1. Common Core Mathematics in a PLC – Sustainable Solutions
Dr. Timothy D. Kanold (tkanold.blogspot.com)
“These standards are not intended to be new names for old ways of doing business. They are a
call to take the next step. It is time for states to work together to build on lessons learned from
two decades of standards-based reforms. It is time to recognize that standards are not just
promises to our children, but promises we intend to keep.”
—Common Core State Standards Initiative (2010), p.5
Matt Larson and I wrote this school leadership book, Common Core Mathematics in a PLC at
Work™, Leaders Guide, because during professional development, we often hear from teachers,
“You need to share this information with our administrators! We need their support!” And so we
chose to provide you with the same message about change that we wrote about to the reader in
each of our four grade level books.
At the same time, we often hear from school leaders, “Please help our teachers to better
understand and deliver on the message you are giving us!” And so, our grade level books –
written by outstanding voices in the field – Skip Fennell, Juli Dixon, Diane Briars, Thomasenia
Lott Adams, David Foster, John Carter, Beth Kobett, Gwen Zimmermann, Mardi Gale, Harold
Asturias, Jon Wray, Mona Toncheff and Matt Larson provide a deeper support to the important
work of your teams that you are expected to lead.
As the Common Core story unfolds in your school or district there will be a thousand voices
telling you what to do. We hope the leadership book as well as the other books in our series will
help you to cut through all of the noise and allow you to just focus on doing a few things really
well. Think: One paradigm at a time! If you already have the benefit of working as a PLC, you
are well on your way to that equity pursuit: “Ready, Set, Action!” Matt and I wish you the best
and invite you to contact us anytime to let us know your story, your concerns and your triumphs!
Enjoy!
One of the greatest problems with mathematics instruction, and instruction in general in most
school districts, is that it is too inconsistent from classroom to classroom, school to school, and
district to district (Morris & Hiebert, 2011). How much mathematics a fourth-, eighth-, or tenth-
grade student in the United States learns, and how deeply he or she learns it, is largely determined
by the school the student attends, and even more significantly, the teacher the student is randomly
(usually) assigned to within that school. The inconsistencies teachers develop in their professional
development practice—often random and in isolation from other teachers—create great inequities
in students’ mathematics instructional and assessment learning experiences that ultimately and
significantly contribute to the year-by-year achievement gap (Ferrini-Mundy, Graham, Johnson,
& Mills, 1998). This issue is especially true in a vertically connected curriculum like
mathematics.
The Education Trust (Ushomirsky & Hall, 2010, p.10), in Stuck Schools: A Framework for
Identifying Schools Where Students Need Change—Now, indicates that in an environment where
funds and capacity are limited at best, educators and policymakers will need to establish clear
Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 1

2. priorities for implementation. The books in this series are designed to provide that sustainable
story for change in your school or district.
The five fundamental paradigm shifts for mathematics: Knowing your focus and
your message.
The CCSS for mathematics expectations for teaching and learning, and the new state assessments
of that learning, usher in an opportunity for unprecedented change of the second-order variety.
First-order change is characterized as working within existing paradigms with marginal
disturbance to the system, and is implemented within the existing knowledge and skill set of those
closest to the action—the faculty and school leaders. Second-order change requires working
outside existing paradigms by embracing new paradigms for how you think and practice (Waters,
Marzano, & McNulty, 2003, pp. 6–7).
Until now, there has been a lot of debate, but no clear turning point with respect to K–12
mathematics education improvement. The CCSS for mathematics represent a collective and
collaborative states’ effort to signal that turning point. It is time to disturb the system as currently
defined. And the CCSS provide the catalyst for that disturbance.
There are five fundamental second-order paradigm shifts (outside of existing paradigms) required
to prepare every student and teacher for the successful implementation of the CCSS in
mathematics and for the general improvement of mathematics learning for K–12 students in the
United States. They are:
1. Professional Development—The CCSS for mathematics require a paradigm shift to
move the grain size of change beyond the individual, isolated teacher or leader. It is the
grade-level or course-based collaborative learning team (collaborative team) within a
PLC that will develop the expanded teacher knowledge capacity necessary for successful
implementation of the CCSS for mathematics. Your leadership role is to provide the
conditions, structures, and culture necessary to eradicate the old paradigm of isolated
teacher decision-making and accidental professional development and growth.
2. Mathematics Instruction: teaching and learning—The CCSS require a paradigm shift
to daily lesson designs that include plans for accommodating the student Mathematical
Practices described in the CCSS. These student practices focus on the process of student
learning and student development of deeper understanding of mathematics. This
paradigm shift requires teaching for procedural fluency and student understanding of the
grade level CCSS content and using student understanding as a precursor to procedural
fluency. Procedural fluency and conceptual understanding should not and cannot exist
without one another (Kilpatrick, Swafford, & Findell, 2001).
3. Mathematics Content—The CCSS require a paradigm shift to “less (fewer standards) is
more (deeper rigor with understanding)” at every grade level. This will require new levels
of knowledge and skill development for every K–12 teacher of mathematics to
Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 2

3. understand what the CCSS expect students to learn blended with how students learn it.
What mathematical knowledge, skills, understandings, and dispositions should be the
result of each unit of mathematics instruction? There is great clarity and low teacher-to-
teacher variance on the question, “Learn what and learn how?”
4. Mathematics Assessment—The CCSS require a paradigm shift toward assessment as a
multifaceted process that reflects the rigor of the standards and models the expectations
for and benefits of formative assessment development around all forms of assessment,
including traditional assessment instruments such as tests and quizzes. How you will
know if each student is learning the essential mathematics skills, concepts,
understandings, and dispositions the CCSS deem most essential, becomes a significant
question for each collaborative team.
5. Mathematics
Intervention—The
CCSS
require
a
paradigm
shift
toward
a
team
and
school
response
to
intervention
(RTI)
that
is
required.
Much
like
the
CCSS
vision
for
teaching
and
learning,
RTI
can
no
longer
be
invitational.
That
is,
the
RTI
needs
to
become R2TI—a “required” response to intervention. Stakeholder implementation of RTI
programs includes a process that requires targeted students to participate and attend. How
will you respond and act on evidence (or lack of evidence) of student learning in your
school or district?
Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 3

4. PLCs at Work™: Common Core Mathematics Paradigms
INSTRUCTION CONTENT
• Fewer standards, greater depth
• Deep conceptual understanding
• Understanding, focus and coherence
• Collaborative lesson design Tool
• Common and higher demand tasks
• Standards for Mathematical Practice
Collaboration
Paradigm
INTERVENTION ASSESSMENT
• Common RRTI Framework response • PLC Teaching-Assessing-Learning cycle
• Differentiated, targeted and intensive • In-class formative assessment processes
• Student equity, access, support and • Common Assessment instruments as
advancement formative learning opportunitties
Key
CCSS
Web
Resources
1. The Center on Education Policy (cep-dc.org/)
2. PARCC Consortium (parcconline.org/)
3. The Common Core State Standards documents in Mathematics and ELA
(corestandards.org/)
4. The Hunt Institute Mathematics
(youtube.com/user/TheHuntInstitute#p/u/14/BNP5MdDDFPY)
5. PARCC Newsletter at
(parcconline.org/sites/parcc/files/PARCC-Place-September2011.pdf)
6. Myths and facts about the CCSS (ped.state.nm.us/CCS/plan/read/CoreFacts.pdf)
Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 4

5. 7. SMARTer Balanced resources and Frameworks
(www.k12.wa.us/SMARTER/default.aspx)
Other Resources for Mathematics
1. For principals
insidemathematics.org/index.php/tools-for-teachers/tools-for-principals-and-
administrators
This portion of the Inside Mathematics website is designed to support school-based
administrators and district mathematics supervisors who have the responsibility for
establishing the structure and vision for the work of grade-level and cross-grade-level
learning teams.
What Every Principal Needs to Know About the Teaching and Learning of Mathematics
(Kanold, Briars, & Fennel, 2012, Solution Tree)
2. Common Core Standards for Mathematical Practice (Inside Mathematics)
insidemathematics.org/index.php/common-core-standards
This site provides classroom videos and lesson samples designed to illustrate the
Mathematical Practices in action.
3. Common Core Mathematics in a PLC at Work™
professional development book series (Solution Tree/NCTM, 2012 – kanold
Series Editor)
http://www.solution-tree.com/products/books/common-core-mathematics
This series (Kanold, et al) provides unit-by-unit professional development
guidance for implementation of the Common Core.
4. NCTM lessons
illuminations.nctm.org/
Illuminations provides standard-based resources that improve the teaching and learning
of mathematics for all students. These materials illuminate the vision for school
mathematics set forth in Principles and Standards for School Mathematics, Curriculum
Focal Points for Prekindergarten through Grade 8 Mathematics, and Focus in High
School Mathematics: Reasoning and Sense Making.
5. Common Core State Standards blog
commoncoretools.wordpress.com/
Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 5

6. Follow Bill McCallum’s blog on tools that are being developed to support the
implementation of the CCSS.
6. CCSS Mathematics Curriculum Materials Analysis Project (Council of Chief
State School Officers, The Brookhill Foundation, and Texas Instruments)
mathedleadership.org/docs/ccss/CCSSO%20Mathematics%20Curriculum%20Analysis%
20Project.Whole%20Document.6.1.11.Final.docx
The CCSS Mathematics Curriculum Analysis Project provides a set of tools to assist K–
12 textbook selection committees, school administrators, and teachers in the analysis and
selection of curriculum materials that support implementation of the CCSS for
mathematics.
7. Illustrative Math Project (Institute for Mathematics and Education)
illustrativemathematics.org
The main goal for this project is to provide guidance to states, assessment consortia,
testing companies, and curriculum developers by illustrating the range and types of
mathematical work that students will experience in implementing the Common Core
State Standards for mathematics.
8. Progressions documents for the Common Core Math Standards (Institute for
Mathematics and Education)
ime.math.arizona.edu/progressions
The CCSS in mathematics were built on progressions: narrative documents describing the
progression of a topic across a number of grade levels, informed both by research on
children's cognitive development and by the logical structure of mathematics. The
progressions detail why standards are sequenced the way they are, point out cognitive
difficulties and provide pedagogical solutions, and provide more detail on particularly
difficult areas of mathematics. The progressions documents found here are useful in
teacher preparation and professional development, organizing curriculum, and provide a
link between mathematics education research and the standards.
9. Common Core State Standards Resources
(www.mathedleadership.org/ccss/materials.html; NCSM, 2011)
These professional development files are ready to use and designed to help
teachers understand how to implement the Mathematical Practices in their
classrooms.
10. Common Core Look-fors (CCL4s) – Mathematics iPad/iPhone App
(splaysoft.com/CCL4s/Welcome.html; Splaysoft, 2011)
Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 6

7. CCL4s is a comprehensive tool designed to help teacher learning teams deepen their
awareness and understanding of the actions and conditions that promote student
engagement with the CCSS for Mathematical Practice, with connections to the content
standards. An exciting blend of creativity, innovation, and strategic technology use, this
app supports purposeful classroom observation though effective staff collaboration.
References
Common Core State Standards Initiative (2010). Common Core State Standards for mathematics.
Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
Dweck, C. S. (2007). Mindset: The new psychology of success. New York, NY: Ballantine Books.
Ferrini-Mundy, J., Graham, K., Johnson, L., & Mills, G., (1998). Making change in mathematics
education: Learning from the field. Reston, VA: National Council of Teachers of
Mathematics.
Kanold, T. D., & Larson, M. R. (2012). Common Core Mathematics in a PLC (K–12): Leaders
Guide [in press]. Bloomington, IN: Solution Tree Press.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn
mathematics. Washington, DC: National Academies Press.
Morris, A. K., & Hiebert, J. (2011, January/February). Creating shared instructional products: An
alternative approach to improving teaching. Educational Researcher, 40(1), 5–14.
Ushomirsky, N., & Hall, D. (2010). Stuck schools: A framework for identifying schools where
students need change—now. Washington, DC: The Education Trust.
Waters, T., Marzano, R. J., & McNulty, B. A. (2003). Balanced leadership: What 30 years of
research tells us about the effect of leadership on student achievement. Aurora, CO: Mid-
continent Research for Education and Learning.
Wiliam, D. (2011). Embedded formative assessment. Bloomington, IN: Solution Tree Press.
Timothy D. Kanold, Ph.D. © 2012 tkanold.blogspot.com and Solution Tree press at www.solution-tree.com 7