KeyMath™–3 Diagnostic Assessment
Overview: Individually administered measure of essential mathamatical concepts and skills
Qualification Level: B, Q2
Age Range: 4:6-21:11; Grades K-12
RTI Tiers: RTI Levels 2 and 3
Completion Time: 30 to 90 minutes
Scores/Interpretation: Areas and Total Test: Grade-and age-based standard scores (M=100, SD=15), grade and age equivalents, percentile ranks and Growth Scale Values. Subtests: Grade- and age-based scale scores (M=10, SD=3), and grade and age equivalents.
Scoring Options: ASSIST™ Software or Manual Scoring
Publication Date: 2007
The KeyMath 3 assessment and instruction system gives you tools to assess and improve math skills of students ages 4½ - 21. This is a comprehensive system consisting of 3 linked components:
- The updated KeyMath 3 Diagnostic Assessment
- ASSIST™ Scoring and Reporting Software
- The new KeyMath 3 Essential Resources instructional program, provides two levels of instruction: Level 1 (K- grade 2) and Level II (grades 3-5/6)
The KeyMath 3 Diagnostic Assessment (KeyMath 3 DA) is a comprehensive, norm-referenced measure of essential mathematical concepts and skills. Like previous versions of the widely used KeyMath assessments this addition to the KeyMath family is untimed and individually administered. However, the KeyMath 3 DA represents a substantial revision in concept and design, including:
- updated content that extends through factoring and solving algebraic expressions
- new subtests
- alignment with national math curriculum standards
- updated norms and new interpretive reports
- link to the KeyMath 3 Essential Resources companion instructional program.
The items are grouped into 10 subtests that represent three general math content areas
- Basic Concepts (conceptual knowledge)
- Operations (computational skills)
- Applications (problem solving)
KeyMath 3 DA content covers the full spectrum of math concepts and skills that are typically taught in kindergarten through ninth grade and can be used with individuals aged 4½ through 21 years who are functioning at these instructional levels. It is available in two parallel forms, designated as Form A and Form B, each of which contains 372 full-color test items.
Each area is further divided into subtests (see Table 1 below), with the content of each subtest spanning kindergarten through eighth- or ninth-grade math curricula. The five basic concepts subtests parallel the five content standards of the National Council of Teachers of Mathematics (NCTM). Much like the NCTM Focal Points, the content of the basic concepts subtests represents a carefully selected set of concepts and skills at each grade level that form the foundation for mathematics learning and connections across subtests. In addition, the KeyMath 3 assessment places more emphasis on math communication, connections, and reasoning than does the KeyMath Revised version (published in 1988).
Unlike the NCTM standards, which embed math operations in the numeration strand, the KeyMath 3 assessment includes two separate written computation subtests (Addition and Subtraction; Multiplication and Division). Operations skills are fundamental for success in mathematics and are often the source of math learning difficulties. By providing separate measures of operational skills, the KeyMath 3 assessment is able to focus particular attention in this important area.
The two applications subtests assess a student’s ability to apply conceptual knowledge and operational skills to solve math problems. The Foundations of Problem Solving subtest includes items that require students to identify missing elements in a problem, operations needed to solve a problem, and optimal strategies for solving the problem. The Applied Problem Solving subtest presents math problems in real-world contexts and includes items that require standard and nonstandard problem-solving strategies.
Table 1: KeyMath 3 Areas, Subtests, and Item Counts
Sample items from three selected subtests are available for your review; Algebra, Mental Computation and Estimation, and Applied Problem Solving. Although these are not actual items from the assessment they are similar to items in the assessment and represent the type of content included in the KeyMath 3 Diagnostic Assessment. Content spans first through eighth grade and demonstrates the broad scope of the assessment.
The KeyMath 3 DA has a substantial advantage over its predecessors in that it provides a means of monitoring an individual’s progress over time. It includes two parallel forms (Form A and Form B), which can be administered in alternating sequence every 3 months, as well as growth scale values (GSVs), which are a type of developmental scale score. GSVs enable users to accurately measure progress across the full range of math concepts and skills. The KeyMath–3 DA ASSIST software application can be used to automatically generate a Progress Report, which (a) shows the amount of change across test administrations, (b) indicates whether an individual has made measurable progress, and (c) compares an individual’s growth rate with the average growth rate of the representative population.
A large sample, consisting of approximately 4,000 individuals representing U.S. demographics by sex, race, socioeconomic status, region, and disability condition, was used to obtain normative data. The norm sample ranges in age from 4 years 5 months through 21 years 11 months. Both age norms and grade (kindergarten - grade 12, fall and spring) norms are available.
Scoring and/or Reporting Options
ASSIST Scoring and Reporting Desktop Software – Scores and generates a variety of reports on your computer.
Several types of norm-referenced scores are provided, including scale and standard scores, percentiles, age and grade equivalents, and growth values.
ASSIST Scoring and Reporting Software
Enjoy the convenience of KeyMath 3 DA ASSIST, software application which electronically generates normative scores and interpretive reports. This time-saving tool can produce an accurate and comprehensive report in as little as five minutes.
KeyMath-3 - A General Overview:
Presenter: Maggie Kjer, PhD & Gloria Maccow, PhD
This Webinar will last one hour and will go over the basics of the KeyMath-3 Diagnostic Assessment and the KeyMath-3 Essential Resources. It will cover the key benefits and features of the KeyMath-3 Diagnostic Assessment, the ASSIST scoring, reporting and narrative software, and how you can use the KeyMath-3 Essential Resources (math interventions) to develop a customized intervention plan based on an individual student’s strengths and weaknesses.
Date: Apr 28, 2011
Frequently asked questions follow. Click on a question to see the response.
KeyMath 3 Diagnostic Assessment
I've been using the KeyMath Revised/NU for years. Why should I upgrade to the KeyMath 3 Diagnostic Assessment?
The KeyMath 3 Diagnostic Assessment offers several new features, including the following:
- Updated and expanded norms. The new norms are based on data collected in the spring and fall of 2006. Age norms now range from 4 years 6 months through 21 years 11 months.
- New item content and a new subtest organization align the assessment with current national math standards.
- The addition of pre-algebra and algebra content makes the assessment more relevant for students at higher grade levels.
- Alignment with the National Council of Teachers of Mathematics Principles and Standards for School Mathematics, published in 2000.
Is the KeyMath 3 Diagnostic Assessment aligned with my state standards?
Yes. The National Council of Teachers of Mathematics (NCTM) published Principles and Standards for School Mathematics in 2000 and the Curriculum Focal Points in 2006. These documents have become the industry standard, as most states use them as guidelines when developing their standards. The KeyMath 3 Diagnostic Assessment is designed around the NCTM standards, and thus, the assessment matches up well to state standards.
How can the KeyMath 3 Diagnostic Assessment be used to monitor progress for students struggling in math?
The KeyMath 3 Diagnostic Assessment includes two versions (Form A and Form B) that can be administered in alternating sequence every 3 months. With the addition of the new Growth Scale Values (GSVs), the assessment provides an accurate measure of student progress across a wide range of math concepts and skills. The new Progress Monitoring Report, which is generated automatically with the KeyMath 3 ASSIST™ Scoring and Reporting Software, plots student performance in each of the three KeyMath 3 areas―basic concepts, operations, and applications―as well as total test performance.
How does the KeyMath 3 Diagnostic Assessment fit into the new response to intervention (RTI) model?
The ASSIST Scoring and Reporting Software includes a Progress Monitoring Report that describes progress in three important ways. It (a) shows the amount of change across assessment administrations, (b) provides information as to whether a student's progress over administrations is significantly greater than 0 (no growth), and (c) compares a student's growth rate with the expected growth rate of the representative population (by grade or age).
Isn't the KeyMath 3 Diagnostic Assessment for special-education students?
Although the previously published KeyMath Revised/NU has been used extensively in special-education classrooms, it is clear that its benefits as a comprehensive measure of mathematical ability extend well to the general-education environment. The KeyMath Revised/NU is currently used by Title 1 programs and in resource rooms around the country. The KeyMath 3 Diagnostic Assessment, with the addition of algebra content and progress-monitoring components (both of which are critical to assisting general-education students who struggle with math), is relevant and useful in a broad range of classroom settings.
How often can I administer the assessment to a student?
The KeyMath 3 Diagnostic Assessment can be administered as often as every 3 months when alternating the Form A and Form B versions.
Can I administer individual subtests?
Each KeyMath 3 Diagnostic Assessment subtest provides important information about a student's level of functioning in a particular strand of mathematics. Subtest performance can be used to design instructional intervention and to prioritize intervention topics. The decision to administer only one or two KeyMath 3 subtests should be limited to cases in which the practitioner has determined the area of greatest need and wants to obtain a greater degree of specificity about the student's ability in that area. Individual subtest administration is not recommended for measuring and reporting progress over time. KeyMath 3 area (basic concepts, operations, and applications) and total test scores, which are highly reliable, are best suited to accurately report student progress.
Can I administer individual areas?
Each of the three KeyMath 3 Diagnostic Assessment areas (basic concepts, operations, and applications) provides a comprehensive and reliable measure of math proficiency. The decision to administer one particular area should be limited to cases in which the practitioner has identified the area of greatest need and wants to target intervention to that area. In such cases, the practitioner should limit retesting to that area because this is the most direct and efficient way to assess the success of the intervention and the student's progress.
Why is the administration time so long?
The KeyMath 3 Diagnostic Assessment is a comprehensive measure of mathematical ability that is designed to meet the needs of a wide range of students. There is nothing else like it available. With a single administration, a practitioner can comprehensively and accurately measure the math proficiency and conceptual knowledge of any student from pre-kindergarten through 12th grade. The assessment uses an adaptive administration procedure that adjusts to an individual's functional level. The assessment's feedback to practitioners and parents is detailed, rich, and most important, immediately actionable.
Administration times for the entire battery of subtests range from 30 to 90 minutes, depending on the student's grade level. Practitioners who have identified a student's area of greatest need (e.g., general conceptual knowledge, computational skills, etc.), may elect to administer only the subtests that correspond to that particular area, which will result in a shorter administration time. The table below shows estimated KeyMath 3 administration times, by area and grade.
Estimated Administration Time (in Minutes), by Area and Grade Grade Basic Concepts Operations Applications Pre-K 10-15 0-5 5-10 K 15-20 0-5 5-10 1 20-25 5-10 10-15 2 30-35 5-10 10-15 3 35-40 10-15 15-20 4 40-45 10-15 15-20 5 40-45 15-20 15-20 6 40-45 15-20 15-20 7 40-45 15-20 15-20 8 40-45 20-25 15-20 9-12+ 40-45 20-25 15-20 Note. Values estimated from standardization data.
How was the KeyMath 3 Diagnostic Assessment normed?
Normative data were obtained in 2006, with a large sample consisting of approximately 4,000 individuals representing U.S. demographics by sex, race, socioeconomic status, region, and disability condition. The norm sample ranges in age from 4 years 6 months through 21 years 11 months. Both age norms and grade (fall and spring) norms are available.
Can I obtain samples of the assessment items?
Sample items corresponding to three of the KeyMath 3 Diagnostic Assessment subtests (Algebra, Applied Problem Solving, and Mental Computation and Estimation) are available at the KeyMath 3 web page. The items are not actual items from the assessment but provide an accurate depiction of item content and difficulty.
Is the KeyMath 3 Diagnostic Assessment aligned with NCTM's Principles and Standards for School Mathematics, published in 2000?
Yes. In fact, as is shown in the table below, the five NCTM content standards are represented almost verbatim in the five KeyMath 3 Basic Operations subtests. Because of the importance of assessing math operations, they remain as stand-alone subtests in the KeyMath 3 Diagnostic Assessment.
Alignment of the KeyMath 3 Diagnostic Assessment With Current NCTM Standards NCTM Standards KeyMath 3 Diagnostic Assessment Number and Operations Numeration Algebra Algebra Geometry Geometry Measurement Measurement Data Analysis and Probability Data Analysis and Probability Note. NCTM = National Council of Teachers of Mathematics.
In addition, the following five NCTM process standards are incorporated in KeyMath 3 items throughout each of the 10 subtests: Communication, Connections, Problem Solving, Reasoning and Proof, and Representation.
Does the KeyMath 3 Diagnostic Assessment include a screener?
The KeyMath 3 Diagnostic Assessment is a comprehensive, individually administered measure of mathematical ability that is designed to be a diagnostic tool with specific, actionable results. However, in instances where the breadth of diagnostic information is not necessary, it is recommended that practitioners administer the five Basic Concepts subtests (Numeration, Algebra, Geometry, Measurement, and Data Analysis and Probability). These subtests cover a broad range of math concepts and provide a level of accuracy that is appropriate for making placement decisions. Administration of only the Basic Concepts subtest also reduces administration time. For students in the early elementary grades (pre-K–2nd grade), administration times ranges from 15 to 30 minutes. for students in 3rd grade and above, administration times range from 35 to 45 minutes.
Why does the Diagnostic Assessment specify content through Grade 9? Why that grade and not another?
Generally speaking, most states mandate that all high school graduates receive instruction in math through Algebra. At the same time, with Algebra being conceived as a strand that begins in kindergarten, it's not clear to say that KeyMath content culminates in Algebra. So, we identify that the content contains material through what's commonly viewed as grade 9 level material. This is generally considered the point at which the foundations of math are completed and students who move in math begin to explore specific areas of math with coursework in geometry, algebra, trigonometry, etc.
KeyMath 3 ASSIST Scoring and Reporting Software
When will the KeyMath 3 ASSIST Scoring and Reporting Software be available?
The KeyMath 3 Diagnostic Assessment will publish September 14, 2007 and the KeyMath 3 ASSIST software will release just a few weeks later on October 18, 2007. Practitioners who order KeyMath kits prior to publication will be shipped their testing easels, manual and record forms when they publish on September 14th. They will be able to begin testing immediately upon receiving their kits but will need to handscore the assessments at that time. When released, ASSIST will automatically ship to all customers who ordered the scoring and reporting software in their kit.
Why do I need the ASSIST software? I've always used the hand-scoring method, and that has worked fine.
The KeyMath 3 ASSIST software ensures that reports are generated accurately on the basis of the data that the practitioner inputs into the application. In addition, the ASSIST software provides the following reports and information, which are otherwise unavailable:
- Progress Report Charts an examinee's progress and provides an analysis of his or her growth. Progress is reported using growth scale values (GSVs), which allow practitioners to track individuals' improvement over time (i.e.; across multiple test administrations). GSVs for each of the three KeyMath 3 DA areas and the Total Test are presented in the graphical and tabular formats.
- Item and Functional-Range Analysis Identifies KeyMath 3 DA items that fall within an individual's functional range, identifies items that may require particular attention, and presents the behaviorial objective measured by each of the items included in the analysis. In addition, the report identifies appropriate lessons contained in the KeyMath 3 ER.
- Narrative Report Provides a description of an examinee's KeyMath 3 DA subtest, area, and Total Test scores. It includes explanations of percentile ranks and descriptive categories (e.g., well-above average, average, below avreage) and describes an examinee's mathematical performance in relation to a nationally representative sample of individuals of the same grade or age.
- Parent/Caregiver Letter This one-page letter provides a means of communicating an examinee's test to his or her parents or caregivers. It briefly describes the various features of the test and provides content area and Total Test percentile ranks and descriptive categories, which are useful in identifying and communicating an examinee's test performance.
- Link to KeyMath 3 Essential Resources The KeyMath 3 ASSIST software also provides a direct link to the KeyMath 3 ER. ASSIST users who have purchased the KeyMath 3 ER will be able to access appropriate, examinee-specific instructional material with the click of a button. The KeyMath 3 ER exercises and practice activities can be used to develop a customized instructional program.
What other types of information and reports are available with the KeyMath 3 ASSIST Scoring and Reporting Software?
The KeyMath 3 ASSIST software includes the following options for interpreting results:
- Score Summary. Presents all KeyMath 3 DA norm-referenced scores (for the Total Test, each of the three content area, and each of the 10 subtests) in a single comprehensive table.
- Score Profile. Provides an excellent tool for identifying and prioritizing instructional programs. Subtest scale scores and area and Total Test standard scores are plotted on a graph, enabling the practitioner to easily and quickly identify an examinee's lowest and highest areas of functioning.
- Area Comparisons. Enables the practitioner or researcher to determine whether an examinee's performance differs significantly across KeyMath 3 DA content areas.
- Focus Items. Provides a tool for identifying items that may require particular attention on the part of the practitioner. For example, an item to which an examinee responded incorrectly that falls below his or her functional range may indicate a specific gap in understanding of prerequisite skills and concepts.
Does the KeyMath 3 ASSIST software include Growth Scale Values (GSVs)?
Yes. The ASSIST Progress Monitoring Report includes a table of GSV scores, by area and total test, for each KeyMath 3 administration. GSV scores are plotted on a graph that includes the developmental growth curve of the normative population. In addition, a least-squares regression line is plotted, which quantifies the individual's rate of growth and can be compared with the rate of change in the normative population. Finally, this report provides a means of evaluating response to intervention by indicating whether the examinee's gain exceeds the level that can be attributed to measurement error.
Can I cut and paste text from the ASSIST Narrative Report into a Microsoft Word document?
Yes. Text and images can be copied directly from the ASSIST report viewer into Microsoft Word or other Microsoft Office applications (e.g., Excel, PowerPoint, etc.).
- To copy text, users can select "Export" from the report viewer to export a document in Rich Text Format (RTF). The RTF document can be saved as is, or the user may elect to manually copy and paste parts of the document into another document.
- To copy graphs or charts, users can select "Export" from the report viewer and then select the "Export to PDF" option. The PDF document can be saved as is, or the user may elect to manually copy and paste individual images into another document.
Do I have to enter in each item into the ASSIST software to get the reports, or can I just enter in the raw scores?
Both item entry and raw score entry options are available.
Can I track multiple students with ASSIST reports?
The KeyMath 3 ASSIST software application does not include a group reports option. However, the application allows users to export results, which can be analyzed with most statistical software applications.
KeyMath 3 Essential Resources
The old KeyMath Teach and Practice (TAP) includes hundreds of worksheets. It seems like there are fewer materials in the new KeyMath 3 Essential Resources program. Why is that?
The KeyMath 3 Essential Resources program, which replaces the previously published KeyMath Teach and Practice (TAP) product, actually contains more curriculum material—more than 2,700 pages of content—than does its predecessor. The table below shows the KeyMath 3 Essential Resources content breakdown.
KeyMath 3 Essential Resources Content Breakdown Level
Easels: cluster overviews, lessons and student displays
Guided practice and independent practice sheets
Readiness tests, posttests, and mastery test
1 400 840 164 2 400 785 144
During research, teachers expressed that they appreciated the convenience of accessing teaching material electronically via CD-ROM. As such, the KeyMath Essential Resource program includes a software application that provides easy-to-navigate content folders. The software tool is a necessary component of the program because, in print form, the materials would easily require three 3-inch binders.
Is the KeyMath 3 Essential Resources program only for instruction with one student or can I teach more than one student at a time?
The KeyMath 3 Essential Resources materials are designed for maximum flexibility and allow teachers to teach to multiple students at one time. The easel presentation of the student activity displays is designed for use with smaller groups of 1-5 students. When working with 6 or more students, teachers may elect to access the same material via the CD-ROM. Thus, teachers have the option to print the pages and use them as blackline masters (for use with projectors such as "Elmos") or as transparencies (for use with standard overhead projectors). Materials can also be added to Microsoft PowerPoint files and presented electronically with a computer and a compatible projector.
What is the difference between guided practice and independent practice?
Guided practice sheets are intended for use by the student during classroom instruction and under the supervision of the teacher. Most often, these sheets contain item content that is the same as or similar to the content included in the easel. Independent practice worksheets are intended for use by the student independent of the teacher. Students may use these during class time, in a study hall, or as homework.
What is the difference between readiness tests, posttests, and mastery tests?
Readiness tests are administered prior to the lesson being taught to determine whether the student has the prerequisite skills necessary to learn the applicable concept(s). Posttests are administered after all activities in the lesson have been taught to determine whether the student has grasped the concept(s). In cases where a student did not grasp the required concept(s), the teacher should re-teach the lesson as necessary. Mastery tests are used to determine whether a student has mastered the applicable concept(s).
Does the KeyMath 3 Essential Resources program include manipulatives?
Some of the program lessons require manipulatives that are commonly found in classrooms (e.g., rulers, cubes, etc). Manipulatives are not provided as part of the KeyMath 3 Essential Resources product.
I'm not buying the KeyMath 3 Diagnostic Assessment. Can I still use the KeyMath3 Essential Resources program?
Yes. Users who do not purchase the KeyMath 3 Diagnostic Assessment will not have a direct link to appropriate curriculum activities in the KeyMath 3 Essential Resources but can use the program nonetheless.
The Essential Resources software contains an easy-to-navigate library of materials, including practice and assessment materials. Users can navigate through the cluster and lesson content to determine which materials are appropriate for a particular student. Readiness tests are available to determine whether a student has the prerequisite skills required to learn the concept(s) in a particular concept cluster. The Essential Resources software also includes a preview function that allows users to view a page before printing it.
Is the old KeyMath Teach and Practice (TAP) compatible with the KeyMath 3 Diagnostic Assessment?
The KeyMath 3 Diagnostic Assessment contains new item content and a new subtest organization. In addition, the KeyMath TAP has been revamped into a new product called the KeyMath 3 Essential Resources.
The KeyMath 3 Diagnostic Assessment and the KeyMath 3 Essential Resources are designed to be compatible to the extent that the ASSIST software report contains narrative text that provides a direct link to the appropriate Essential Resources curriculum material. Customers should note that, when the two products are purchased as a package, they are very affordable.
Still, the KeyMath TAP is a good product with excellent content and is still very relevant in a remedial math environment. Customers who continue to use the TAP should feel confident that they are using a good product.
Can I use the Keymath 3 Essential Resources program with my current KeyMath Revised/NU?
Yes. The KeyMath3 Essential resources program can be used as a stand-alone curriculum product. However, users should be aware that the KeyMath 3 Revised/NU does not provide a direct link to the KeyMath 3 Essential Resources program.
The Essential Resources software contains an easily accessible library of materials, including practice and assessments materials. Users can navigate through the cluster and lesson content to determine which concept material to use with a particular student. Readiness tests are available to determine whether a student has the prerequisite skills necessary to learn the concept(s) in a particular concept cluster. The software includes a preview function that allows users to view a page before printing it.