Common Core
State Standards for Mathematics
and South Carolina
ITE Faculty Meeting
Columbia, SC
March 2, 2012
Ed Dickey
Mathematics for the 21st Century
• U.S. Secretary of Education Arne Duncan at
NCTM Annual Meeting, 15 April 2011
• “Curricular materials cover so much ground too
superficially, failing to provide students with an
understanding of the concepts that are essential
for success.”
• “Tests don’t always measure what’s important,
or provide information back to you to help you
Common Core Standards
• Sponsored by the Council of Chief State School
Officers (CCSS) and the National Governors
Association (NGA)
• First significant attempt to systematically align K-12
standards across the U.S.
• Building on NCTM’s standards documents from
1980, 1989, 2000, 2006, and 2009
• NCTM among groups providing feedback
Common Core Standards
• Different from most current state standards
• Based on most recent research regarding students’
learning trajectories related to mathematics content
• Includes detailed description of the way
mathematics is learned and used by students
(Mathematical Practice)
Common Core Development
• Initially 48 states and three territories signed
• Final Standards released June 2, 2010, at
• Adoption required for Race to the Top
• As of today, 46 states have officially adopted
(plus DC, US VI, & N. Mariana I)
• Non-adopters: Virginia and the P-Governors
Benefits for States and Districts
Allows collaborative professional development based on
best practices
Allows development of common assessments and other
tools (SC in SMARTER Balanced and PARCC)
Enables comparison of policies and achievement across
states and districts
Creates potential for collaborative groups to get more
economic mileage (“economy of scale”) for:
– Curriculum development, assessment, and professional
South Carolina
• State Board of Education adopted the Common Core for
SC on July 14, 2010
• In November 2010, Mick Zais was elected
Superintendent of Education and with Governor Haley
has chosen to not apply for Race to the Top funds
• In May 2011 Senator Mike Fair introduced a Proviso in
the SC Budget to prohibit the SC Department of
Education from spending related to the Common Core
• In October 2011, the SC Board and Department of
Education continue to move toward implementation
South Carolina 2012
• In February 2012 the state Board of Education selected
Smarter Balanced Assessment Consortium as the SC
assessment system (3 members opposed)
• Sen. Fair re-introduced S. 604 to block fund for the
Common Core (moving to full Senate with negative
recommendation for the Education subcommittee)
• SC remains on a timeline to implement the Common Core
by the 2014-2015 school year.
• Opposition for political and other reasons BOTH from the
right and the left.
CCSSM stands for
Common Core State Standards
for Mathematics
Implementation in SC
• Where are we in mathematics?
• Some are aware and working diligently
on implementation
• Others might have been waiting to see
if it would go away
• Reality HAS set in…
Understanding learning progressions
Vertical articulation
Addressing the mathematical practices
Emphasis on understanding
High school courses vs standards
Common Core - Standards
• Standards are content statements. An example
content statement is: “Use properties of operations
to generate equivalent expressions.”
• Progressions of increasing complexity from grade
to grade
• Requires attention to vertical articulation…
• … particularly in transition from current standards
• Articulated progressions of topics and
performances that are developmental and
connected to other progressions
• Conceptual understanding AND procedural
skills stressed equally
NCTM states coherence also means that
instruction, assessment, and curriculum are
• Key ideas, understandings, and skills are
• Deep learning of concepts is emphasized
– That is, time is spent on a topic and on
learning the topic well. This counters
the “mile wide, inch deep” criticism
leveled at most current U.S. standards.
• Word Cloud
Learning Trajectories
• Descriptions of children’s thinking and learning in a
specific mathematical domain, and
• a related conjectured route through a set of instructional
tasks designed to engender those mental processes or
actions hypothesized to move children through a
developmental progression of levels of thinking,
• created with the intent of supporting children’s
achievement of specific goals in that mathematical
• Clements and Sarama, 2004
Learning Trajectories or Progressions
• Teachers use ordered set of instructional
experiences and tasks
• Students think and learn through a developmental
progression of levels to reach goal
• Van Hiele Levels in Geometry (since 1970s)
• Formative Assessments more recently
Adding Fractions
• As expressed by Hung-Hsi Wu, in Fall 2011, American
• In the past…
• Memorize steps and mimic process without attention to
• Adding whole numbers is “combining”… how is adding of
fractions combining things?
Adding Fractions Learning Trajectory
• In CCSSM, learning trajectories for adding fraction spans
grades 3-5
• In grade 3, students learn to think of a fraction as a point
on a line.
• Unit fractions, like 1/6 and copies of the unit like 5/6
• Mathematics curriculum in Japan has long
used learning trajectories developed
from lesson studies.
CCSSM Mathematical Practices
• Common Core includes a set of Standards
of Mathematical Practices that all teachers
should develop in their students.
• Similar to NCTM’s Mathematical Processes
from the Principles and Standards for
School Mathematics.
• Practices MUST be assessed
8 CCSSM Mathematical Practices
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.
8 CCSSM Mathematical Practices
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
High School Pathways
• Four years of mathematics:
– One course in each of the first two years
– Followed by two options for year three
and a variety of relevant courses for year
• Course descriptions
– Define what is covered in a course
– Are not prescriptions for the curriculum or
High School Pathways
• Pathway A: Consists of two algebra courses
and a geometry course, with some data,
probability and statistics infused throughout
each (traditional)
• Pathway B: Typically seen internationally that
consists of a sequence of 3 courses each of
which treats aspects of algebra, geometry and
data, probability, and statistics.
NCTM President
Michael Shaughnessy
• An Opportune Time to Consider Integrated
Mathematics March, 2011
• “Students need to see mathematics as an integrated whole,
with connections across the content domains...
• …the United States will never show well in international
comparisons of mathematics performance as long as other
countries have an integrated mathematics, and we take a
“layer cake” approach.
• … we have an unprecedented opportunity… to integrate the
content of our secondary mathematics…”
Promising, Opportune… but Perfect?
Problem areas:
• CCSSM has never been field tested
• Can the assessments address
understanding and measure the Practices?
• How to accommodate exceptional learners?
• Learning trajectories require careful vertical
Not Perfect …
Problem areas:
• Too little technology particularly in K-8
• No statistics in K-5
• Piling on in Grade 6
Math Common Core Resources
2012 Institutes
High School Reasoning & Sense Making:
July 24-26, Los Angeles, California
K-8 Algebra Readiness Institute:
July 31- August 2, Atlanta, Georgia
Additional Information
• For grades preK-8, a model of
implementation can be found in
NCTM’s Curriculum Focal Points
• For the secondary level, please see
NCTM’s Focus in High School
Mathematics: Reasoning and Sense
• CCSSO/NGA. (2010). Common core state standards for
mathematics. Washington, DC: Council of Chief State School
Officers and the National Governors Association Center for Best
Practices. Retrieved from
• Clements, D., & Sarama, J. (2004). Learning trajectories in
mathematics education. Mathematical Thinking and Learning, 6(2),
• Clements, D., & Sarama, J. (2009). Learning and Teaching Early
Math: The learning Trajectories Approach.New York: Routledge.
• Daro, Phil, Frederic Moser, and Tom Corcoran( (2011) Learning Trajectories in
Mathematics. Retrieved from
• Dojinsha, Kyoiku. Mathematics Workbook (Grade 1 to 6). Global Education
• National Council of Teachers of Mathematics. Position Statement on Teacher
Evaluation. Retrieved from
• Wu, Hung-Hsi (2011) Phoenix Rising: Bring the Common Core State Mathematics
Standards to Life. American Educator, Fall 2011. Retrieved from
Web Resources
• Common Core:
• Math Common Core Resources:
• South Carolina Common Core:
Thank you…
[email protected]

An overview of Common Core State Standards for Math and South