California
Common Core State
Standards:
A Leadership Perspective
CaCCSS in Mathematics: A
Leadership Perspective
Karen Arth, Director of San Joaquin Valley Mathematics Project
Awareness
 CCSS adopted in
California August 19,
2010
 CCSS – Mathematics is
45 states strong…it is not
going anywhere…
 Purpose: College and
Career Readiness
Google Glasses…our
world is changing can
our schools prepare our
students?
Awareness
 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:
 Assessment: SMARTER Balanced
Assessment Consortium (SBAC)
 Standards for Mathematical Practice
Standards for Mathematical Practice
 Describe habits of mind of a
mathematically expert student
 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
Continuously
evaluate
progress
Check
results

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
Make a conjecture
Build a logical progression of
statements to explore the
conjecture
Analyze situations by breaking
them into cases
Recognize and use counter
examples

© 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.co m
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
The Five by Eight Card: A tool for observing
SERP: Strategic Education Research Partnership
http://math.serpmedia.org/tools_5x8.html
The Five by Eight Card:
A tool for observing
Standards for Mathematical Practice
 Require classroom
changes
• Teacher-centered 
student centered
• 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).
 Use the form y=a(x-h)2+k
 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
 This affects
• Classroom Management
• Pedagogical Strategies
o
Study Team Strategies
 Pairs Check
 Reciprocal Teaching
 Huddle
 Swapmeet…
Purposely incorporate at least
two of the SMP now!!!
The Elephant
(that may be) in the room:
 Direct Instruction
• How and where does it fit?
Assessment: SBAC
 Tests both the content standards and
the Standards for Mathematical
Practice
 Assessments: 2014 – 2015
 Grades 3 – 8 and Grade 11
 Problem Types
Selected Response
o Constructed Response
o Technology Enhanced
o Performance Tasks
o
Example Performance
Tasks
http://dese.mo.gov/divimprove/assess/documents/asmt-sbacmath-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.
 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
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.—
Sample online Test
http://sampleitems.smarterbalanced.org/itempreview/sbac/index.htm#
Share these sample items
with your teachers to help
drive the change
Pilot Test
http://www.smarterbalanced.org/wordpress/wp-content/uploads/2013/01/SmarterBalanced-Pilot-Test-School-Participation-Details.pdf
 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/pilot-test/
 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)
• To participate in the volunteer portion of the Pilot
Test, complete the online survey by March 27,
2013
Pilot Test
http://www.smarterbalanced.org/wordpress/wp-content/uploads/2013/01/SmarterBalanced-Pilot-Test-School-Participation-Details.pdf
 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
8.G
Understand congruence and similarity using physical
modes, transparencies, or geometry software.
Standard
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
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…
Cluster
page 55, CCSS-M
Progressions
 Draft K–6 Progression on Geometry
 Draft K–5 Progression on Measurement and Data (measurement part)
 Draft K–5 progression on Measurement and Data (data part)
 Draft K–5 Progression on Number and Operations in Base Ten
 Draft K–5 Progression on Counting and Cardinality and Operations and
Algebraic Thinking
 Draft 3–5 progression on Number and Operations—Fractions
 Draft 6–8 Progression on Statistics and Probability
 Draft 6–8 Progression on Expressions and Equations
 Draft 6–7 Progression on Ratios and Proportional Relationships
 Draft High School Progression on Statistics and Probability
 Draft High School Progression on Algebra
 Draft High School Progression on Functions
Progressions
An Excerpt from…
K–5, Number and Operations in Base Ten
Have teachers read and
discuss the progressions and
content standards affecting
their grade level
http://www.illustrativemathematics.org/standa
rds/k8
High School Mathematics
 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
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…
What’s Happening with the
California Common Core State
Standards for Mathematics?
January 25, 2013
Jon Dueck
Fresno County Office of Education
Julie Joseph
Tulare County Office of Education
55
Standards - Revised
SB 1200
56
Tulare County Office of Education
57
58
SBE Adopted Standards – January
16, 2013
 None of Original CCSS (June 2010) Removed.
 Removed “Unique Grade 8 Algebra 1 Course”
 Removed duplicate standards from 6th and 7th that had
been “pushed down” from CCSS Grade 8
 Removed many of the California additions
 Added Grade Level “Critical Areas” pages, Glossary
and Tables from original CCSS document.
59
K-8: CA Additions
Grade
Previous Number of CA
Additions
Current Number of CA
Additions
K
1
0
1
3
0
2
7
3
3
4
0
4
4
2
5
4
1
6
3 (from grade 7)
0
7
5 (from Grade 8)
1 other addition
0
8
0
0
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High School: CA Additions
Section
Previous Number of
CA Additions
Current Number of CA
Additions
Standards for
Mathematical
Practice
3
1 - revised
Number and
Quantity
0
0
Algebra
6
2 - revised
Functions
9
2 – no change
2 – revised
1 - moved to Geometry
Modeling
0
0
Geometry
10
5 - revised
1 – moved from Functions
Statistics and
Probability
0
0
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Courses are
based primarily
on Appendix A
62
CA Model Courses
 Integrated
 Mathematics I
 Mathematics II
 Mathematics III
 Traditional
 Algebra I
 Geometry
 Algebra II
Draft framework contains a model 4th year course.
Framework
63
Framework Timeline
IQC approves draft Mathematics Framework for March 2013
initial 60-day public review period
CFCC final meeting
February 13-14,
2013
60-day public review period prior to IQC
recommendation to SBE, pursuant to 5 CCR,
§9515(a)(3)
April to May 2013
Required 60-day public review and comment on July to August
IQC’s recommended Mathematics Framework
2013
Section §95159(c)
SBE action on IQC’s recommended Mathematics
Framework includes public hearing.
November 2013
64
Draft Framework
 Utilized Various Resources






Common Core Standards Document from June 2010
Progressions
Appendix A
K-8 Publisher’s Criteria
Illustrative Mathematics Tasks
Assessment Consortium Documents
 PARCC
 SBAC
 Other State Documents
 Kansas Flip Books
 North Carolina
 Ohio
 Arizona
 Other
65
Framework Format
 Will be available online (with links) and in print format
66
Grade 8
 8th grade course is CCSS Grade 8
 Will present options for acceleration in middle school
so some grade 8 students could take the 9th grade
course (Mathematics I or Integrated I) in grade 8.
 Will present options for acceleration in high school for
students who take the 9th grade course in 9th grade.
67
Key Instruction Shifts of the Common
Core State Standards for Mathematics
• Focus strongly where the Standards focus
• Think across grades and link to major topics
within grades
• In major topics, pursue with equal intensity:
o Conceptual understanding
o Procedural skill and fluency
o Application
K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics, July 20, 2012, corestandards.org
68
carried out through the Standards for Mathematical Practice.
To say that some things have greater emphasis is not to say that anything in the standards can safely be
neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may
leave students unprepared for the challenges of a later grade. The following table identifies the Major
Clusters, Additional Clusters, and Supporting Clusters for this grade.
Keeping Focus and Coherence
Key:
Major Clusters;
Supporting Clusters;
Additional Clusters
Operations and Algebraic Thinking
Represent and solve problems involving addition and subtraction.
Understand and apply properties of operations and the relationship between addition and
subtraction.
Add and subtract within 20.
Work with addition and subtraction equations.
Number and Operations in Base Ten
Extending the counting sequence.
Understand place value.
Use place value understanding and properties of operations to add and subtract.
Measurement and Data
Measure lengths indirectly and by iterating length units.
Tell and write time.
Represent and interpret data.
Geometry
Reason with shapes and their attributes..
69
Key Instruction Shifts of the Common Core State Standards for Mathematics, achievethecore.org
materials
70
Supplemental Instructional Materials Review
(SIMR)
 Category 1 – Supplemental Materials have
been reviewed and list is posted on CDE
website.
 FCOE had a reviewer on panel
 Category 2 – General supplements usable with
any program
 Materials will be reviewed starting in February
2013.
 Will be recommended to SBE July 2013
 FCOE will have a review on panel
71
Assembly Bill (AB) 1246
(Brownley)
 Allows SBE to adopt Instructional Materials for grades
K-8 aligned to CCSS.
 Adoption will include Integrated I and Algebra I
materials.
 Changes the requirement for use of instructional
materials funds to allow local education agencies
(LEAs) to adopt non-State Board of Education (SBE)adopted instructional materials.
 Must be done by March 30, 2014.
72
AB 1246 (Brownley) (Cont.)
“…a local educational agency may use instructional
materials that are aligned with the academic content
standards …, including instructional materials that have
not been adopted by the state board….”
Education Code (EC) 60210(a)
73
AB 1246 (Brownley) (Cont.)
“If a local educational agency chooses
to use instructional materials that have
not been adopted by the state board,
the local educational agency shall
ensure that a majority of the
participants of any review process
conducted by the local educational
agency are classroom teachers who
are assigned to the subject area or
grade level of the materials.”
EC 60210 (c)
74
Materials Adoption
 CDE Currently Requesting Reviewers.
 Materials will be reviewed this summer and
recommended to the SBE.
 Materials scheduled to be approved March 2014.
75
Criteria for Instructional Materials
 Adopted by SBE January 16, 2013
 Based heavily on K-8 Publisher’s Criteria released July
2012.
 Focus, Coherence, and Rigor
 Large majority of time on major work of grade
 Connect practice standards with content emphasized in
the Standards.
76
Other CDE ACtions
Academic Program Survey (APS)
77
Academic Program Survey (APS)
Updates
Essential Program Components (EPCs)
Updated:








EPC 1 Instructional Materials
EPC 2 Instructional Time
EPC 3 Pacing Guide
EPC 4 Principal Professional Development
EPC 5 Teacher Professional Development
EPC 6 Instructional Assistance
EPC 7 Data Systems/Assessment
EPC 8 Teacher Collaboration
78
California Standards
Testing (CST)
79
Recommendation to Legislature
and Governor
Requires Legislation
80
SBAC Blueprint
8
1
Summative Assessment for
Accountability
Final 12 weeks of school year
 Performance Tasks
 1 reading/writing and 1 math
 Delivered via computer
 Time – 1 to 1.5 hours
Grades 3-8
1 hour
Grade 11
1.5 hours
 Computer Adaptive Assessments
 30-45 Items types
Selected-response
Constructed response
Technology-enhanced items
 Time – 1.5 to 2 hours
 Retake option
Grades 3-5 1.5
hours
Grade 6-8, 11
2 hours
Each student may complete one retake
No cost
82
Overview of SBAC Claims
 Claim 1 – Concepts and Procedures
 Students can explain and apply mathematical concepts and interpret and
carry out mathematical procedures with precision and fluency.
 Claim 2 – Problem Solving
 Students can solve a range of complex, well-posed problems in pure and
applied mathematics, making productive use of knowledge and problem
solving strategies.
 Claim 3 – Communicating Reasoning
 Students can clearly and precisely construct viable arguments to support
their own reasoning and to critique the reasoning of others.
 Claim 4 – Modeling and Data Analysis
 Students can analyze complex, real-world scenarios and can construct
and use mathematical models to interpret and solve problems.
Claims 2 and 4 are Combined
http://www.smarterbalanced.org
83
Professional
Development
84
Professional Development
 CDE Modules
 Regional PD
 County Offices
 SJVMP
 Resources
85
Contact Information
 Jon Dueck
 (559) 497-3792
 jdueck@fcoe.org
 http://stem.fcoe.org
 Julie Joseph
 (559) 651-3641
 jjoseph@ers.tcoe.org
 http://commoncore.tcoe.org
86