New York State Education Department Forum on NYS Learning Standard for Mathematics

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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
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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.

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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)

• 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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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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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 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 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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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
  Superintendents Conference Day to score math.

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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

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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

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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)

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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.

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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.

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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

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Mathematics 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 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.ht
  ml )
• 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

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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

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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

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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

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• Board of Regents Adopts
• NYS Learning Standard in
• Mathematics

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
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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 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 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.
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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.
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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

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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
Major Understanding
Strand
Performance Indicator
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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
Strand
Performance Indicator
Band
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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 students 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.
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For the Latest Information on the 3-8 Testing
Program
Go tohttp//www.emsc.nysed.gov/3-8/home.html
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