smaller unit.
– Represent and interpret data.
– Geometric measurement: understand concepts of angle and measure
angles.
• Geometry
– Draw and identify lines and angles, and classify shapes by properties of
their lines and angles.
Elaborations of Standards:
Mathematical Content—Grade 4
• Number and Operations in Base Ten
– Generalize place value understanding for multidigit whole numbers.
– Use place value understanding and properties of operations to perform
multi-digit arithmetic.
******************************************************
4. Fluently add and subtract multi-digit whole numbers using the
Standard Algorithm.
5. Multiply a whole number of up to 4 digits by a 1-digit whole
number, and multiply two 2-digit numbers, using strategies based
on place value and the properties of operations. Illustrate and
explain the calculation by using equations, rectangular arrays,
and/or area models.
Illustrate and explain the calculation by using using
equations, rectangular arrays, and/or area models.
• (4 × 32) = 4(30 + 2) = 4(30) + 4(2) = [(4 × 3) × 10] + 8 =
128
10
10
100
4
2 x 12
40
2(10)
2
20
8
12 x 14 = 100 + 40 + 20 + 8 = 168
********** **
********** **
(2 x 10) + (2 x 2)
20
+ 4
24
32
x4
8
120
128
These Alternatives are a Basis for
Understanding and Later Connections
• (x + 3) (x + 5) = x(x + 5) + 3(x + 5) =
(x2 + 5x) + (3x + 15) = x2 + 8x + 15
x
5
x
x2
5x
3
3x
15
Standards for Mathematical
Practice—Algebra
Units
1. Relationships Between Quantities
and Reasoning with Equations
Content
• Reason quantitatively and use units to
solve problems.
• Interpret the structure of expressions.
• Create equations that describe
numbers or relationships.
• Understand solving equations as a
process of reasoning and explain the
reasoning.
• Solve equations and inequalities in
one variable.
Units
2. Linear and
Exponential
Relationships
Content
• Extend the properties of exponents to rational
exponents.
• Solve systems of equations.
• Represent and solve equations and inequalities
graphically.
• Understand the concept of a function and use
function notation.
• Interpret functions that arise in applications in
terms of a context.
• Analyze functions using different
representations.
• Build a function that models a relationship
between two quantities.
• Build new functions from existing functions.
• Construct and compare linear, quadratic, and
exponential models and solve problems.
• Interpret expressions for functions in terms of the
situation they model.
Units
Content
3. Descriptive Statistics
(note step-up)
• Summarize, represent, and interpret data on a
single count or measurement variable.
• Summarize, represent, and interpret data on
two categorical and quantitative variables.
• Interpret linear models.
4. Expressions and
Equations
• Interpret the structure of expressions.
• Write expressions in equivalent forms to solve
problems.
• Perform arithmetic operations on polynomials.
• Create equations that describe numbers or
relationships.
• Solve equations and inequalities in one
variable.
• Solve systems of equations.
Units
Quadratic Functions and
Modeling
Content
• Use properties of rational and irrational numbers.
• Interpret functions that arise in applications in
terms of a context.
• Analyze functions using different representations.
• Build a function that models a relationship
between two quantities.
• Build new functions from existing functions.
• Construct and compare linear, quadratic, and
exponential models and solve problems.
Pattern to Quantity to Variable to
Expression to Model
• Data
• Pattern
1
4
7
10
13…
Pattern to Quantity to Variable to
Expression to Model
•
•
•
•
•
•
•
Data
1
4
7
10 13…
Pattern
“Initially 1—Then add 3s”
Quantity
1 + 3n where n is a whole #
Represent
list, graph, words, symbols
Evaluation
“If n = 13, what is 1 + 3n?”
Equation
“Does 100 appear in the list?”
Model “What if the start or jump changes? ”
Analyze Functions Using Different Representations
Key to Selecting and Ordering
CCSSM Standards
• Greater focus on fewer topics in a given year.
• Coherent progressions among grade levels.
• Rigor increased by developing concepts,
procedures and fluency, and applications
with equal emphasis.
Steps to Conceptual Fluency
Can students:
• recognize label and generate examples and nonexamples of
concepts
• use and interrelate models, diagrams, manipulatives, and other
representations of concepts
• identify and apply principles (that is, valid statements generalizing
relationships among concepts in “if …, then….” form.
• know and apply facts and definitions
• recognize, interpret, and apply the signs, symbols, and terms used
to represent concepts
Steps to Procedural
Understanding and Fluency
Can students:
• connect an algorithmic process with a problem situation
• perform algorithmic processes correctly
• justify the correctness of an algorithmic process
• communicate the results of an algorithmic process
• perform noncomputational processes such as estimating and
rounding or geometric measurements or constructions
• read and produce graphs and tables
• execute geometric constructions
Steps to Problem Solving and
Modeling
Can students:
• recognize and formulate problems & models for problem situations
• determine the sufficiency and consistency of the data involved
• list assumptions made in working within a given context
• use strategies (draw a picture, find a pattern, make a data table,…)
and relevant mathematics in attempts to understand a mathematical
situation
• apply reasoning (inductive, deductive, statistical, spatial, or
proportional) in correct and productive ways
• judge the reasonableness and correctness of purported solutions or
models test the robustness or generalizability of a solution
What’s the Truth?
Meet the Players
No Child
Left Behind
2001
?
Smarter Balanced
Assessment
Partnership for
Assessment of
Readiness for
College and Careers
Race to
the Top
2009
$400 M
(Population)
$4.35 B
(Sample)
What is Not To Like About
CCSSM?
Myths, Misdirection, &
Concerns
The CCSS is NOT a Federal Program
The CCSS was constructed by the
National Governors’ Association
&
Council of Chief State School Officers
(NGA told the DoEd to not tie their Race to the Top
Program to the CCSS, but the DoEd did anyway)
The DoEd tied its Race to the
Top language to the CCSS
• Race to the Top was a federal program designed
by DoEd staff after the CCSS were already
underway. The RTT is a FEDERAL program
focused on these steps, but DoEd was asked by
the Governors to stay clear of the CCSS as they
were a STATES’ agenda. But the Federal
government went ahead with the SBA and
PARCC tests development and “encouraging”
states to adopt them or lose some core funding.
The CCSS does not Mandate:
–
–
–
–
Evaluation of teachers by students’ test scores (RTT)
States to increase the number of charter schools (RTT)
States to develop high-quality assessments (NCLB)
States to adopt “college and career ready standards” (RTT)
(Common Core were the implicit set of standards)
– States to turn-around low performing schools by firing the
principal and part or all of the staff (NCLB)
These are parts of NCLB (2001) & Race to the Top (2009)
Federal-but not Common Core State Standards Dictums
The CCSS is NOT A Curriculum
• A curriculum requires:
– Objectives--which the CCSS does have
– Delivery method for specified students--not in
CCSS
– Specified instructional materials--not in CCSS
– Teaching methods--not in CCSS
– Evaluation plan--not in CCSS
There is work to be done in states to make it a curriculum.
CCSS had public input
• There were hearings held in the states with open
access to drafts.
• The Feedback Committee provided voluminous
written feedback at three stages of the
development.
• Feedback was requested from individuals
representing varied communities associated with
K-12 schooling and the mathematics community
through all three stages of drafts.
Not a Myth, but a Serious CCSSM
Implementation Process Flaw
• The Governors and CCSSO failed to adequately
plan ongoing professional development for the
nation’s mathematics teachers K-12. There first
needs to be an introduction, then local
implementation plans tied to state expectations,
then assistance to assessment programs if any.
The states and NCTM working with the ASSM
did this following the 1989 NCTM Standards.
States need to provide serious, ongoing, professional development.
There are Myths & Concerns!
• The CCSS is turning the education of the nation’s
young over to CEOs, hedge funds, entrepreneurs,
and real-estate investment corporations who are
investing enthusiastically in this emerging
market, encouraged by federal tax credits, lavish
fees, and the wringing of huge profits from
taxpayer dollars at our children’s expense.
…
• Braun, Jenkins, Grigg, &Tirre. (2006). A Closer Look at Charter
Schools Using Hierarchical Linear Modeling. Washington, D.C.:
National Center for Education Statistics.
Other Issues:
• The RTT suggested a call for vouchers & an
increase in charter schools.
• Currently, House and Senate are considering rewrites
of the NCLB bill (Elem. & Sec. Ed. Act). House com.
pass it out in 5 days as block grant letting states decide
how to spend their share & approves portable Title I
vouchers for public schools. The Senate bill is
currently is currently being drafted in closed session by
a bipartisan staff and is expected to be out for debate in
March/April. See this mornings Star and NYTimes’
editorials.
What Research Base supports the CCSSM?
•
•
•
•
•
•
Previous NCTM, state, and other standards
Detailed study of Peer Country math standards
NAEP Results
TIMSS International Results
OECD PISA International Results
Content hierarchies based on cognitive research
in mathematics learning patterns
A Modern History of Steps to CCSSM:
• 1983 Conference Board of the Mathematical
Sciences Report: The Mathematical Sciences
Curriculum K-12: What Is Still Fundamental and
What Is Not-a community response to a Nation at
Risk
• 1989 the National Council of Teachers of
Mathematics released their Standards document
for the mathematics content students should know
as a result of K-12 schooling.
• In 1991 and 1995 they released Standards for
mathematics teacher education and assessment.
• 2000 NCTM releases Principles and Standards
for School Mathematics that is more specific and
puts the previous 3 sets of standards (content,
teacher education, and assessment) together.
• 2006 NCTM releases K-8 Curriculum Focal
Points that further sharpen grade level foci.
• 2006 the College Board releases Mathematics and
Statistics: College Board Standards for College
Success
• 2007 the CCSSO and NGA start to address the
need for common core standards across states,
building on all of the foregoing activities.
FOCUS: 8th Grade Topics Taught in JPN & US
17%
Findings from SIMS and
TIMSS International
Assessments—not only
JPN, but also many other
EU and Asian Rim countries
95%
TIMSS Countries 8th Grade 2011
Coherence: CCSSM and K-8 Topics in
TIMSS High Achieving Countries
In 2010, 22% of
youth aged 5 to 17
years-of-age were not
born in the state in
which they currently
reside.
Textbooks cover every
topic that might appear
on any of the major
states’ curricula—many
teachers teach it all or
weak curricula call for
all of it. A textbook is
an aid not a program!
Lack of Coherence in MI and OH Sites’
K-8 Mathematics Curricula
49
TIMSS Trends in Achievement at
Grade 8
*
*
*
* Increased at all levels
OECD-PISA 2012 Problem Solving
15-year-olds
th
4
Grade NAEP Results over Time
MA
AZ
LA
th
8
Grade NAEP Results over Time
MA
AZ
AL
Long Term Trend Data (Nearly Constant Test Over Time)
What’s Your Choice for Our Youth?– Continued Progress or a
Continuum of Controversy?