Presented by Anise Flowers, Ph.D.

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• Presented by Anise Flowers, Ph.D.
• Measurement Consultant
• Pearson

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The Power of Three!
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Introduction KeyMath3 Diagnostic Assessment

• Nationally standardized and criterion referenced
  diagnostic assessment of mathematics concepts and
  skills
• Untimed and individually administered
• Covers full spectrum from rote counting to
  factoring polynomials solving linear equations.
• Designed to meet requirements for RtI Service
  Delivery Model for Tiers II and III.

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Overview

• KeyMath3 measures a students understanding and
  application of critical math concepts
• Age Range 46 through 2111
• Content Range Pre-K through 9
• 30-90 minute administration time
• Convenient computer scoring
• Essential Resources intervention material

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KM3 - Key Features

• Aligned to the National Council of Teachers of
  Mathematics (NCTM) Principles and Standards of
  Mathematics
• Most state Math standards aligned to NCTM
  Principles and Standards
• Ability to measure progress in 3 month intervals
• Useful for Progress Monitoring and Response to
  Intervention Models (RtI)

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KeyMath3 Revisions Whats New?

• Includes Algebra at all levels
• New Subtests
• All new items
• Updated norms
• More emphasis on math communication, connections,
  reasoning
• Linked to interventions
• 372 full color items in each form

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Norms Development

• 3,360 individuals from 4 years 6 months to 21
  years 11 months old
• Both Age and Grade for Fall and Spring 2006
• Norms for the entire assessment and for specific
  areas
• Norm sample matched to 2005 U.S. census for
• Sex, ethnicity, socioeconomic status, region and
  Special Education classification

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Applications

• Measure math proficiency
• Measure student progress
• Develop instructional plans
• Support educational placement decisions

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Examiner Qualifications

• Minimum of bachelors degree including
• Coursework in principles of measurement and in
  interpretation of tests
• Formal training in mathematics
• Users include, but are not limited to
• Educational diagnosticians
• School psychologists
• Special Education professionals

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Applications Other Users

• Title 1 Teachers
• General educators with struggling students
• Math Teachers and Coaches

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KM3 Diagnostic Assessment Program Components

• Manual
• Two easels
• Record form (A or B) and student response booklet
  for computation
• ASSIST computer scoring and reporting software
• Also needed pen or pencil calculator
• Calculator for 3rd grade up on Applied Problem
  Solving subtest

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Administration Time

• PreK K 15 - 35 minutes
• Grades 1 -2 35 60 minutes
• Grades 3 7 60 - 80 minutes
• Grades 8-12 75 90 minutes
• Areas may be administered individually
• Focus on students area of greatest need
• Shorter administration time

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10 NCTM Standards

• Five Content
• Number and Operations, Algebra, Geometry,
  Measurement, Data Analysis Probability
• Match Basic Concepts subtests
• Five Process
• Problem Solving, Connections, Communication,
  Representation, Reasoning Proof
• Incorporated into the KeyMath3 items throughout
  the 10 subtests

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NCTM Standards Match
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NCTM Process Standards

• Problem Solving
• Solving problems when method for solution is not
  readily apparent
• Connections
• Connecting mathematical concepts skills in a
  variety of contexts
• Communication
• Communicating ideas explaining reasoning

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NCTM Process Standards

• Representation
• Using symbolic expressions, diagrams, charts
• Reasoning Proof
• Using reasoning to form insights, recognize
  patterns, explore phenomena, make conjectures,
  justify results

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KeyMath3 Content Areas

• Basic Concepts (Conceptual Knowledge)
• Operations (Computational Skills)
• Applications (Problem Solving)
• The same as KeyMath-R/NU

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KeyMath3Basic Concepts Subtests

• Numeration
• Algebra
• Geometry
• Measurement
• Data Analysis and Probability

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Basic Concepts SubtestsNumeration

• Early number awareness
• Place value and number sense
• Magnitude of numbers
• Fractions
• Decimals
• Percentages
• Exponents, integers, multiples, factors

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KeyMath3Basic Concepts Numeration

• Grade Level 3rd grade
• Representation process standard because it shows
  alternative representations of the number 253.
• Connections process standard because it connects
  the students understanding of addition and place
  value.

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Basic Concepts Numeration

• Grade Level 6th grade
• Connections process standard because it requires
  the student to link his/her understanding of
  decimal and fraction.

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Basic Concepts SubtestsAlegbra

• Early algebraic awareness
• Algebraic uses of numbers geometry
• Symbolic representation
• Ratio proportion
• Coordinate graphing

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Basic Concepts Algebra

• Grade Level 3rd grade
• Connections process standard it requires the
  student to connect their understanding of
  multiplication to sets of objects presented in
  rows.
• Representation process standardit requires the
  student to recognize an alternative
  representation of multiplication repeated
  addition.

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KeyMath3Basic Concepts Algebra

• Grade Level 8th grade
• Both the Problem Solving and the Representation
  process standards. Without the benefit of a
  solution that is evident, the student must apply
  strategies to identify a mathematical
  relationship between the numbers in the two
  columns then choose the function that represents
  that relationship.

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Basic Concepts SubtestsGeometry

• Early geometric awareness
• Two-dimensional shapes
• Three-dimensional shapes
• Lines angles
• Formulas
• Grids coordinate plans

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KeyMath3Basic Concepts Geometry

• Grade Level 8th grade
• Communication process standard because the
  student is required to precisely express the
  mathematical concept of similarity.
• Reasoning and Proof process standard is
  addressed because the student must use reasoning
  to formulate the proof.

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Basic Concepts SubtestsMeasurement

• Early awareness of measurement
• Standard units
• Time
• Money

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Basic Concepts Measurement

• Grade Level 2nd Grade
• Problem Solving process standard because the
  solution is not readily apparent. Applying trial
  and error with various coin values is a common
  strategy for this problem.

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Basic Concepts Measurement

• Grade Level 9th grade
• Reasoning and Proof process standard by
  requiring the student to development an argument.
• Communication process standard because the
  student must explain with accurate mathematical
  language.
• Connection process standard because it applies
  math in a real-world context.

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Basic Concepts SubtestsData Analysis
Probability

• Early awareness of data probability
• Charts, tables graphs
• Graphical representation
• Statistics
• Probability

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Basic Concepts Data Analysis and Probability

• Grade Level 3rd grade
• Reasoning process standard as it requires a
  degree of reasoning for young students to
  recognize that the only real choice is the
  question with three options.

• Data are represented in a bar chart thus, it
  addresses the Representation process standard.
  Connections process standard because it applies
  to a situation not that unfamiliar to students
  that is outside of mathematics.

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Basic Concepts Data Analysis and Probability

• Grade Level 5th grade
• Reasoning and Proof process
• standard as the student must
• identify which of the four options is most likely
• Communications process standard as they then
  have to explain their reasoning
• Connections process standard because it connects
  to a topic familiar to students and that is
  outside of mathematics.

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KeyMath3Operations Subtests

• Mental Computation and Estimation
• Addition and Subtraction
• Multiplication and Division
• Items mixed and ordered by relative difficulty

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Operations SubtestsMental Computation
Estimation

• Early awareness of mental computation
• Mental computation
• Chains
• Whole numbers
• Rational numbers
• Estimation
• Whole numbers
• Rational numbers

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Operations Mental Computation and Estimation
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Operations Mental Computation and Estimation
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Operations SubtestsAddition Subtraction

• Algorithms to add subtract whole numbers
• Involves regrouping multidigit numbers
• Algorithms to add subtract rational numbers
• Explores decimals, fractions, mixed numbers
• Integers
• Algebra
• Explores monomials polynomials.

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KeyMath3OperationsAddition/Subtraction
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KeyMath3Operations Addition/Subtraction
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Operations SubtestsMultiplication Division

• Algorithms to multiply divide whole numbers
• Involves regrouping one/two-digit multipliers
  divisors
• Algorithms to multiply divide rational numbers
• Explores decimals, fractions, mixed numbers
• Integers
• Algebra
• Explores monomials polynomials.

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Operations Multiplication/Division
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Operations Multiplication/Division
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KeyMath3Applications Subtests

• Foundations of Problem Solving
• Identify missing elements in a problem,
  operations needed, or optimal strategy
• Applied Problem Solving
• Math problems in real-world contexts
• Requires standard non-standard problem solving
  strategies

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Applications SubtestsFoundations of Problem
Solving

• Analysis of problems
• Whether sufficient information is present
• Operations needed
• Relationships in relevant information
• Word problems
• Creating word problems and creating clues
• Problem-solving strategies
• Identify strategies that would address problems

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Applications Foundations of Problem Solving

• Grade Level 1st-2nd
• Representing information
• for word problems in the
• form of a number sentence
• is a foundational part of
• formal problem solving
• Content Standard- Algebra

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Applications Foundations of Problem Solving

• Grade Level 7-8th grade
• Connections- student must
• connect this information to the
• concept of volume while also maintaining the
  correct units.
• Content Standard - Measurement

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Applications SubtestsApplied Problem Solving

• Numeration
• Algebra
• Geometry
• Measurement
• Data Analysis and Probability

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Applications Applied Problem Solving

• Grade Level 8th grade
• Process Standards - Communication, Problem
  Solving, Connections, Reasoning and Proof
• Content Standard - Numeration

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Applications Applied Problem Solving

• Grade Level 2nd grade
• Representation - Information given is expressed
  or represented in a number sentence.
• Content Standard Data Analysis Probability

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KeyMath3Administration

• Areas may be administered individually
• Tailor intervention to that area
• Assess effectiveness of intervention for that
  area
• Monitor progress in that area
• Parallel Forms A and B
• Alternate every three months
• Forms matched statistically and by content

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KeyMath3 Screening Option

• Administer 5 Basic Concepts subtests to obtain
  information on essential math concepts
• Administration time
• Prek-2nd 15-30 minutes
• 3rd 12 35-45 minutes

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KeyMath-3 Content Areas Subtests
Total Test
OPERATIONS
APPLICATIONS
BASIC CONCEPTS
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KeyMath3 Scores

• For Areas (Basic Concepts, Operations, and
  Applications) and Total Test
• Standard Scores
• (x100, SD15,Range 55-145)
• Confidence Intervals
• Grade Equivalent or Age Equivalent
• Percentile Rank

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KeyMath3 Scores

• For Subtests
• Scaled Scores (x 10, SD3,Range 1-19)
• Confidence Intervals
• Grade Equivalent or Age Equivalent

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Descriptive Categories
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Scoring Program ASSIST

• Quickly and accurately scores the test
• Pinpoints students strengths weaknesses
• Linked to Essential Resources intervention
  program
• Provides the assessment link for the RtI model
• Available in Network Client/Server version in 2008

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ASSIST Data Entry Options
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ASSIST Data Entry Options
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ASSIST Report Options
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ASSIST Reports

• Score Summaries
• Area Comparisons
• Score Profiles
• Score Summary Narrative
• Item and Functional Range Analysis
• Progress Report (GSV)
• Parent/Caregiver Letter

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ASSIST Score Summary

• Norm-referenced scores
• An excellent tool for identifying and
  prioritizing instructional programs
• Easily and quickly identify an examinees lowest
  and highest areas of functioning

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ASSIST Score Summary
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Score Profile

• ASSIST
• Presents a graphical representation of an
  examinees subtest scale scores, and area and
  total test standard scores
• Quickly and easily identify students strengths
  and weaknesses
• Interpretation
• Facilitates prioritizing instruction
• Supports analysis of severity of a performance
  deficit

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ASSIST Score Profiles
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ASSIST Area Comparisons

• Allows direct comparison of an individuals
  performance in one area with his or her
  performance in the other areas
• Indicates level of statistical significance of
  the difference
• Indicates frequency of that difference in the
  norm sample

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ASSIST Area Comparisons
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ASSIST Score Summary Narrative

• Describes students subtest, area, and total test
  scores.
• Explains percentile ranks and descriptive
  categories
• Describes a students mathematical performance in
  relation to a nationally representative sample of
  individuals of the same grade or age

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ASSIST Score Summary Narrative
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ASSIST Item and Functional Range Analysis

• Identifies KeyMath-3 DA items that fall within an
  individuals functional range
• Notes items that may require particular attention
• Presents the behavioral objective measured by
  each of the items included in the analysis
• Identifies appropriate lessons in the KeyMath-3
  Essential Resources

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ASSIST Item and Functional Range Analysis
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Functional RangeInterpretation

• Pay attention to items in functional range
  answered incorrectly
• Look for relationships among these items which
  might represent an instructional unit
• Identify concepts skills that are prerequisites
  for subsequent learning
• Appendix F lists objectives for each item

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Functional RangeInterpretation

• Look for relationships between Numeration subtest
  and each of the others since number concepts
  are foundational to other skills
• Computation skills facilitate applied problem
  solving
• Also consider students current grade level
  have they received instruction on this objective?

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Focus Items Interpretation

• Items below the functional range which were
  answered incorrectly
• Reflects gaps in understanding
• Skills that need particular attention
• Items above the functional range which were
  answered correctly
• Exceptional Competence with particular skill

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KeyMath3 Developmental Scores

• To Measure Growth
• Grade Equivalents
• Age Equivalents
• Growth Scale Value (GSV) available only with
  the ASSIST scoring program

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Measuring Growth

• Growth Scale Value (GSV)
• Based on IRT ability Scale
• Designed for measuring change
• Reflects absolute performance like a raw score
  not relative standing (normative)
• Allows direct comparison of GSV scores obtained
  on the alternate forms of an area
• Useful for documenting progress (AYP)
• Helpful in measuring response to intervention

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ASSIST Report Options
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ASSIST Progress Report

• Evaluates the effectiveness of math intervention
  programs for individuals and groups
• GSVs have a significant advantage for measuring
  growth and tracking progress over standard scores
  and percentile ranks
• Report can be obtained for Total Test and each of
  the 3 Areas

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ASSIST Progress Report

• Answers the following questions
• 1) How much gain occurred? (GSV units per year)
• 2) Is that gain significant?
• If not significant they are not responding
  adequately to the intervention
• If significant then they are showing progress
  that is reliably greater than zero (no growth)
• 3) How does the students growth compare to the
  population?

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ASSIST Progress Report Table

• Shows percentile rank, change in GSV since 1st
  administration, and growth rates
• Grade level expressed in grade month of the
  year (August is 0)
• Change over baseline significantly greater than
  zero indicated with an asterisk

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ASSIST Progress Report Graph

• Vertical axis is GSV scores
• Horizontal is grade or age level
• Curved line is average GSV OF NORM GROUP
• Students GSV scores are connected red dots
• Dashed line is students growth average across
  administrations shows growth trend

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ASSIST Parent/Caregiver Letter

• Provides a means of communicating an examinees
  test results to his or her parents or caregivers
  through a one-page letter
• Briefly describes the various features of the
  test and provides content area and total test
  percentile ranks and descriptive categories
• Useful in communicating an examinees test
  performance

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ASSIST Parent Caregiver Report
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Reliability

• Internal Consistency of Form A

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Reliability
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Concurrent Validity KeyMath-3 with Sections of
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Validity
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Essential Resources

• Interventions integrated with KeyMath-3 content,
  organization and range
• Three program levels
• Level I Pre-K grade 2 June 2008
• Level II grades 3 5 June 2008
• Level III grades 6 8 Coming soon

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Essential Resources Features

• Comprehensive supplement to a basal mathematics
  program
• Provides alternative teaching presentations
• Clearly identify concepts and skills
• Maintains conceptual continuity through careful
  pacing and thoroughness
• Facilitates precise teaching through unique
  format
• Connects directly with KeyMath 3 Assessment
  results.

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Essential Resources

• Organized into 10 content strands
• Content clusters within each strand
• Individual lessons activities within cluster
• Lessons can be covered in a single class period
• ER can be used with individual, small group, or
  whole class

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Essential Resources Components

• Two easels
• Teaching in individual or small group
• Easel Activity Display develops concepts and
  skills through the use of representations,
  structured discussions, and specific activities.
• Manual
• CD-ROM
• Contains several hundred masters for guided
  independent practice
• Contains images from easel to produce
  transparencies or use with a computer.

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KM-3 Essential Resources

• ASSIST links directly to recommended
  instructional materials based on the students
  KeyMath-3 DA results
• OR material can be used independently,
  incorporating these engaging activities into a
  teaching program
• Conveniently organized for easy browsing

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Essential Resources Steps

• Obtain recommended lessons from the Diagnostic
  Assessment results
• Review for appropriateness for the student
• Administer Readiness assessment
• Teach the specific lesson with Guided practice
  sheets
• Student completes Independent practice
• Administer Review assessment
• If needed, re-teach lesson with variations
• Administer Mastery assessment

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KM-3 Essential Resources

• Targeted materials to build a customized
  instructional program for your student
• Over 400 Lessons with activities per level
• Over 200 guided and nearly 450 independent
  worksheets per level
• Nearly 150 assessments per level including
  readiness, review, mastery and alternative
• Progress Monitoring Report one for each of the
  10 content strands

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KM-3 Essential Resources

• Automatically highlights recommended lessons
  based on DA results

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KM-3 Essential Resources

• Conveniently preview thumbnails of all material

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Easel Teacher Display

• Convenient teaching easel
• Reverse side of Student Display
• Specific Instructions

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Student Display
Engaging graphics Easel or CD for use with small
or large groups Clip-ins transparent and opaque



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Guided Practice

• Used during the lesson tied to lesson display
• Available on CD print as many as you need

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Independent Practice

• Used by students during class time, after school
  or as homework
• Reduced verbal load from the guided practice

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Readiness Assessment

• Available at the cluster level
• Determine whether the student has the
  pre-requisites needed to learn the lesson you are
  about to teach

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Review Assessment

• Available at the cluster level
• Determine whether the student has mastered the
  concept

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Mastery Assessment

• Similar to the
• review assessment
• Useful when re-teaching the lesson is necessary

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Alternative Assessment

• Useful with students who are unable to take
  traditional assessments.

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Progress Monitoring

• Record for each of the 10 content strands
• Monitor individual student progress with KM3 ER
  assessments as you move through the lessons
• Monitor progress and determine any needed
  adjustments to student instructional plan

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Progress Monitoring

• Track student performance over time
• Determine possible adjustments to education plan

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KeyMath3 RTI
Additional diagnostic assessment with
KeyMath3 Interventions from Essential
Resources May include Special Education
referral/placement
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KeyMath3 Diagnostic Assessment for
students not responding to Tier 1
interventions KeyMath3 Essential Resources
Lessons specified by DA results Track progress
using Cluster Review Mastery assessments in
ER Retest with DA after 3 months
II
Math screening for all students (such as BASI,
GMADE or PASeries)
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Schema adapted from Michelle Windmueller
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