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 OutreachJudi 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.

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Goals for This Session

• Share Updated information about CCSSM• Experience the mathematical practices• Share ideas about beginning to implement• Discuss next steps• Provide links to resources

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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

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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 20106/30/2011

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 content6/30/2011

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

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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

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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

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Standards for Mathematical Content• Counting and Cardinality (K)

• Operations and Algebraic

Thinking (K-5)

• Number and Operations in

Base Ten (K-5)

• Measurement and Data (K-5)

• Geometry (K-HS)

• Number and Operations –

Fractions (3-5)

• Ratios and Proportional

Relationships (6-7)

• The Number System (6-8)

• Expressions and Equations (6-8)

• Statistics and Probability (6-HS)

• Functions (8-HS)

• Number and Quantity (HS)

• Algebra (HS)

• Modeling (HS)

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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

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Why do we need to make changes in our present content?• 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

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70%Intensive Focus

20%Rethink and

Link

10%Sampling

K‐2examples

Addition and Subtraction concepts, skills and problems

Geometry and measurement

PatternsStatistics/DataProbabilityEstimating computation

3‐5examples

Multiplication and division of whole numbers and fractions, balance of concepts, skills, problem solving

Area, volume PatternsStatistics/DataProbability

6‐8examples

Proportional reasoning and linearityAlgebraGeometric measurement

Quantitative relationships and functions

Statistics

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Everyone's Time and Effort0%

20%

40%

60%

80%

100%

Sample

Rethink & Link

Intensive Focus

Focus in K-5: The new version

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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

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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)

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Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively3. Construct viable arguments and critique

the reasoning of others4. Model with mathematics

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Standards for Mathematical Practice

5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in

repeated reasoning

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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?’ ”

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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.”

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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

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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?

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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

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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.

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Do the Math!

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Video: Multiplying Fractions with Mixed Numbers

Sixth grade, CMP lesson: Bits and Pieces II, Problem 3.3

Developing an Algorithm for Fraction Multiplication

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Viewing the Video

Identify evidence of students using the mathematical practices.

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Video: Graphing Linear Functions

• TIMSS video

• Eighth grade, review lesson following unit of work on this topic; 36 students enrolled

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Lesson Graph

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Viewing the Video

Identify evidence of students using the mathematical practices.

http://timssvideo.com/58

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NYS Timeline (As of 6/27/11)• 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.

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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

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What else?

• Talk with others---you are not alone; NYS is not alone; this is a national effort!!!

• Sorry, there’s no easy fix!!!

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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

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• 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

Possible Next Steps for Your District

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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

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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 CCSSM6/30/2011

How can we continue to support you in this process?

Developing a cadre of CCSSM leaders to provide

support in their own districts:RCSDRegionally if possible

Providing Professional Development Opportunities:Partnering with BOCESSummer 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 resources6/30/2011

References• 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

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Warner Center for Professional Development and Reform

http://it.warner.rochester.edu/content/warnercenter/

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