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New York State Education Department Forum on NYS Learning Standard for Mathematics Michelle Kline, Associate in Mathematics Education Revised March 16, 2005

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Grades 3-8 Testing in Mathematics

OVERVIEW: 

OVERVIEW Why test in grades 3 through 8 every year? What will these tests look like? How will these tests be scored? How will test results be used? Information to help schools prepare.

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

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

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.

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.

Testing Times for Mathematics: 

Testing Times for Mathematics

Testing Times for Mathematics: 

Testing Times for Mathematics * 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

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.

NYS Learning Standards: 

NYS 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

Resource Guides with Core Curriculum: 

Resource Guides with Core Curriculum 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

NYS Mathematics Learning Standards(Revisited): 

NYS Mathematics Learning Standards (Revisited) Commissioner appointed Independent Panel on Math A (July 2003) Board of Regents accepted Independent Panel on Math A Report (October 2003)

Mathematics Learning Standards(Revisited): 

Mathematics Learning Standards (Revisited) Independent Panel on Math A Report Recommendations 1A: 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.

Mathematics Learning Standards(Revisited): 

Mathematics Learning Standards (Revisited) Independent Panel on Math A Report Recommendations 1C: 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.

Mathematics Standards Committee: 

Mathematics 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

Mathematics Standards Committee: 

Mathematics Standards Committee Period of Public Comment SED Summary of Public Comment Report to Regents and Regents Action Curriculum Guidance Materials

Mathematics Advisory Group: 

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

Mathematics Curriculum Committee: 

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.”

Mathematics Curriculum Committee: 

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

Performance Indicators for Pre/Post-March Testing: 

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

Commercial Product Analysis Template: 

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

Curriculum Guidance Materials: 

Curriculum Guidance Materials Mathematics Toolkit www.emsc.nysed.gov/3-8/guidance

KEY DATES: 

KEY 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 Mathematics October 20, 2004 SED conducts a series of Regional Forums December 2004 – April 2005 Mathematics Standards Committee Report to the Board of Regents November 2004, January 2005, March 2005 Public Comment Period on Proposed Mathematics Standards November 2004 – December 2004

KEY DATES(continued): 

KEY DATES (continued) Introductory Booklet on Grades 3-8 ELA and Mathematics Testing Winter 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

KEY DATES(continued): 

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 &ELA May 2005 SED shares a toolkit to support local districts in aligning their curriculum to new Mathematics Standards May 2005 KEY DATES (continued)

KEY DATES(continued): 

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 Tests March 2006 KEY 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 NYS Learning Standard in Mathematics

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Mathematics, Science, and Technology Standard 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 3 The 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 3 Process and Content Strands

The Five Process Strands: 

The Five Process Strands

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Problem 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 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 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 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 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.

The Five Content Strands: 

The Five Content Strands

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Number Sense and Operations 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 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 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 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 Strand Students will: •collect, organize, display, and analyze data; •make predictions that are based upon data analysis; •understand and apply concepts of probability.

Bands within the Content Strands: 

Bands within the Content Strands

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Number Sense and Operations Bands Number Systems Number Theory Operations Estimation

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Algebra Bands Variables and Expressions Equations and Inequalities Patterns, Relations, and Functions Coordinate Geometry Trigonometric Functions

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Geometry Bands •Shapes •Geometric Relationships •Transformational Geometry •Coordinate Geometry •Constructions •Locus •Informal and Formal Proofs

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Measurement Bands Units of Measurement Tools and Methods Units Error and Magnitude Estimation

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Statistics and Probability Bands Collection of Data Organization and Display of Data Analysis of Data Predictions from Data Probability

Guide to Reading the Document: 

Guide to Reading the Document

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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 Performance Indicator Strand Major Understanding

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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 Band Performance Indicator Strand

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Performance 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 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 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 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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Discover Students will make note of possible patterns and generalizations that result from investigation/exploration.

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Conjecture Students will make an overall statement, thought to be true, about the new discovery.

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Reasoning Students will engage in a process that leads to knowing something to be true or false.

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Argument 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/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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Proof Students will present a valid argument, expressed in written form, justified by axioms, definitions, and theorems.

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Apply Students will use a theorem or concept to solve an algebraic or numerical problem.

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Algebra 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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Geometry 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 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.

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

For the Latest Information on the 3-8 Testing Program Go to http://www.emsc.nysed.gov/3-8/home.html