implementing the nys p-12 common core learning standards for mathematics

www.engageNY.orgwww.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

New York State Education Department. (2011).

EngageNY. Retrieved from

http://engageny.org/

The Common Core State Standards Initiative

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/

Why Common Core State Standards?

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.

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

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

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

Underlying FrameworksStrands of Mathematical Proficiency

Strategic Competence

Adaptive Reasoning

Conceptual Understanding Productive

Disposition

Procedural Fluency

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

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

Helping Children Learn Mathematics. Washington, DC: National Academies

Press.

www.engageNY.orgwww.engageNY.org 7

Improving K-12

Mathematics is an

URGENT Matter!

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?

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.

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

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

TIMSS 2007 Assessment 8th Grade Math

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

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

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.

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

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

PISA 2003

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

PISA 2006

The “Thin Elite Layer”

NAEP 2011 NY State

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 4th Grade Math

NAEP Math Results

234238 240

247253

CA NY U.S. MD MA

Grade 4

NAEP Math Results

273280 283 288

CA NY U.S. MD MA

Grade 8

NAEP 8th Grade Math

NYS P-12 Common CoreLearning Standards for Mathematics

New York State Education Department. (2011). Common Core in Mathematics:

Overview. Retrieved from http://engageny.org/resource/ common-core-in-mathematics-overview/

Common Core Learning Standards

Instructional Shifts . . .

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.

Reflection

Read the “Shift”

What does the “Shift” mean to you?

What does it look like in mathematics classrooms (provide specific examples)?

Trends in International Mathematics and Science Study (TIMSS)

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

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

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

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

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

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.

Reflection

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

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=UUF0pa3nE3aZAfBMT8pqM5

PA&playnext=1

The Structure is the Standardsby Phil Daro, Bill McCallum, Jason

ZimbaA Grecian Urn

You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will send one piece a day in an envelope for the next year. You object; he says “don’t worry, I’ll make sure that you get every single piece, and the markings are clear, so you’ll be able to glue them all back together. I’ve got it covered.” Absurd, no? But this is the way many school systems require teachers to deliver mathematics to their students; one piece (i.e. one standard) at a time. They promise their customers (the taxpayers) that by the end of the year they will have “covered” the standards…

The Structure is the Standardsby Phil Daro, Bill McCallum, Jason Zimba

Once you have read the article, please answer the questions below with an elbow partner.

1. How do the authors describe the standards?

Provide evidence in the text.

2. How were the Common Core State Standards developed? Point to evidence in the text.

3. Why did they use the word “structure” in the title? Discuss with your elbow partner.

Daro, P., McCallum, B., & Zimba, J. (2012, February 16). The Structure is the

Standards [Web log post]. Retrieved from http://commoncoretools.me/2012/02/ 16/the-structure-is-the-standards/

Dividing Fractions

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

Dividing Fractions

How would you present the following problem:

1 ¾ ÷ ½ ?

Knowing and Teaching Elementary Mathematics – Liping Ma

What is the common phrase we hear teacherssay when teaching students to divide fractions?

Ma, L. (2010). Knowing and Teaching Elementary Mathematics: Teachers'

Understanding of Fundamental Mathematics in China and the United States

(Studies in Mathematical Thinking and Learning Series) (2nd ed.).

Routledge.

Most of the Chinese teachers use the phrase “dividing by a number is equivalent to multiplying by its reciprocal” instead of what many U.S. teachers say “invert and multiply.”

Dividing by 2 is the same as multiplying by ½, therefore dividing by ½ is the same as multiplying by 2.

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

Let’s share and record all the various ways.

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)

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

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.

Reflection

Granny Prix

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

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

Key Fluencies

Grade Required Fluency

K Add/subtract within 5

1 Add/subtract within 10

2Add/subtract within 20

Add/subtract within 100 (pencil and paper)

3Multiply/divide within 100

Add/subtract within 1000

4 Add/subtract within 1,000,000

5 Multi-digit multiplication

6Multi-digit division

Multi-digit decimal operations

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

8 Solve simple 22 systems by inspection

Mathematical Fluency: A Balanced Approach

Balanced between procedural fluency and conceptual understanding, with examples

Building on required fluencies

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

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

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.

Reflection

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.

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.

Reflection

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.

Reflection

When Not Knowing Math Can Cost You $15,000

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

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

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

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

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

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

Assessment of Learning

The Next Shift

New York State Assessment Transition Plan: ELA and Mathematics

1 The PARCC assessments are scheduled to be operational in 2014-15 and are subject to adoption by the New York State Board of Regents. The PARCC assessments are still in development. All PARCC assessments will be aligned to the Common Core.

2 Funding Pending.

3 The PARCC consortium is developing ELA and mathematics assessments that will cover grades 3-11. New York State will continue to monitor the development of these assessments to determine how the PARCC assessments might intersect with the Regents Exams. Note that all new Regents Exams and PARCC assessments will be implemented starting with the end-of-year administration, rather than the winter or summer administrations.

4 The names of New York State’s Mathematics Regents Exams are expected to change to reflect the new alignment of these assessments to the Common Core. For additional information about the upper-level mathematics course sequence and related standards, see the “Traditional Pathway” section of Common Core Mathematics Appendix A (http://engageny.org/news/traditional-course-pathway-for-high-school-mathematics-courses-approved/).

5 This transition plan is specific to the NYSAA in ELA and mathematics.

6 New York State is a member of the NCSC national alternate assessment consortium that is engaged in research and development of new alternate assessments for alternate achievement standards. The NCSC assessments are scheduled to be operational in 2014-15 and are subject to adoption by the New York State Board of Regents.

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

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

Grades 9-10 Aligned to the Common Core2

PARCC1

Grade 11 Regents

Aligned to 2005 Standards Regents Exam Aligned to the Common Core3

Regents Exam Aligned to the Common Core / PARCC1, 3

Grades 3-8 Aligned to the Common Core PARCC1

Algebra I

Geometry

Regents Exams Aligned to the Common Core3,4

Algebra II

Aligned to 2005 Standards Aligned to 2005 Standards

Aligned to the 2005 Standards

Regents Exams Aligned to the Common Core / PARCC1, 3,4

Additional State Assessments

NYSAA5 Aligned to 2005 Standards Aligned to the Common Core

NYSESLAT Aligned to 1996 Standards Aligned to the Common Core

As of October 12, 2012 (Subject to Revision)

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

*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.)

Resources

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

Common Core Resources on EngageNY

collaboratively built tools

informed and approved by the authors of the CCSS,

which evaluate the Common Core alignment of curricular

materials collaboratively built to

informed and approved by the authors of the CCSS,

which evaluate the Common Core alignment of curricular

materials

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

Scope & Sequence

1/6 Module

3/6 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

Video Exemplars

Materials July 2012 Fall/Winter 2012

Spring/Summer 2013

Winter 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

The End

implementing the nys p-12 common core learning standards for mathematics

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