www.engageNY.org

Implementing the NYS P-12 Common Core Learning Standards

for Mathematics

Please visit www.engageNY.org for additional information regarding the Common Core Learning

Standards

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New York State Education Department. (2011).

EngageNY. Retrieved from

     http://engageny.org/

www.engageNY.org

The Common Core State Standards Initiative

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Beginning in the spring of 2009, Governors and State Commissioners of Education from 48 states, 2

territories and the District of Columbia committed to developing a common core of state K-12 English

language arts (ELA) and mathematics standards.

The Common Core State Standards Initiative (CCSSI) is a state-led effort coordinated by the National

Governors Association (NGA) and the Council of Chief State School Officers (CCSSO).

www.corestandards.org

Common Core State Standards Initiative. (2011). Common Core State Standards.

     Retrieved from http://www.corestandards.org/

www.engageNY.org

Why Common Core State Standards?

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www.engageNY.org

Why Common Core State Standards?

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Preparation: The standards are college- and career-ready. They will help prepare students with the knowledge and skills

they need to succeed in education and training after high school.

Competition: The standards are internationally benchmarked. Common standards will help ensure our students are

globally competitive.

Equity: Expectations are consistent for all – and not dependent on a student’s zip code.

Clarity: The standards are focused, coherent, and clear. Clearer standards help students (and parents and teachers)

understand what is expected of them.

Collaboration: The standards create a foundation to work collaboratively across states and districts, pooling resources and

expertise, to create curricular tools, professional development, common assessments and other materials.

www.engageNY.org

The Mathematics Standards: How They Were Developed and

Who Was Involved Key Points from Video

• General discussion of mathematics standards • Aspirations for mathematics instruction at higher levels • Greater mastery through focus and coherence • Review of groups involved • General discussion of mathematics progressions • What is and is not included at the elementary level • What happens at middle school• Discussion of migration away from strands and into domains

of mathematics

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McCallum, W. (2011). Mathematic Standards: How They Were Developed and Who Was

     Involved [Video file]. Retrieved from http://www.youtube.com/watch?v=dnjbwJdcPjE

www.engageNY.org

Underlying FrameworksStrands of Mathematical Proficiency

Strategic Competence

Adaptive Reasoning

Conceptual

UnderstandingProductive Disposition

Procedural Fluency

NRC (2001). Adding It Up. Washington, D.C.:

National Academies Press.

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Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it Up:

     Helping Children Learn Mathematics. Washington, DC: National Academies

     Press.

www.engageNY.org7

Improving K-12

Mathematics is an

URGENT Matter!

www.engageNY.org

Key Questions

What is the current state of mathematics performance…

• In the United States compared to other nations?

• In the United States?• In New York State compared to other states?• In your school/district compared to other

districts in New York State?

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www.engageNY.org

What is TIMSS? The

Trends in International Mathematics and Science Study (TIMSS) compares math and science achievement of 4th and 8th graders internationally.

TIMSS is closely linked to the curricula of the participating countries, providing an indication of the degree to which students have learned concepts in mathematics and science they have encountered in school

To date, more than 50 countries have participated.

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Trends in International Mathematics and Science Study(TIMSS). (n.d.). Retrieved

     from Institute of Educational Science website: http://nces.ed.gov/timss/

www.engageNY.org

TIMSS 2007 Assessment 8th

Grade Math

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Gonzales, P. (2009). Highlights From TIMSS 2007:Mathematics and Science

     Achievement of U.S. Fourth and Eighth-Grade Students in an International

     Context. Retrieved from National Center for Education Statistics

     website: http://nces.ed.gov/pubs2009/2009001.pdf

www.engageNY.org

TIMSS: Countries Behind U.S.

Armenia, Australia, Sweden, Malta, Scotland, Serbia, Italy, Malaysia, Norway, Cyprus, Bulgaria, Israel, Ukraine, Romania, Bosnia and Herzegovina, Lebanon, Thailand, Turkey, Jordan, Tunisia, Georgia, Iran, Islamic Rep of, Bahrain, Indonesia, Syrian Arab Republic, Egypt, Algeria, Colombia, Oman, Palestinian Nat'l Auth., Botswana, Kuwait, El Salvador, Saudi Arabia, Ghana, Qatar, Morocco

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What is PISA

PISA (Programme for International Student Assessment)

is an international study which began in the year 2000. It aims to evaluate education systems worldwide by testing the skills and knowledge of 15-year-old students in participating countries/economies. Since the year 2000 over 70 countries and economies have participated in PISA.

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Programme for International Student Assessment (PISA). (n.d.). Retrieved from

     Organisation for Economic Co-operation and Development website:

     http://www.oecd.org/document/61/

     0,3746,en_32252351_32235731_46567613_1_1_1_1,00.html

www.engageNY.org

PISA

PISA assesses how far students near the end of compulsory education have acquired some of the knowledge and skills that are essential for full participation in society. In all cycles, the domains of reading, mathematical and scientific literacy are covered not merely in terms of mastery of the school curriculum, but in terms of important knowledge and skills needed in adult life.

In the PISA 2003 cycle, an additional domain of problem solving was introduced to continue the examination of cross-curriculum competencies.

Take the Test

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www.engageNY.org

PISA 2003

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Programme for International Student Assessment. (n.d.). First Results from PISA

     2003 [Executive Summary]. Retrieved from Organisation for Economic

     Co-operation and Development website: http://www.oecd.org/dataoecd/1/63/      34002454.pdf

www.engageNY.org

PISA 2006

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www.engageNY.org

The “Thin Elite Layer”

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www.engageNY.org

NAEP 2011 NY State

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National Center for Education Statistics. (n.d.). National Assessment of

     Educational Progress (NAEP). Retrieved from U.S. Department of Education

     website: http://nces.ed.gov/nationsreportcard/

www.engageNY.org

NAEP 4th Grade Math

National Center for Education Statistics. (n.d.). National Assessment of

     Educational Progress (NAEP). Retrieved from U.S. Department of Education

     website: http://nces.ed.gov/nationsreportcard/

NAEP Math Results

234238 240

247253

200

210

220

230

240

250

260

CA NY U.S. MD MA

Grade 4

Av

era

ge

Sc

ale

Sc

ore

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www.engageNY.org19

NAEP Math Results

273280 283 288

299

200

220

240

260

280

300

320

CA NY U.S. MD MA

Grade 8

Av

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Sc

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NAEP 8th Grade Math

National Center for Education Statistics. (n.d.). National Assessment of

     Educational Progress (NAEP). Retrieved from U.S. Department of Education

     website: http://nces.ed.gov/nationsreportcard/

www.engageNY.org

Common Core Learning Standards

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www.engageNY.org

Instructional Shifts . . .

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www.engageNY.org

Shift 1 Focus

Teachers use the power of the eraser and significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades.

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www.engageNY.org

The Importance of Focus in Mathematics

• First-year college remediation challenges • Mismatch between higher education and K-12 --

more mastery of fewer topics vs. covering more • Focus as it relates to teachers' needs to build a solid

foundation in early grades • Solid early foundation enables greater success later

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Zimba, J., & McCallum, W. (n.d.). The Importance of Focus in Mathematics [Motion

     picture]. Retrieved from http://www.youtube.com/

     watch?v=2rje1NOgHWs&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=18&feature=plcp

www.engageNY.org

Trends in International Mathematics and Science Study (TIMSS)

Test your mathematics and science knowledge by completing test items in the Dare to Compare challenge!

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NCES Kids' Zone. (n.d.). Dare to Compare. Retrieved from U.S. Department of

     Education website: http://nces.ed.gov/nceskids/eyk/?flash=true

www.engageNY.org

Shift 2 Coherence

Principals and teachers carefully connect the learning within and across grades so that, for example, fractions or multiplication spiral across grade levels and students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

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www.engageNY.org

The Importance of Coherence in Mathematics• Mathematics consists of pieces that make sense; they are not

just independent manipulation/skills to be practiced and memorized – as perceived by many students.

• These individual pieces progress through different grades (in organized structures we called “flows”) and can/should be unified together into a coherent whole.

• Algebra as an example

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Zimba, J., & McCallum, W. (n.d.). The Importance of Coherence In Mathematics

     [Motion picture]. Retrieved from http://www.youtube.com/

     watch?v=2rje1NOgHWs&feature=autoplay&list=UUF0pa3nE3aZAfBMT8pqM5PA&playnext=1

www.engageNY.org

Dividing Fractions

Imagine you are beginning to teach students division with fractions. What would you do to introduce this concept to students?

What is the common phrase we hear teachers

say when teaching students to divide fractions?

Why does it work?

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www.engageNY.org

Knowing and Teaching Elementary Mathematics – Liping Ma

How many different ways can we solve/model the problem 1 ¾ ÷ ½ ?

Let’s share and record all the various ways. (i.e., number lines, measuring cups,

manipulatives, etc)

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www.engageNY.org

Knowing and Teaching Elementary Mathematics – Liping Ma

Measurement Model – “How many ½s in 1 ¾?” (e.g., apples, graham

crackers, piece of wood)Partitive Model – “Finding a number such

that ½ of it is 1 ¾” (e.g., box of candy, cake, pizza, distance)

Factors and Product – “Find a factor that when multiplied by ½ will make 1 ¾” (e.g., area of a rectangle)

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www.engageNY.org

Knowing and Teaching Elementary Mathematics – Liping Ma

The meaning of division by

fractions

Meaning of division with whole

numbers

The concept of inverse

operations

Meaning of multiplication with

whole numbers

Meaning of multiplication with

fractions

Concept of fraction

Concept of unit

Meaning of addition

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www.engageNY.org

Shift 3 Fluency

Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions such as multiplication tables so that they are more able to understand and manipulate more complex concepts.

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www.engageNY.org32

Granny Prix

Oliver, N. (n.d.). Granny Prix [Math Game]. Retrieved from multiplication.com

     website: http://www.multiplication.com/flashgames/GrannyPrix.htm

www.engageNY.org

Key Fluencies

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Grade Required Fluency

K Add/subtract within 5

1 Add/subtract within 10

2Add/subtract within 20Add/subtract within 100 (pencil and paper)

3Multiply/divide within 100Add/subtract within 1000

4 Add/subtract within 1,000,000

5 Multi-digit multiplication

6Multi-digit divisionMulti-digit decimal operations

7 Solve px + q = r, p(x + q) = r

8 Solve simple 22 systems by inspection

www.engageNY.org

Mathematical Fluency: A Balanced Approach

Balanced between procedural fluency and conceptual understanding, with examples

Building on required fluencies

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McCallum, B., & Zimba, J. (n.d.). Mathematics Fluency A Balance Approach [Video

     file]. Retrieved from http://www.youtube.com/watch?v=ZFUAV00bTwA.

www.engageNY.org

Shift 4 Deep Understanding

Teachers teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of core math concepts by applying them to new situations. as well as writing and speaking about their understanding.

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www.engageNY.org

Deep Conceptual Understanding

McDonald’s ClaimWikipedia reports that 8% of all Americans eat at McDonalds every

day.

In the U.S., there are approximately 310 million people and 12,800

McDonalds.

Do you believe the Wikipedia report to be true? Create a mathematical argument to

justify your position.36

www.engageNY.org

Shift 5 Applications

Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations. Teachers in content areas outside of math, particularly science, ensure that students are using math – at all grade levels – to make meaning of and access content.

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www.engageNY.org

Shift 6 Dual IntensityStudents are practicing and

understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity. Teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math concepts. The amount of time and energy spent practicing and understanding learning environments is driven by the specific mathematical concept and therefore, varies throughout the given school year.

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www.engageNY.org

When Not Knowing Math Can Cost You $15,000

“Who wants to be a Millionaire?”Question for $16,000

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Mathclips. (2007, July 26). When Not Knowing Math Can Cost You $15,000 [Motion

     picture]. http://www.youtube.com/watch?v=BbX44YSsQ2I

www.engageNY.org

When Not Knowing Math Can Cost You $15,000

Which of these square numbers also happens to be the sum of two smaller square numbers?

A. 16 B. 25C. 36 D. 49

List strategies to help students remember square numbers

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www.engageNY.org

The Mathematics Standards and the Shifts They Require

• Calls for Conceptual Understanding, Procedural Fluency, and Problem Solving

• Content and skills need to be connected with the Standards of Mathematical Practices

• Greater focus and better coherence

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Zimba, J. (n.d.). The Mathematics Standards and the Shifts They Require [Video

     file]. Retrieved from http://www.youtube.com/

     watch?v=5pBOnvzC_Yw&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=29&feature=plcp

www.engageNY.org

Assessment of Learning

The Next Shift

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www.engageNY.org

NYS Assessment Transition

2012-13: the content of the NYS Grades 3-8 Mathematics tests will be aligned to the NYS P-12 Common Core Learning Standards for Mathematics.

2013-14 First administration of the Algebra I and Geometry Regents Exams

2014-15 First administration of the Algebra II and Trig Regents Exams

2014-15 transition to PARCC Assessments pending Board of Regents approval

Assessment – Subject / Grade

2011-12 2012-13 2013-14 2014-15

ELA

Grades 3-8 Aligned to 2005 Standards Aligned to the Common Core PARCC1

Grade 11 Regents Aligned to 2005 Standards Regents Exam Aligned to the Common Core2

Regents Exam Aligned to the Common Core / PARCC1, 2

Math

Grades 3-8 Aligned to the Common Core PARCC1

Algebra I

Geometry

Regents Exams Aligned to the Common Core2,3

Algebra II

Aligned to 2005 Standards Aligned to 2005 Standards

Aligned to the 2005 Standards

Regents Exams Aligned to the Common Core / PARCC1, 2, 3

Additional State Assessments

NYSAA4 Aligned to 2005 Standards Aligned to the Common Core NCSC5

NYSESLAT Aligned to 1996 Standards Aligned to the Common Core

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www.engageNY.org

What will assessment look like in relation to the Common Core Shifts?

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*Recent update for Shift 3

In a memo dated March 2012, Deputy Commission Slentz stated the following:

Grade 6 students must have the use of a four-function calculator with a square

root key or a scientific calculator for the entire test. (Schools may choose which

type they purchase.)

www.engageNY.org

Resources

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http://engageny.org/resource/math-toolkit/

www.engageNY.org

Common Core Resources on EngageNY

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www.engageNY.org

collaboratively built tools

informed and approved by the authors of the CCSS,

which evaluate the Common Core alignment of curricular materials

collaboratively built tools

informed and approved by the authors of the CCSS,

which evaluate the Common Core alignment of curricular materials

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www.engageNY.org

as of 3/5/12; subject to revision

NYSED is delivering Curriculum Modules aligned to the Core in ELA & Math

Scope and Sequence available in July 2012

P-5 Modules begin arriving in quarter-length chunks beginning in August.

6-12 Modules begin arriving in quarter-length chunks beginning in the Fall.

Modules: ELA & Math

Modules Summer 2012 Fall 2012 Spring 2013 Summer 2013

P-5Scope & Sequence

1/6 Module3/6 Modules 4/6 Modules 6/6 Modules

6-12 Scope & Sequence 2/6 Modules 4/6 Modules 6/6 Modules

PD for NTs, Teachers, Principals

Week Long Summer Intensive P-5

Ongoing

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www.engageNY.org

Video Exemplars

Materials July 2012 Fall/Winter 2012Spring/Summer

2013Winter 2013/14

Common Core Shifts 2 7 11 100 Videos Total

Teacher Practice Videos

45 114 227 Videos Total

Principal Practice Videos

27 68 135 Videos Total

Data Driven Instruction

2 6 15 30 Videos Total

Studio Videos 24 Videos Total

NYSED is delivering more than 500 videos to:

Exemplify the New York State CCLS aligned instruction from NYS teachers

Use for calibration of teacher and principal evaluation

Model data driven instruction cycles

Instruct and Inform regarding CCLS, DDI, TLE

as of 3/5/12; subject to revision

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www.engageNY.org

The End

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