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New York State Education New York State Education Department Forum on NYS Department Forum on NYS

Learning Standard for Learning Standard for MathematicsMathematics

Michelle Kline, Associate in Mathematics Michelle Kline, Associate in Mathematics EducationEducation

Revised March 16, 2005

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Grades 3-8 Testing Grades 3-8 Testing in in

MathematicsMathematics

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OVERVIEWOVERVIEW

I. Why test in grades 3 through 8 every year?

II. What will these tests look like?

III. How will these tests be scored?

IV. How will test results be used?

V. Information to help schools prepare.

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I.I. Why Test in Grades 3 Through 8?Why Test in Grades 3 Through 8?

Initially, mandated by federal government

Also presents the opportunity to:• Evaluate the implementation of the learning

standards annually• Measure student progress• Gather information about student readiness

for study at the next level

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No Child Left Behind (NCLB)No Child Left Behind (NCLB)

Specifies that statewide tests must:• Address the depth and breadth of the

state content standards

• Be valid, reliable, and of high technical quality

• Be designed to provide a coherent system across grades and subjects

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II.II. What Will These Tests Look Like?What Will These Tests Look Like?

• The NYS tests are designed to measure student achievement in mathematics in grades 3 through 8.

• The tests reflect New York State content/process standards in each grade and subject area.– Signal priority content– Are instructionally sensitive

• Tests in mathematics will be similar in format to existing Grade 4 and 8 assessments.

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II.II. What Will These Tests Look Like?What Will These Tests Look Like?

• See the “Introduction to the Grades 3-8 Testing Program in ELA and Mathematics” for test design

• See the “Appendix B Sample Mathematics Questions for sample math questions for grades 3 through 8.

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Testing Times for MathematicsTesting Times for Mathematics

Test Time

(approx.)

Prep Time

(approx.)

Grade 3 Session 1 40 min. 10 min.

Session 2 35 min. 10 min.

Grade 4 Session 1 50 min. 10 min.

Session 2 45 min. 10 min.

Session 3 45 min. 10 min.

Grade 5 Session 1 45 min. 10 min.

Session 2 50 min. 10 min.

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Testing Times for MathematicsTesting Times for Mathematics

Test Time

(approx.)

Prep Time

(approx.)

Grade 6 Session 1 40 min. 10 min.

Session 2 60min. 10 min.

Session 3 N/A N/A

Grade 7 Session 1 50 min. 10 min.

Session 2 50 min. 10 min.

Grade 8* Session 1 45 min. 10 min.

Session 2 35 min. 10 min.

Session 3 65 min. 10 min.

* Sessions 1 and 2 will be given on one day – both ELA and math.

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Test Administration•Field Testing – May 23-27, 2005 Change from Original Schedule Due to Demands of Test Development and the Approval of New Math Standards

•Operational Grades 3-8 – March 2006

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III.III. How Will These Tests be Scored?How Will These Tests be Scored?

•We are working to design an Electronic Distributive Scoring System, but that will take 2 years.

•A number of scoring models are being considered: For year 1, districts will have to hand-score.

•We are looking at authorizing the use of a Superintendent’s Conference Day to

score math.

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NYS Learning StandardsNYS Learning Standards

1996: Board of Regents approved English Language Arts (ELA) & Mathematics, Science and Technology (MST) learning standards

1998-1999: SED issued - ELA Resource Guide with Core Curriculum

- Mathematics Resource Guide with Core Curriculum

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Resource Guides with Core Resource Guides with Core CurriculumCurriculum

• Developed by SED staff with NYS educators

• Provide additional level of specificity to the learning standards (performance indicators, learning experiences, sample tasks, formative assessments)

• Organized by grade level clusters

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NYS Mathematics Learning StandardsNYS Mathematics Learning Standards(Revisited)(Revisited)

• Commissioner appointed Independent Panel on Math A (July 2003)

• Board of Regents accepted Independent Panel on Math A Report (October 2003)

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Mathematics Learning StandardsMathematics Learning Standards(Revisited)(Revisited)

Independent Panel on Math A Report Recommendations1A: Educationally useful standards must be developed in mathematics for each grade, K-8, and for Math A and Math B, that consist of a clear, well-defined set of skills, the mastery of which is demonstrable.

1B: SED should establish a mathematics standards committee to rewrite the standards into functional form, and to meet regularly in the future to analyze test results, thus ensuring continuous relevance.

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Mathematics Learning StandardsMathematics Learning Standards(Revisited)(Revisited)

Independent Panel on Math A Report Recommendations1C: SED should develop and disseminate suggested curricula for mathematics instruction for each grade K-8, and for Math A and Math B.

1D: To benefit from the extensive research and deliberation of the current Math A Panel, some of the current Panel members should be included in both new committees recommended in this report, i.e., the standards committee, and the curriculum development committee.

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Mathematics Standards CommitteeMathematics Standards Committee

• Appointed by Commissioner January 2004“examine the existing Regents standards in

mathematics, consider relevant research and other standards from the U.S. and other nations, and then propose modifications to the Regents mathematics standards to improve clarity, specificity, and functionality”

http://www.emsc.nysed.gov/msc

• Report to Board of Regents November 2004• Report to Board of Regents Jan/March 2005

http://www.regents.nysed.gov

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Mathematics Standards CommitteeMathematics Standards Committee

• Period of Public Comment

• SED Summary of Public Comment

• Report to Regents and Regents Action

• Curriculum Guidance Materials

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Mathematics Advisory Group

Established by the Office of Curriculum and Instructional Support

“to advise the NYS Education Department on the statewide rollout of:– The New York State Learning Standard in

Mathematics (Standard 3)– Curriculum guidance materials and resources– Grades 3-8 Testing in Mathematics”

http://www.emsc.nysed.gov/3-8/home.html

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Mathematics Curriculum Committee

Established by the Office of Curriculum and Instructional Support

“to develop curriculum guidance resources/ materials to assist the field in the implementation of the new mathematics standard, content strands, process strands, and performance indicators.”

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Mathematics Curriculum Committee

Resources will include but are not limited to:• Crosswalk from the “old” to the “new”• Sample tasks for each performance indicator• Glossary (for teachers)• Vocabulary lists by grade level (for students)• Instructional guidelines• Role of manipulatives• Role of Technology• Calculator Guidelines• Assessment Module

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Performance Indicators for Pre/Post-March Testing

• For grades 3-8, content performance indicators are categorized as Pre-March or Post-March

• Guide to development of local curriculum maps

• All process performance indicators could be tested at a given grade level

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Commercial Product Analysis Template

• A form for districts to compare the new grade-by-grade performance indicators to their current math series/program

• Allow districts to determine where supplements to the math series/program will be needed

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Curriculum Guidance Materials

Mathematics Toolkit

www.emsc.nysed.gov/3-8/guidance

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KEY DATESKEY DATES• SED launches new website on NYS Learning

Standards & Grades 3-8 Testing in ELA and Mathematics (http://www.emsc.nysed.gov/3-8/home.html )October 1, 2004

• Statewide Teleconference: NYS Learning Standards & Grades 3-8 Testing in ELA and MathematicsOctober 20, 2004

• SED conducts a series of Regional ForumsDecember 2004 – April 2005

• Mathematics Standards Committee Report to the Board of Regents November 2004, January 2005, March 2005

• Public Comment Period on Proposed Mathematics StandardsNovember 2004 – December 2004

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KEY DATESKEY DATES(continued)

• Introductory Booklet on Grades 3-8 ELA and Mathematics TestingWinter 2005

• Board of Regents Action on Proposed Mathematics Standards January 2005, March 2005

• Statewide Administration of NYS Elementary and Intermediate ELA Assessment (based on existing ELA standards)January 2005

• Field Testing of Grades 3-8 English Language Arts February 2005

• Field Testing of Grades 3-8 Mathematics May 2005

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• SED shares template to be used by local districts to analyze their commercial standards-based programs in relationship to new Mathematics Standards

March 2005

• Statewide Administration of NYS Elementary and Intermediate Mathematics Assessment (based on existing MST standards)May 2005

• SED posts NYS Core Curriculum in Mathematics &ELAMay 2005

• SED shares a toolkit to support local districts in aligning their curriculum to new Mathematics Standards

May 2005

KEY DATESKEY DATES(continued)

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• SED posts a revised NYS Learning Standards for Mathematics, Science, and Technology

May 2005

• SED updates NYS Virtual Learning System to reflect grade-by-grade content standards

May 2005

• SED issues Sample Test Forms for Grades 3-8 Testing in ELA and Mathematics

Fall 2005

• Administration of NYS Grades 3-8 ELA Tests January 2006

• Administration of NYS Grades 3-8 Mathematics TestsMarch 2006

KEY DATESKEY DATES(continued)

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On March 15, 2005 the Board of Regents adopted

the performance indicators for Algebra, Geometry,

and Algebra 2 and Trigonometry, along with the

alignment modifications to prekindergarten through

grade 8.

http://www.emsc.nysed.gov/3-8/m-home.htm

Board of Regents Adopts Board of Regents Adopts

NYS Learning Standard inNYS Learning Standard in

MathematicsMathematics

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Mathematics, Science, and TechnologyMathematics, Science, and Technology

Standard 3: MathematicsStandard 3: Mathematics

Students will:

•understand the concepts of and become proficient with the skills of mathematics;

•communicate and reason mathematically;

•become problem solvers by using appropriate tools and strategies;

 

through the integrated study of number sense and operations, algebra, geometry, measurement, and statistics and probability.

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Standard 3Standard 3

The Three ComponentsThe Three Components

•Conceptual Understanding consists of those relationships constructed internally and connected to already existing ideas.

•Procedural fluency is the skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.

•Problem solving is the ability to formulate, represent, and solve mathematical problems.

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Standard 3Standard 3

Process and Content StrandsProcess and Content Strands

The Five Process Strands The Five Content Strands

Problem Solving

Number Sense and Operations

Reasoning and Proof Algebra

Communication Geometry

Connections Measurement

Representation Statistics and Probability

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The Five Process StrandsThe Five Process Strands

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Problem Solving StrandProblem Solving Strand

Students will:

•build new mathematical knowledge through problem solving;

•solve problems that arise in mathematics and in other contexts;

•apply and adapt a variety of appropriate strategies to solve problems;

•monitor and reflect on the process of mathematical problem solving.

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Reasoning and Proof StrandReasoning and Proof Strand

Students will:

•recognize reasoning and proof as fundamental aspects of mathematics;

•make and investigate mathematical conjectures;

•develop and evaluate mathematical arguments and proofs;

•select and use various types of reasoning and methods of proof.

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Communication StrandCommunication Strand

Students will:

•organize and consolidate their mathematical thinking through communication;

•communicate their mathematical thinking coherently and clearly to peers, teachers, and others;

•analyze and evaluate the mathematical thinking and strategies of others;

•use the language of mathematics to express mathematical ideas precisely.

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Connections StrandConnections Strand

Students will:

•recognize and use connections among mathematical ideas;

•understand how mathematical ideas interconnect and build on one another to produce a coherent whole;

•recognize and apply mathematics in contexts outside of mathematics.

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Representation StrandRepresentation Strand

Students will:

•create and use representations to organize, record, and communicate mathematical ideas;

•select, apply, and translate among mathematical representations to solve problems;

•use representations to model and interpret physical, social, and mathematical phenomena.

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The Five Content StrandsThe Five Content Strands

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Number Sense and Number Sense and

Operations StrandOperations Strand

Students will:

•understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems;

•understand meanings of operations and procedures, and how they relate to one another;

•compute accurately and make reasonable estimates.

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Algebra StrandAlgebra Strand

Students will:

•represent and analyze algebraically a wide variety of problem solving situations;

•perform algebraic procedures accurately;

•recognize, use, and represent algebraically patterns, relations, and functions.

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Geometry StrandGeometry Strand

 Students will:

•use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes;

•identify and justify geometric relationships, formally and informally;

•apply transformations and symmetry to analyze problem solving situations;

•apply coordinate geometry to analyze problem solving situations.

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Measurement StrandMeasurement Strand

Students will:

•determine what can be measured and how, using appropriate methods and formulas;

•use units to give meaning to measurements;

•understand that all measurement contains error and be able to determine its significance;

•develop strategies for estimating measurements.

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Statistics and Probability StrandStatistics and Probability Strand

Students will:

•collect, organize, display, and analyze data;

•make predictions that are based upon data analysis;

•understand and apply concepts of probability.

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Bands within the Bands within the Content StrandsContent Strands

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Number Sense and Operations Number Sense and Operations BandsBands

•Number Systems

•Number Theory

•Operations

•Estimation

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Algebra BandsAlgebra Bands

•Variables and Expressions

•Equations and Inequalities

•Patterns, Relations, and Functions

•Coordinate Geometry

•Trigonometric Functions

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Geometry BandsGeometry Bands

•Shapes

•Geometric Relationships

•Transformational Geometry

•Coordinate Geometry

•Constructions

•Locus

•Informal and Formal Proofs

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Measurement BandsMeasurement Bands

•Units of Measurement

•Tools and Methods

•Units

•Error and Magnitude

•Estimation

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Statistics and Probability BandsStatistics and Probability Bands

•Collection of Data

•Organization and Display of Data

•Analysis of Data

•Predictions from Data

•Probability

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Guide to Reading Guide to Reading the Documentthe Document

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Prekindergarten Prekindergarten

Problem Solving

 Students will build new mathematical knowledge through problem solving. 

PK.PS.1 Explore, examine, and make observations about a social problem or mathematical situation

PerformanceIndicator

Strand

Major Understanding

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Prekindergarten Prekindergarten

Number Sense and Operations  

Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.

Number Systems  PK.N.1 Count the items in a collection and know the last counting word tells how many items are in the collection (1 to 10)

Major Understanding

BandPerformance

Indicator

Strand

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Performance Indicator GuidePerformance Indicator Guide

PK – Prekindergarten

K – Kindergarten

PS – Problem Solving

RP – Reasoning and Proof

CM – Communication

CN – Connections

R – Representation

N – Number Sense and Operations

A – Algebra

G – Geometry

M – Measurement

S – Statistics and Probability

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Alignment ModificationsAlignment Modifications

•During the MSC review of the high school

performance indicators, they noted that alignment

modifications needed to be made to the Regents-

approved prekindergarten through Grade 8

document in order to ensure strong alignment

across all the grades.

•The alignment modifications are available online

at http://www.emsc.nysed.gov/3-8/alignmod.htm

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Definition of TermsDefinition of Terms

The performance indicators use the words

investigate, explore, discover, conjecture,

reasoning, argument, justify, explain, proof, and

apply. Each of these terms is an important

component in developing a student’s mathematical

reasoning ability. It is therefore important that a

clear and common definition of these terms be

understood. The order of these terms reflects

different stages of the reasoning process.

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Investigate/Explore Investigate/Explore

Students will be given situations in which

they will be asked to look for patterns or

relationships between elements within the

setting.

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DiscoverDiscover

Students will make note of possible

patterns and generalizations that result

from investigation/exploration.

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ConjectureConjecture

Students will make an overall statement,

thought to be true, about the new

discovery.

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ReasoningReasoning

Students will engage in a process that

leads to knowing something to be true or

false.

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ArgumentArgument

Students will communicate, in verbal or

written form, the reasoning process that

leads to a conclusion. A valid argument is

the end result of the conjecture/reasoning

process.

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Justify/ExplainJustify/Explain

Students will provide an argument for a

mathematical conjecture. It may be an intuitive

argument or a set of examples that support the

conjecture. The argument may include, but is

not limited to, a written paragraph,

measurement using appropriate tools, the use

of dynamic software, or a written proof.

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ProofProof

Students will present a valid argument,

expressed in written form, justified by

axioms, definitions, and theorems.

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ApplyApply

Students will use a theorem or concept to

solve an algebraic or numerical problem.

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AlgebraAlgebra

In implementing the Algebra process and content performance indicators, it is expected that

students will identify and justify mathematical relationships. The intent of both the process and

content performance indicators is to provide a variety of ways for students to acquire and

demonstrate mathematical reasoning ability when solving problems. Local curriculum and local/state assessments must support and allow students to

use any mathematically correct method when solving a problem.

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GeometryGeometry

In implementing the Geometry process and content performance indicators, it is expected that students

will identify and justify geometric relationships, formally and informally. For example, students will

begin with a definition of a figure and from that definition students will be expected to develop a list of conjectured properties of the figure and to justify each conjecture informally or with formal proof. Students will also be expected to list the assumptions that are needed in order to justify each conjectured property and present their findings in an organized manner.

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Algebra 2 and TrigonometryAlgebra 2 and Trigonometry

In implementing the Algebra 2 and Trigonometry process and content performance indicators, it is

expected that students will identify and justify mathematical relationships, formally and

informally. The intent of both the process and content performance indicators is to provide a

variety of ways for students to acquire and demonstrate mathematical reasoning ability when

solving problems. Local curriculum and local/state assessments must support and allow students to

use any mathematically correct method when solving a problem.

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For the Latest Information on For the Latest Information on the 3-8 Testing Programthe 3-8 Testing Program

Go to

http://www.emsc.nysed.gov/3-8/home.html

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