Download The Standards for Mathematical Practice describe the ways in which

Supporting the Implementation
of the Common Core State
Standards in Mathematics
What are its implications for teaching and
evaluating mathematics instruction
for our nation? New York State?
Your district?
6/30/2011
WARNER CENTER FOR
PROFESSIONAL DEVELOPMENT
& EDUCATION REFORM
UNIVERSITY OF ROCHESTER
Mathematics Outreach
Judi Fonzi, Ph.D.
Cindy Callard, Ed.D.
Stephanie Martin
Jane LaVoie
6/30/2011
The Warner Center's Mission
To foster and support research-based
innovative professional practice and
systemic change.
• This is accomplished through professional
development and systemic reform
initiatives based on current research and
collaboration with our partners.
6/30/2011
Goals for This Session
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Share Updated information about CCSSM
Experience the mathematical practices
Share ideas about beginning to implement
Discuss next steps
Provide links to resources
6/30/2011
The Common Core
Standards in Mathematics:
Why is this so important?
• This initiative will affect 45.1 million
students across the United States
• A common set of academic standards for
students will create a common set of
rigorous student achievement
expectations across the country
• Opportunities for states to pool resources
on supporting materials and assessments
6/30/2011
What’s different about CCSSM?
• Designed as a tool to raise achievement
• Provides more clarity on what students are
expected to learn
• Provides an opportunity for mathematics
education to be more consistent across the
states in our nation
• Serves as a guide for teachers and parents in
preparing students for the challenges of the
workplace or post secondary study
Source: NCTM 2010
6/30/2011
What’s different about CCSSM?
• 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.
Source: CCSS (2010, p. 5)
6/30/2011
CCSSM Characteristics
• Aligned with college and career
expectations—prepare all students for
success on graduating from high school
• Internationally benchmarked so that all
students are prepared for succeeding in our
global economy and society
• Includes rigorous content and application of
higher-order skills—an ability to apply
concepts and skills to new situations is
expected
• Research based
• Organized around 8 Mathematical Practices
that should be intertwined with content
6/30/2011
Common Core State Standards:
Designed to raise achievement
• Cleared out the clutter from the basement and
attic of the curriculum—fewer and more rigorous
• Opportunities to not only deepen
understandings, but engage in new mathematics
ideas
• Provides depth, focus, coherence nationally
• Opportunity to align curriculum, instruction and
assessment
6/30/2011
FOCUS
• Key Ideas, understandings and skills are
identified
• Deep learning of concepts is emphasized
• Provides adequate time to devote to a
topic and learning it well
• Counters the “mile wide, inch deep”
criticism leveled at most U.S. standards
6/30/2011
COHERENCE
• Articulated progressions of topics and
performances that are developmental and
connected to other progressions—designed
around research-based learning
progressions (NC State, University of Arizona)
• Conceptual understanding and procedural
skills stressed equally
• NCTM states coherence also means that
instruction, assessment, and curriculum
are aligned
6/30/2011
Standards for Mathematical Content
• Counting and Cardinality (K)
• Operations and Algebraic
Thinking (K-5)
• Number and Operations in
Base Ten (K-5)
• Ratios and Proportional
Relationships (6-7)
• The Number System (6-8)
• Expressions and Equations (6-8)
• Statistics and Probability (6-HS)
• Measurement and Data (K-5) • Functions (8-HS)
• Geometry (K-HS)
• Number and Quantity (HS)
• Number and Operations –
• Algebra (HS)
Fractions (3-5)
6/30/2011
• Modeling (HS)
Where are we in NYS?
• Present approach—Shopping Cart—all is
equally important in curriculum, instruction
and assessment
• Strands are separated, not integrated
• When the going gets tough, move on
(Lots to cover!!)
• The process standards are hardly included
in assessments
6/30/2011
Why do we need to make
changes in our present content?
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The Grain size is a major issue
“Strands” are too big and vague; e.g. number
Present lessons are too small. We need to plan in units.
We need to stop managing lessons and start managing
units—engage students with particular ideas in service of
the big ideas
• Content across grades must reflect what is mathematically
meaningful and what is known from research and practice
about learning mathematics
• Need opportunities for students to develop conceptual
understandings
• Need to engage students in mathematical practices
6/30/2011
70%
Intensive Focus
Addition and Subtraction
K‐2
examples concepts, skills and
20%
Rethink and
Link
Geometry and
measurement
Patterns
Statistics/Data
Probability
Estimating
computation
Area, volume
Patterns
Statistics/Data
Probability
Quantitative
relationships and
functions
Statistics
problems
Multiplication and division
3‐5
examples of whole numbers and
fractions, balance of
concepts, skills, problem
solving
6‐8
Proportional reasoning
examples and linearity
Algebra
Geometric
measurement
6/30/2011
10%
Sampling
Focus in K-5: The new version
100%
80%
Sample
60%
Rethink & Link
40%
Intensive Focus
20%
0%
Everyone's Time and Effort
6/30/2011
What do we need to be doing?
Bringing the Common Core to Life: A Webinar
from NYSED (April 28, 2011—David Coleman)
• Teach less, learn more; Have a deep focus on
arithmetic in K-8
• Develop fluency, understanding and be able to
apply in novel situations
• Stop treating standards like a checklist
• Stop letting textbooks determine what you focus on
• Stop making things easy!!—Change what we think
of our practice and kids!!
• Emphasize critical thinking skills
6/30/2011
STANDARDS FOR
MATHEMATICAL PRACTICE
“The Standards for Mathematical Practice
describe the varieties of expertise that
mathematics educators at all levels should
seek to develop in their students. These
practices rest on important ‘processes and
proficiencies’ with long standing
importance in mathematics education.”
(CCSS, 2010)
6/30/2011
Standards for Mathematical
Practice
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
6/30/2011
Standards for Mathematical
Practice
5.
6.
7.
8.
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in
repeated reasoning
6/30/2011
Standards for Mathematical
Practice
• Describe the thinking processes, habits of
mind and dispositions that students need to
develop a deep, flexible, and enduring
understanding of mathematics; in this sense,
they are also a means to an end.
MP1. Make sense of problems
“…they [students] analyze givens, constraints,
relationships and goals…they monitor and evaluate
their progress and change course if necessary…and
the continually as themselves ‘Does this make
sense?’ ”
6/30/2011
Standards for Mathematical
Practice
AND…Describe mathematical content students
need to learn.
MP1. Make sense of problems
“…students can explain correspondences
between equations, verbal descriptions,
tables, and graphs or draw diagrams of
important features and relationships, graph
data, and search for regularity or trends.”
6/30/2011
Standards for [Student]
Mathematical Practice
• “Not all tasks are created equal, and
different tasks will provoke different
levels and kinds of student thinking.”
Stein, Smith, Henningson & Silver, 2000
• “The level and kind of thinking in which
students engage determines what they
will learn.”
Hiebert, Carpenter, Fenemma, Fuson, Werner, Murray, Oliver and
Hannah, 1997
6/30/2011
Do all students have the opportunity
to engage in mathematical tasks
that promote students’ attainment
of the mathematical practices
on a regular basis?
So how can we begin to implement
these new ideas?
6/30/2011
Helping all develop a vision of what
teaching and learning should look
like in a CCSSM classroom
• Why an image?
– Many of our own experiences do not reflect
the latest research on the teaching and
learning of mathematics
– Teachers need to be reflective and craft their
own practice to support student learning
– Administrators need to know what to look for
in a CCSSM supportive class
6/30/2011
Teaching Mathematics Through the
Mathematical Practices
The Standards for Mathematical Practice
describe the ways in which developing
student practitioners of the discipline of
mathematics increasingly ought to engage
with the subject matter as they grow in
mathematical maturity and expertise
throughout the elementary, middle and high
school years. Designers of curricula,
assessments, and professional development
should all attend to the need to connect the
mathematical practices to mathematical
content in mathematics instruction.
6/30/2011
Do the Math!
6/30/2011
Video: Multiplying Fractions
with Mixed Numbers
Sixth grade, CMP lesson: Bits and Pieces II, Problem 3.3
Developing an Algorithm for Fraction Multiplication
6/30/2011
Viewing the Video
Identify evidence of students using
the mathematical practices.
6/30/2011
Video: Graphing Linear Functions
• TIMSS video
• Eighth grade, review lesson
following unit of work on this topic;
36 students enrolled
6/30/2011
Lesson Graph
6/30/2011
Viewing the Video
Identify evidence of students using
the mathematical practices.
http://timssvideo.com/58
6/30/2011
NYS Timeline (As of 6/27/11)
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2010-2011 • Student achievement expectations are based on the 2005 ELA
and Mathematics Learning Standards and Core Curricula.
Districts begin developing curricula aligned to CCSS (Jan. 2011) with a goal
of implementing the new state curricula in Sept. 2012. 2011-2012 • Student
achievement expectations are based on the 2005 ELA and Mathematics
Learning Standards.
Districts continue to develop curricula and begin implementing instruction
aligned to CCSS.
The 3-8 Testing program and Regents examinations in ELA and
Mathematics are aligned to the 2005 ELA and Mathematics Learning
Standards.
2012-2013 • Student achievement expectations are based on CCSS and
state standards as added.
CCSS Interim Assessments are administered.
Partnership for Assessment of Readiness for College and Careers
(PARCC) field testing will occur.
2013-2014 • Student achievement expectations are based on CCSS and
state standards as added. 2014-15 • CCSS PARCC assessments are
operational.
6/30/2011
So what do we need to move
forward?
• Well aligned and coordinated attention to
curriculum, assessment and instruction
• Professional development that effectively
support teachers in their implementation of
the shared vision of CCSSM and NCTM
• Opportunities for teachers to enhance their
understandings of mathematics that
encompasses and transcends what they
expect of their own students
• Rethinking of mathematics in terms of big
ideas and connections rather than a checklist
6/30/2011
What else?
• Talk with others---you are not alone; NYS
is not alone; this is a national effort!!!
• Sorry, there’s no easy fix!!!
6/30/2011
Possible Next Steps for Your District
• Look forward, not backwards—don’t spend
time developing crosswalks—remember the
size of the grain
• When you look at the CCSSM focus on the
big ideas and domains; Look at the
progressions within and across domains
• Look at how the math standards are related
to Language Arts and for connections
between them (in particular the practices)
• Implement changes in content at the preK-2
level now
6/30/2011
Possible Next Steps for Your District
• Have all teachers provide experiences for students
to begin to implement the mathematical practices
• Provide opportunities for students to engage in
tasks that have a high level of cognitive demand
• Support teachers, administrators and other key
players in attending professional development
opportunities to unpack the standards, deepen
their own mathematical content knowledge, etc.
• Collaborate with others in your own district to
examine student work to look for evidence of the
mathematical practices
6/30/2011
Possible Next Steps for Your
District
• September 2011 through April 2012 continue with
the old NYS content standards
• May/June 2012 switch to CCSSM—are their any
major ideas students at your grade level may be
missing???
• Don’t buy anything—there are no easy fixes to
existing resources
• For NSF curricula look to the curriculum developers
• John King—Dare to focus on what’s important;
Deepen your own understandings; engage your
colleagues in conversations; work to incorporate
practices
6/30/2011
Possible Next Steps for Teachers
• Build on the knowledge learners already have
• Expose and discuss common misconceptions
• Use higher-order questions
• Use cooperative small group work
• Emphasize reasons rather than answers
• Use rich collaborative tasks
• Create connections between topics
• Use technology in appropriate ways
Phil Daro—one of the authors of CCSSM
6/30/2011
How can we continue to support
you in this process?
Developing a cadre of CCSSM leaders to provide
support in their own districts:
 RCSD
 Regionally if possible
Providing Professional Development Opportunities:
 Partnering with BOCES
 Summer Opportunities with Warner
Continuing to develop and maintain partnerships with
local districts to support their implementations of
mathematics programs
Providing a link to our website with updated resources
6/30/2011
References
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NCSM
NCTM
Webinar from NYSED (David Coleman)
CCSS
TIMMS Video
Phil Daro—one of the authors of CCSSM
Connected Mathematics Project
New York State Education Department
6/30/2011
Warner Center for Professional
Development and Reform
http://it.warner.rochester.edu/content/warnercenter/
6/30/2011