From NECAP to the Common Core Mathematics and New Assessments

April 26, 2011

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AGENDAFrom NECAP to the Common Core Mathematics

and New Assessments

Introduction and background information

Transition Timeline (NECAP to the Common Core and New assessments)

Overview of Mathematics CCSS Design and Organization Similarities/Differences between CCSS &

GLEs/GSEs

Time for Questions and Answers

Next Steps2

Introduction and Background Information

State-led and developed common core standards for K-12 in English/language arts and mathematics

Focus on learning expectations for students, not how students get there.

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Why Now?

Disparate standards across states

Student mobility

Global competition

Today’s jobs require different skills

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Why Important?

Prepares students with the knowledge and skills they need to succeed in college and work

Ensures consistent expectations regardless of a student’s zip code

Provides educators, parents, and students with clear, focused guideposts

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From NECAP to the Next Generation Assessment Systems

Transition / Timeline

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So what? Implications & Impact in NH

Adoption State Board adopted the CCSS “in principle” and is

committed to a thoughtful, orderly transition process for implementation and assessment

Alignment Process began this summer to look at gaps and

matches and grade differentials DOE putting together a broad view to post &

distribute Focus groups currently meeting to review analysis

Implementation TAKE IT SLOW! NECAP in place for at least three years Toolkit for administrators & curriculum leaders in

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Now what? Transition Timeline

2010-2011 – NECAP as usual Begin review of standards-Use Toolkit NECAP Management Team releases plan to principals in April 2011

2011-2012 – NECAP as usual2012 2013 – NECAP (with transitional items)

2013 2014 – final NECAP (best possible transitional test)

2014-2015 – no fall NECAP test NECAP Science remains New assessments based CCSS

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Curriculum and Assessment Timeline for New Hampshire (adjusted format)

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2010-2011 2011-2012 2012-2013 2013-2014 2014-2015

NH Curriculum Standards for English language arts and mathematics*

NH Curriculum Frameworks for ELA and Math

NH Curriculum Frameworks for ELA and Math

NH Curriculum Frameworks for ELA and Math (supplemented with some differences)

NH Common Core Standards in English language arts and mathematics in use

NH Common Core Standards in English language arts and mathematics in use

Common Core State Standards for ELA and mathematics

Begin Review Using Toolkit – The goal is to familiarize

Continue Review, using NH Toolkit –Begin implementation of K-2 standards

Begin to seriously map the grade level differences between NH and CCSS to plan for SY13-14

First year for new standards to be used in classrooms

CCSS with NH specific enhancements fully implemented in classrooms

State Assessment in Reading, Writing, Mathematics

NECAP (fall) NECAP (fall) NECAP (fall) NECAP (fall) New SBAC Adaptive Test (spring)

State Assessment in Science

NECAP (spring) NECAP (spring) NECAP (spring) NECAP (spring) NECAP (spring)

*NH Curriculum Standards in all other content areas remain in place

http://www.education.nh.gov/spotlight/k12_ccss.htm

A place to start:

Fewer and more rigorous. Aligned with college and career expectations Internationally benchmarked Rigorous content and application of higher-

order skills. Builds on strengths and lessons of current

state standards. Research based

Mathematics Common Core Standards

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Review of Major Components of the Mathematics CCSS

Presentation for the NH Department of Education

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Intent of the Common Core

The same goals for all students Coherence Focus Clarity and Specificity

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Key Features: Mathematics Learning progressions that follow how students

learn concepts Understanding the mathematics AND procedural

skill are equally important “processes and proficiencies” from the NCTM

process standards & Adding It Up 8 mathematical practices are the same

throughout the grades Standards for content vary by grade Mastery of standards through grade 7 prepares

students for algebra in grade 8 Appendix: Designing HS Mathematics Courses

[http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf ]

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Common Core State Standards

Introduction Application of CCSS for ELLs Application to Students with Special Needs Mathematics Standards

Standards for Mathematical Practice Grade levels/strand introductions Domains, Clusters and Standards

Appendix A: Model Pathways for High School Courses

[http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf ]

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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 others 4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

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[Explain and make conjectures…]

[Make sense of ...]

[Understand and use…]

[Apply and interpret…]

[Consider and Detect]

[Communicate precisely to others…]

[Discern and recognize…]

[Notice and pay attention to….]

Key Advances Properties of operations: Their role in

arithmetic and algebra Mental math and “algebra” vs. algorithms Operations and the problems they solve Units and unitizing

Unit fractions Unit rates

Quantities-variables-functions-modeling Number-expression-equation-function Modeling Practices

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Common Core Format

High School

Conceptual Category

Domain

Cluster

Standards

K-8

Grade

Domain

Cluster

Standards

(There are no preK Common Core Standards)

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Mathematics Standards:

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Mathematics K-8 : Design & Organization

Introduction Page Highlights: 2-3 Critical Areas Provides: Emphasis of Content

Overview Page Provides:

Domains Cluster Headings Mathematical Practices

DOMAINCLUSTER HEADINGS

Standards within the CLUSTER

FOOTNOTES

Components: K-8 grade level Mathematics Standards

Grade Level DomainsHigh School Conceptual Categories

K – 5 Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations – Fractions Measurement and Data Geometry

6-8 Ratios and Proportional Relationships The Number System Expressions and Equations Functions Geometry Statistics and Probability

Number and Quantity Algebra Functions Modeling Geometry Statistics and

Probability

Standards forMathematical Content

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Distribution of the Domains (K-8)

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Overview: Mathematics Grades K - 5

Introduction at earlier grade Addition, subtraction, multiplication, and division of

whole numbers and other rational numbers

Introduction at later grade Statistics & probability is introduced as a domain in

Grade 6 Expressions & Equations is introduced as a domain

in Grade 6

More specificity Focus on operations with whole numbers, fractions,

and decimals as the foundation for more demanding math concepts and procedures

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Overview: Mathematics Grades 6 – 8

Introduction at earlier grade Percent increase and decrease and interest rate Histograms, box plots, quartiles and inter-quartile

range

Introduction at later grade Functions as a domain is introduced in grade 8

More specificity Grades 6 & 7 standards: ramp up to algebraic

concepts in Gr. 8 Grade 8 standards focus is on linear equations and

functions

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Grade Level Domains High School Conceptual CategoriesK – 5

Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations – Fractions Measurement and Data Geometry

6-8 Ratios and Proportional Relationships The Number System Expressions and Equations Functions Geometry Statistics and Probability

Number and Quantity (N)

Algebra (A)

Functions (F)

Modeling (*)

Geometry (G)

Statistics and Probability (S)

Standards forMathematical Content

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High School Standards• Conceptual Categories

– Cross course boundaries – Span high school years

• Standards– “Core” for common mathematics curriculum

for all students to be college and career ready– “College Ready” for entry level credit

bearing course – (+) Additional mathematics that students

should learn in order to take courses such as calculus, discrete mathematics, or advanced statistics.

Components: High School Mathematics Standard

DOMAIN CLUSTER HEADING

Standards within the CLUSTER

*Modeling

The STAR indicates Modeling is expected to demonstrate proficiency

and may be indicated at the DOMAIN, CLUSTER, CLUSTER HEADING or STANDARD level.•Students are expected to demonstrate proficiency of this

Cluster by applying their knowledge within a real word application.

Conceptual Categories: Domains

Number and Quantity The Real Number System Quantities The Complex Number System Vector and Matrix

Algebra Seeing Structure in Expressions Arithmetic with Polynomials & Rational Functions Creating Equations Reasoning with Equations and Inequalities

Functions Interpreting Functions Building Functions Linear, Quadratic, & Exponential Models Trigonometric Functions

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Conceptual Categories: Domains (continued)

Modeling Geometry

Congruence Similarity, Right Triangles, and Trigonometry Circles Expressing Geometric Properties with Equations Geometric Measurement & Dimension Modeling with Geometry

Statistics and Probability Interpreting Categorical and Quantitative Data Making Inferences and Justifying Conclusion Conditional Probability and Rules of Probability Using Probability to Make Decisions

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Overview: Mathematics High School

Introduction at earlier grade Complex numbers Quadratic, logarithmic, & trigonometric functions Logarithmic identities

Specificity Reflects four years of instruction 1st three years prepare students for college or career 4th year allows for course of choice STEM standards (+) Modeling is integrated throughout all the domains (*)

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Traditional Integrated ALGEBRA I GEOMETRY ALGEBRA II 4th Year Mathematics

Course

MATHEMATICS I MATHEMATICS II MATHEMATICS III 4th Year Mathematics

Course

Model Course Pathways in Mathematics

COMPACTED: •Grades 7 & 8 Standards + Algebra I Standards OR Mathematics I Standards•Instruction occurs over 2 years (during Grades 7 & 8)

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Cracking the High School Mathematics “Code”

High School Number and Quantity

The Real Number System N-RN Quantities N-Q The Complex Number System N-CN Vector and Matrix N-VM

Algebra Seeing Structure in Expressions A-SSE Arithmetic with Polynomials & Rational Functions A-APR Creating Equations A-CED Reasoning with Equations and Inequalities A-REI

N.RNN.QN.CNN.VM

A.SSEA.APRA.CED A.REI

PATHWAYS

Cracking the High School Mathematics “Code” (continued)

Functions Interpreting Functions F-IF Building Functions F-BF Linear, Quadratic, & Exponential Models F-LE Trigonometric Functions F-TF

Modeling *

Geometry Congruence G-CO Similarity, Right Triangles, and Trigonometry G-SRT Circles G-C Expressing Geometric Properties with Equations G-GPE Geometric Measurement and Dimension G-GMD Modeling with Geometry G-MG

F.IFF.BFF.LEF.TF

G.COG.SRTG.CG.GPEG.GMDG.MG

PATHWAYS

How to read a Common Core High School Mathematics Standard

A-SSE.1b

Letter & Number indicating the

Standard withinthe Cluster

ConceptualCategory

ALGEBRASeeing Structure in Expressions A-SSE

Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context.*

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.

Domain

How to read a Common Core High School PATHWAYS Mathematics

Standard

(+)N.CN.4,5,6

Numbers indicating the Standards withinthe Cluster Heading

ConceptualCategory Domain

Number & Quantity The Complex Number System

Represent complex numbers and their operations on the complex plane.4. (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a give complex number represent the same number. 5. (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 1200.6. (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

Indicates: STEM standard

CONCEPTUAL CATEGORY

DOMAIN

Standards within the CLUSTER

CLUSTER HEADING

For grades preK-8, a model of implementation can be found in NCTM’s Curriculum Focal Points

For the secondary level, please see NCTM’s Focus in High School Mathematics: Reasoning and Sense Making

See Handout w/additional resources

www.nctm.org/cfp

www.nctm.org/FHSM

Additional Information

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Reflections: Now What?

What actions will you take based upon what we worked on today?

What do you need to learn? Who will you work with? What do you need to integrate into

your practice? Who will support you?

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Want to know more?

NH DOE Website:http://www.education.nh.gov/spotlight/k12_ccss.htm

Maine Department of Education

http://www.maine.gov/education/lres/math/standards.html

NCSM November 30 2010 Webinar on CCSS http://www.carnegielearning.com/webinars/getting-started-with-the-common-core-state-standards-first-steps-for-mathematics-education-leaders/

Rhode Island Department of Education http://www.ride.ri.gov/Instruction/CommonCoreMaterials.aspx#HowToReadPPT

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