California
Common Core State
Standards:
A Leadership Perspective
CaCCSS in Mathematics: A
Leadership Perspective
Karen Arth, Director of San Joaquin Valley Mathematics Project
Awareness
v  CCSS adopted in
California August 19,
2010
v  CCSS – Mathematics is
45 states strong…it is
not going anywhere…
v  Purpose: College and
Career Readiness
Google Glasses…our
world is changing can
our schools prepare
our students?
Awareness
v  All key players need to
be involved in the
conversation
•  Board Members
•  Administrators
•  Teachers
•  Parents!
Don’t forget to include the parents as part of the process!
This is challenging enough; we want support, not push-back
Two of the biggest driving
forces for change:
v  Standards for Mathematical
Practice
v  Assessment: SMARTER Balanced
Assessment Consortium (SBAC)
Standards for Mathematical Practice
v  Describe habits of mind of a
mathematically expert student
v  Meant to be studied, not just read
Standards for Mathematical Practice
•  MAKE SENSE of problems and PERSEVERE in solving them
•  REASON ABSTRACTLY and QUANTITATIVELY
•  Construct VIABLE ARGUMENTS and CRITIQUE the reasoning
of others
•  MODEL with mathematics
•  Use appropriate TOOLS strategically
•  Attend to PRECISION
•  Look for and make use of
STRUCTURE
•  Look for and express regularity in REPEATED REASONING
—
© Institute for Mathematics & Education 2011
MP 1: Make Sense of problems and
persevere in solving them
MP 6: Attend to Precision
Grouping Standards for Mathematical Process
MP2: Reason abstractly and
quantitatively
MP3. Construct viable
arguments and critique the
reasoning of others
Reasoning and
Explaining
MP4. Model with mathematics
MP5: Use appropriate tools
strategically
Modeling and Using
Tools
MP7. Look for and make use of
structure
MP8 .Look for and express
regularity in repeated
reasoning
Seeing Structure and
Generalizing
SMP 1: Make sense of problems and
persevere in solving them.
Mathematically Proficient Students:
Explain the meaning of the problem to themselves
Look for entry points
Analyze givens, constraints, relationships, goals
Make conjectures about the solution
Plan a solution pathway
Consider analogous problems
Try special cases and similar forms
Monitor and evaluate progress, and change course if
necessary
—  Check their answer to problems using a different method
—  Continually ask themselves “Does this make sense?”
—
—
—
—
—
—
—
—
Gather
Information
Make a
plan
Anticipate
possible
solutions
Check
results
Continuously
evaluate
progress
—
Question
sense of
solutions
© Institute for Mathematics & Education 2011
SMP 2: Reason abstractly and quantitatively
Decontextualize
Represent as symbols, abstract the situation
5
½
Mathematical
Problem
P
x x x x
Contextualize
Pause as needed to refer back to situation
—
© Institute for Mathematics & Education 2011
*SMP 3: Construct viable arguments and critique
the reasoning of others
Use
as
defin sumption
i
s
prev tions, an ,
ious
d
resu
lts
Make a conjecture
Build a logical progression of
statements to explore the
conjecture
orrect
Distinguish c
logic
Explain flaws
Analyze situations by breaking
them into cases
Recognize and use counter
examples
Ask clarifying
questions
—
© Institute for Mathematics & Education 2011
SMP 4: Model with mathematics
Problems in
everyday life…
…reasoned using
mathematical
methods
Mathematically proficient students
•  make assumptions and approximations to simplify a
situation, realizing these may need revision later
•  interpret mathematical results in the context of the
situation and reflect on whether they make sense
—
© Institute for Mathematics & Education 2011
Images: http://tandrageemaths.wordpress.com, asiabcs.com, ehow.com, judsonmagnet.org, life123.com, teamuptutors.com, enwikipedia.org, glennsasscer.com
SMP 5: Use appropriate tools strategically
Proficient students
•
are sufficiently familiar with
appropriate tools to decide when
each tool is helpful, knowing both
the benefit and limitations
•
detect possible errors
•
identify relevant external
mathematical resources, and use
them to pose or solve problems
—
© Institute for Mathematics & Education 2011
SMP 6: Attend to precision
Mathematically proficient students
•  communicate precisely to others
•  use clear definitions
•  state the meaning of the symbols they use
•  specify units of measurement
•  label the axes to clarify correspondence with problem
•  calculate accurately and efficiently
•  express numerical answers with an appropriate degree of
precision
Comic: http://forums.xkcd.com/viewtopic.php?f=7&t=66819
—
© Institute for Mathematics & Education 2011
SMP 7: Look for and make use of structure
Mathematically proficient students
•  look closely to discern a pattern or
structure
•  step back for an overview and shift
perspective
•  see complicated things as single objects,
or as composed of several objects
—
© Institute for Mathematics & Education 2011
SMP 8: Look for and express regularity in repeated
reasoning
Mathematically proficient
students
•  notice if calculations are
repeated and look both for
general methods and for
shortcuts
•  maintain oversight of the
process while attending to
the details, as they work to
solve a problem
•  continually evaluate the
reasonableness of their
intermediate results
—
© Institute for Mathematics & Education 2011
Standards for Mathematical Practice
v  Require classroom
changes
•  Teacher-centered
student centered
è
•  Delivery of instruction
•  Larger tasks in context
Traditional versus Common
Core
…the Same Problem Twice
A Traditional Type Algebra
Problem:
Write the equation of a parabola going
through the points (0,0); (20,50) and
(40,0).
v  Use the form y=a(x-h)2+k
v  Solve for y when x = 25
McDougal’s Restaurant has a play area for children
under and around their giant arch (in the shape of a
parabola with negative orientation). They plan to set
up a new activity that allows children to bungee jump
from the arch. The manager, upon hearing of your
team’s expertise, hires you to calculate the maximum
stretch of the rope that will keep the kids safe. The
arch is 50 feet high and 40 feet wide at the base. The
jumping location will be 5 horizontal feet away from the
axis of symmetry of the arch.
a. Write an equation to model the shape of the arch.
b. What’s the maximum length to which the cord could
stretch to keep McDougal’s safe from lawsuits?
Standards for Mathematical Practice
v  This affects
•  Classroom Management
•  Pedagogical Strategies
o
Study Team Strategies
² Pairs Check
² Reciprocal Teaching
² Huddle
² Swapmeet…
Purposely incorporate at
least two of the SMP now!!!
The Elephant
(that may be) in the room:
v  Direction Instruction
•  How and where does it
fit?
Assessment: SBAC
v  Tests both the content standards
and the Standards for
Mathematical Practice
•  Problem Types
Selected Response
o  Constructed Response
o  Technology Enhanced
o  Performance Tasks
o
Example Performance
Tasks
http://dese.mo.gov/divimprove/assess/documents/asmtsbac-math-gr4-sample-items.pdf
Remodeling a Bedroom
You are remodeling a bedroom for a client. Your job will include
installing new flooring, painting the walls, buying new furniture,
and then arranging the new furniture in the bedroom. Your
client has set a total budget of $4500 for this project.
v  Part A – New Flooring
—  The bedroom floor is in the shape of a rectangle. It is 15 feet
long and 12 feet wide.
—  Your client has requested that you install either oak flooring
or maple flooring.
—  The oak flooring costs $6.75 per square foot for materials.
The maple flooring costs $8.00 per square foot for materials.
—  The cost you charge for labor will be the same for either
flooring option.
—  How much money will your client save if you install oak
flooring instead of maple flooring? Explain or show your
reasoning. You may use diagrams, drawings, or equations as
well as words.
High School Performance Task
Sample online Test
http://sampleitems.smarterbalanced.org/itempreview/sbac/
index.htm#
Share these with your
teachers to help drive the
change
Pilot Test
http://www.smarterbalanced.org/wordpress/wp-content/uploads/2013/01/
Smarter-Balanced-Pilot-Test-School-Participation-Details.pdf
v  Scientific Sample
•  Designed and monitored by Smarter
Balanced psychometricians to ensure that
the full system is exposed to a representative
sample of schools under specific conditions.
•  Roughly 10 percent of schools from each
governing state will be scientifically selected
to participate in the pilot.
•  Specifically assigned two-week windows
between February 20 and May 10, 2013
Pilot Test
http://www.smarterbalanced.org/wordpress/wp-content/uploads/2013/01/
Smarter-Balanced-Pilot-Test-School-Participation-Details.pdf
v  Volunteer Pilot
•  provides an “open house” of the system, to
ensure that all interested schools provide the
opportunity for students to access some of
its features and functions
•  Interested schools must to register as
volunteers in order to ensure participation
•  Test may be administered at any time within
the window (Early April—May 10, 2013)
Pilot Test
http://www.smarterbalanced.org/wordpress/wp-content/uploads/2013/01/
Smarter-Balanced-Pilot-Test-School-Participation-Details.pdf
v  Broad Field Test
•  A broader Field Test will follow in spring 2014
•  At the start of the 2014-2015 school year, the
interim assessment item bank will be fully
accessible to schools and teachers
•  Teachers will have access to a digital library of
formative assessment strategies and practices,
including instructional best practices and
professional development on assessment literacy
•  The end-of-the-year summative assessment will
start in Spring 2015—
Resources
Inside Mathematics
http://www.insidemathematics.org
Videos on the CCSS: Hunt Institute
http://www.youtube.com/user/TheHuntInstitute
SERP: Strategic Education Research Partnership
http://math.serpmedia.org/tools_ccss.html
http://commoncoretools.me/tools/
Gearing up for the Common Core
State Standards in Mathematics
Five initial domains for professional development
in Grades K-8
In addition to recommending that all professional
development incorporate the Standards for Mathematical
Practice, this report outlines five recommended domains for
initial professional development efforts in K–8:
—  Grades K–2, Counting and Cardinality and Number and
Operations in Base Ten
—  Grades K–5 Operations and Algebraic Thinking
—  Grades 3–5 Number and Operations—Fractions
—  Grades 6–7 Ratios and Proportional Reasoning
—  Grade 8 Geometry
Domain K-8
K
1
2
3
4
Counting
&
Cardinality
5
6
7
8
Ratios & Proportional
Relationships
Operations and Algebraic Thinking
Numbers and Operations in Base Ten
The Number System
Expressions and Equations
Function
s
Fractions
Measurement and Data
Geometry
Geometry
Statistics & Probability
Grade Level Standard
Domain
8th Grade Example
GEOMETRY
Understand congruence and similarity using physical
modes, transparencies, or geometry software.
Standard
8.G
1.  Verify experimentally the properties of rotations, reflections,
and translations:
a)  Lines are taken to lines, and line segments to line
segments of the same length
b)  Angles are taken to angles of the same measure
Cluster
c)  Parallel lines are taken to parallel lines.
2.  Understand that a two-dimensional figure is congruent to
another if the second can be obtained from the first by a
sequence of rotations, reflections, and translations; given two
congruent figures, describe a sequence that exhibits the
congruence between them.
3.  Describe the effect of dilations, translations, rotations and
reflections on two dimensional figures using coordinates
4.  Understand…
page 55, CCSS-M
Progressions
An Excerpt from…
K–5, Number and Operations in Base Ten
Have teachers read and
discuss the progressions
affecting their grade level
http://www.illustrativemathematics.org/
standards/k8
Using the Sample Items and Tasks
—  Smarter Balanced Theory of Action notes
that an effective assessment system must be
a part of an integrated system of standards,
curriculum, assessment, instruction and
teacher development. The sample items and
tasks illustrate the knowledge and skill
students will be expected to demonstrate on
Smarter Balanced assessments, giving
educators clear benchmarks to inform their
instruction.—
High School Mathematics
v  Things to think about:
•  Traditional versus integrated
courses
•  The California Standards/
Common Core State
Standards Gap
o
It’s not the same old Algebra 1
course
California State Board of Education
v  Recent Changes
•  CA 8th Grade Algebra Standards
(removed)
v  Recent Recommendations
•  CSTs
v  Mathematics Framework
•  News from the Framework
Committee
Articulation is needed and
professional development is
a necessity!
This is a journey, it will take
time, a lot of time. If you
haven’t started, now is a
great time…