Presented by Anise Flowers, Ph.D. Measurement Consultant Pearson The Power of Three! Diagnostic ASSIST™ Essential Assessment computer Resources scoring and intervention reporting program system 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. Overview • KeyMath3 measures a student’s understanding and application of critical math concepts • Age Range: 4:6 through 21:11 • Content Range: Pre-K through 9 • 30-90 minute administration time • Convenient computer scoring • Essential Resources intervention material 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) KeyMath3 Revisions: What’s 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 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 Applications • Measure math proficiency • Measure student progress • Develop instructional plans • Support educational placement decisions Examiner Qualifications • Minimum of bachelor’s 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 Applications: Other Users • Title 1 Teachers • General educators with struggling students • Math Teachers and Coaches 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 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 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 NCTM Standards Match KeyMath™-3 Subtests Content Standards Numeration & Numeration Operations Algebra Algebra Geometry Geometry Measurement Measurement Data Analysis & Data Analysis & Probability Probability 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 NCTM Process Standards • Representation – Using symbolic expressions, diagrams, charts • Reasoning & Proof: – Using reasoning to form insights, recognize patterns, explore phenomena, make conjectures, & justify results KeyMath3 Content Areas • Basic Concepts (Conceptual Knowledge) • Operations (Computational Skills) • Applications (Problem Solving) The same as KeyMath-R/NU KeyMath3 Basic Concepts Subtests • Numeration • Algebra • Geometry • Measurement • Data Analysis and Probability Basic Concepts Subtests: Numeration • Early number awareness • Place value and number sense • Magnitude of numbers • Fractions • Decimals • Percentages • Exponents, integers, multiples, & factors KeyMath3 Basic 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 student’s understanding of addition and place value. Basic Concepts: Numeration Grade Level: 6th grade • Connections process standard because it requires the student to link his/her understanding of decimal and fraction. Basic Concepts Subtests: Alegbra • Early algebraic awareness • Algebraic uses of numbers & geometry • Symbolic representation • Ratio & proportion • Coordinate graphing 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 standard–it requires the student to recognize an alternative representation of multiplication – repeated addition. KeyMath3 Basic 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. Basic Concepts Subtests: Geometry • Early geometric awareness • Two-dimensional shapes • Three-dimensional shapes • Lines & angles • Formulas • Grids & coordinate plans KeyMath3 Basic 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. Basic Concepts Subtests: Measurement • Early awareness of measurement • Standard units • Time • Money 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. 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. Basic Concepts Subtests: Data Analysis & Probability • Early awareness of data & probability • Charts, tables & graphs • Graphical representation • Statistics • Probability 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. 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. KeyMath3 Operations Subtests • Mental Computation and Estimation • Addition and Subtraction* • Multiplication and Division* *Items mixed and ordered by relative difficulty Operations Subtests: Mental Computation & Estimation • Early awareness of mental computation • Mental computation – Chains – Whole numbers – Rational numbers • Estimation – Whole numbers – Rational numbers Operations: Mental Computation and Estimation Operations: Mental Computation and Estimation Operations Subtests: Addition & 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. KeyMath3 Operations: Addition/Subtraction KeyMath3 Operations: Addition/Subtraction Operations Subtests: Multiplication & 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. Operations: Multiplication/Division Operations: Multiplication/Division KeyMath3 Applications 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 Applications Subtests: Foundations 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 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 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 Applications Subtests: Applied Problem Solving • Numeration • Algebra • Geometry • Measurement • Data Analysis and Probability Applications: Applied Problem Solving Grade Level: 8th grade •Process Standards - Communication, Problem Solving, Connections, Reasoning and Proof •Content Standard - Numeration Applications: Applied Problem Solving Grade Level: 2nd grade • Representation - Information given is expressed or represented in a number sentence. •Content Standard – Data Analysis & Probability KeyMath3 Administration • 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 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 KeyMath™-3 Content Areas & Subtests Total Test BASIC CONCEPTS OPERATIONS APPLICATIONS Numeration Mental Computation Foundations of & Estimation Problem Solving Algebra Addition & Applied Problem Geometry Subtraction Solving Multiplication & Measurement Division Data Analysis & Probability KeyMath3 Scores • For Areas (Basic Concepts, Operations, and Applications) and Total Test: – Standard Scores (x=100, SD=15,Range 55-145) – Confidence Intervals – Grade Equivalent or Age Equivalent – Percentile Rank KeyMath3 Scores • For Subtests: – Scaled Scores (x =10, SD=3,Range 1-19) – Confidence Intervals – Grade Equivalent or Age Equivalent Descriptive Categories Scale Score Standard Score Well-below 2 or below 70 or below average Below average 5-7 71-85 Average 8-12 86-114 Above average 13-15 115-129 Well-above 16 or above 130 or above average Scoring Program: ASSIST • Quickly and accurately scores the test • Pinpoints student’s strengths & weaknesses • Linked to Essential Resources intervention program • Provides the assessment link for the RtI model • Available in Network Client/Server version in 2008 ASSIST Data Entry Options ASSIST Data Entry Options ASSIST™ Report Options ASSIST Reports • Score Summaries • Area Comparisons • Score Profiles • Score Summary Narrative • Item and Functional Range Analysis • Progress Report (GSV) • Parent/Caregiver Letter ASSIST Score Summary • Norm-referenced scores • An excellent tool for identifying and prioritizing instructional programs • Easily and quickly identify an examinee’s lowest and highest areas of functioning ASSIST Score Summary Score Profile • ASSIST: – Presents a graphical representation of an examinee’s subtest scale scores, and area and total test standard scores – Quickly and easily identify student’s strengths and weaknesses • Interpretation: – Facilitates prioritizing instruction – Supports analysis of severity of a performance deficit ASSIST Score Profiles ASSIST Area Comparisons • Allows direct comparison of an individual’s 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 ASSIST Area Comparisons ASSIST Score Summary Narrative • Describes student’s subtest, area, and total test scores. • Explains percentile ranks and descriptive categories • Describes a student’s mathematical performance in relation to a nationally representative sample of individuals of the same grade or age ASSIST Score Summary Narrative ASSIST Item and Functional Range Analysis • Identifies KeyMath-3 DA items that fall within an individual’s 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 ASSIST Item and Functional Range Analysis Functional Range: Interpretation • 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 Functional Range: Interpretation • 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 student’s current grade level – have they received instruction on this objective? 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 KeyMath3 Developmental Scores To Measure Growth • Grade Equivalents • Age Equivalents • Growth Scale Value (GSV) – available only with the ASSIST scoring program 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 ASSIST™ Report Options 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 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 student’s growth compare to the population? 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 ASSIST Progress Report Graph • Vertical axis is GSV scores • Horizontal is grade or age level • Curved line is average GSV OF NORM GROUP • Student’s GSV scores are connected red dots • Dashed line is student’s growth average across administrations – shows growth trend ASSIST Parent/Caregiver Letter •Provides a means of communicating an examinee’s 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 examinee’s test performance ASSIST Parent Caregiver Report Reliability Internal Consistency of Form A Grade Basic Operations Applications Total Concepts K-5 .92 .89 .85 .95 6-12 .96 .94 .89 .98 Reliability Basic Operations Applications Total Concepts Alternate- .94 .93 .88 .96 form Test-retest .95 .93 .93 .97 Concurrent Validity – KeyMath™-3 with Sections of: Applied Basic Problem Concepts Operations Solving KTEA-II .79 .82 .68 (gr k-5) ITBS .78 .75 .75 (gr k-8) GMADE .83 .63 .75 (gr k-5) MAP .81 .80 .75 (gr k-5) KTEA-II .85 .87 .76 (gr 6-12) GMADE .83 .84 .74 (gr 6-12) MAP .86 .87 .82 (gr 6-12) Validity Clinical Group Mean Difference LD Math -15.6 LD Reading -12.5 Combined LD Math and -22.2 Reading Mild Intellectual -34 Disability ADHD -1.1 Gifted and Talented 16.6 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…] 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. 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 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. KM-3 Essential Resources • ASSIST links directly to recommended instructional materials based on the student’s KeyMath-3 DA results • OR material can be used independently, incorporating these engaging activities into a teaching program – Conveniently organized for easy browsing 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 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 KM-3 Essential Resources • Automatically highlights recommended lessons based on DA results KM-3 Essential Resources • Conveniently preview thumbnails of all material Easel Teacher Display • Convenient teaching easel • Reverse side of Student Display • Specific Instructions Student Display Engaging + graphics Easel or CD + for use with small or large groups Clip-ins – + transparent and opaque Guided Practice • Used during the lesson – tied to lesson display • Available on CD – print as many as you need Independent Practice • Used by students during class time, after school or as homework • Reduced verbal load from the guided practice 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 Review Assessment • Available at the cluster level • Determine whether the student has mastered the concept Mastery Assessment • Similar to the review assessment • Useful when re- teaching the lesson is necessary Alternative Assessment • Useful with students who are unable to take traditional assessments. 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 Progress Monitoring • Track student performance over time • Determine possible adjustments to education plan KeyMath3 & RTI III Additional diagnostic assessment with KeyMath3 Interventions from Essential Resources May include Special Education referral/placement II 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 I Math screening for all students (such as BASI, GMADE or PASeries) 109 Schema adapted from Michelle Windmueller QUESTIONS? firstname.lastname@example.org 866-305-3216 YOU’VE BEEN GREAT PARTICIPANTS!!
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