FastBridge
Adaptive Math (aMath)

Descriptive Information

Please provide a description of your tool:

FastBridge Adaptive Math (aMath) is a brief, reliable, and valid assessment used for universal screening and monitoring of student growth throughout the year for students in Kindergarten through Grade 12. Screening scores identify each students’ academic performance level using risk benchmarks and national norms, provide growth rates and growth norms to assess progress toward end of year goals, and indicate the concepts and skills that are above, below, and within the students instructional range. The aMath adaptive algorithm draws items from a large standards-aligned item bank to provide an assessment of broad math skills that is individualized for each student. The adaptive methodology provides efficient and highly accurate estimates of student ability in just 15-30 minutes. The content and response format of the aMath items is similar to many state assessments and assesses skills and domains including numbers and operations, algebraic thinking, geometry, measurement, data analysis, expressions, and functions.

The tool is intended for use with the following grade(s).

Preschool / Pre - kindergarten
Kindergarten
First grade
Second grade
Third grade
Fourth grade
Fifth grade
Sixth grade
Seventh grade
Eighth grade
Ninth grade
Tenth grade
Eleventh grade
Twelfth grade

The tool is intended for use with the following age(s).

0-4 years old
5 years old
6 years old
7 years old
8 years old
9 years old
10 years old
11 years old
12 years old
13 years old
14 years old
15 years old
16 years old
17 years old
18 years old

The tool is intended for use with the following student populations.

Students in general education
Students with disabilities
English language learners

ACADEMIC ONLY: What skills does the tool screen?

Reading

Phonological processing:

RAN
Memory
Awareness
Letter sound correspondence
Phonics
Structural analysis

Word ID

Accuracy
Speed

Nonword

Accuracy
Speed

Spelling

Accuracy
Speed

Passage

Accuracy
Speed

Reading comprehension:

Multiple choice questions
Cloze
Constructed Response
Retell
Maze
Sentence verification
Other (please describe):

Listening comprehension:

Multiple choice questions
Cloze
Constructed Response
Retell
Maze
Sentence verification
Vocabulary
Expressive
Receptive

Mathematics

Global Indicator of Math Competence

Accuracy
Speed
Multiple Choice
Constructed Response

Early Numeracy

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematics Concepts

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematics Computation

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematic Application

Accuracy
Speed
Multiple Choice
Constructed Response

Fractions/Decimals

Accuracy
Speed
Multiple Choice
Constructed Response

Algebra

Accuracy
Speed
Multiple Choice
Constructed Response

Geometry

Accuracy
Speed
Multiple Choice
Constructed Response

Other (please describe):

Please describe specific domain, skills or subtests:

BEHAVIOR ONLY: Which category of behaviors does your tool target?

Internalizing
Externalizing
Internalizing and Externalizing

BEHAVIOR ONLY: Please identify which broad domain(s)/construct(s) are measured by your tool and define each sub-domain or sub-construct.

Acquisition and Cost Information

Where to obtain:

Email Address

info@fastbridge.org

Address

150 South Fifth Street Suite 600 Minneapolis, MN 55402

Phone Number

612-254-2534

Website

www.fastbridge.org

Initial cost for implementing program:

Cost

$7.50

Unit of cost

student

Replacement cost per unit for subsequent use:

Cost

$7.50

Unit of cost

student

Duration of license

year

Additional cost information:

Describe basic pricing plan and structure of the tool. Provide information on what is included in the published tool, as well as what is not included but required for implementation.

The FastBridge system is provided to customers through an annual subscription that is priced on a per student basis. The subscription rate for school year 2020–21 is $7.50 per student. There are no additional fixed costs. FastBridge subscriptions are all inclusive providing access to all FastBridge reading, math, and behavior assessments, the data management and reporting system, embedded online training, basic implementation, and client support. The academic assessment suite includes adaptive assessments for reading and math screening as well as curriculum-based measurement for universal screening, progress monitoring and skills diagnostics for K – 12. The behavior suite includes screeners completed by both teachers (K-12) and students (2-12) and a direct behavior rating system for progress monitoring for K – 12. In addition to the online training modules embedded within the FastBridge system, Illuminate Education offers both onsite and online training options. All day-long sessions include 6 hours of content. All sessions are capped at a maximum of 30 participants in order to provide a high-quality learning experience. Concurrent sessions of 30 participants are available. The costs are as follows: 1 Day Onsite is $3000 with a 30-participant maximum; 1 Day Online (three, 2-hour sessions) is $1500 with a 30-participant maximum; 2-hour Online Module is $500 with a 30-participant maximum. Training packages include beginner and advanced levels as well as individual online sessions on specific topics. FastBridge recommends that all new users purchase the 2-day FAST Essentials beginner package. This option includes one day on universal screening and a second day on progress monitoring. Advanced options for FastBridge training include day-long FAST Focus sessions, provided either onsite or online and cover topics such as leader reports, data-based decision making, and using FastBridge with special populations. Finally, single-topic sessions selected from the FastBridge module library are available for 2-hour online webinars. FastBridge trainings are provided by highly trained veteran educators who are expert with not only FastBridge features but also how to use the data to support student leaning.

Provide information about special accommodations for students with disabilities.

The FastBridge system is a fully cloud-based system, and therefore computer and Internet access are required for full use of the application. Some of the assessments are computer-administered and others are teacher-administered. A paraprofessional can administer the assessment as a Group Proctor in the FastBridge system. There are embedded online training courses included in the platform and these include certification tests. The courses require between 15 and 30 minutes each to complete. The number of assessments that a teacher needs to administer varies by grade level and so total training time will vary. The system allows for the following accommodations to support accessibility for students with documented disabilities: • Text magnification • Sound amplification • Enlarged and printed paper materials are available upon request • Extended time on selected assessments (FastBridge adaptive assessments are untimed, thus, students take as much time as needed) • Extra breaks (the adaptive assessments can be paused for breaks) • Preferential seating • Small group or individual sessions • Proxy responses • Scratch paper on selected subtests o As part of item development, all items were reviewed for bias and fairness.

Administration

BEHAVIOR ONLY: What type of administrator is your tool designed for?

General education teacher
Special education teacher
Parent
Child
External observer
Other

If other, please specify:

What is the administration setting?

Direct observation
Rating scale
Checklist
Performance measure
Questionnaire
Direct: Computerized
One-to-one
Other

If other, please specify:

Does the tool require technology?

Yes

If yes, what technology is required to implement your tool? (Select all that apply)

Computer or tablet
Internet connection
Other technology (please specify)

If your program requires additional technology not listed above, please describe the required technology and the extent to which it is combined with teacher small-group instruction/intervention:

What is the administration context?

Individual
Small group   If small group, n=
Large group   If large group, n=
Computer-administered
Other

If other, please specify:

What is the administration time?

Time in minutes

25

per (student/group/other unit)

student

Additional scoring time:

Time in minutes

per (student/group/other unit)

ACADEMIC ONLY: What are the discontinue rules?

No discontinue rules provided
Basals
Ceilings
Other

If other, please specify:

CAT stop criteria where standard error of measurement equals 0.20 and a minimum of 25 items.

Are norms available?

Yes

Are benchmarks available?

Yes

If yes, how many benchmarks per year?

3

If yes, for which months are benchmarks available?

August - November, December - mid-March, Mid-March - July

BEHAVIOR ONLY: Can students be rated concurrently by one administrator?

If yes, how many students can be rated concurrently?

Training & Scoring

Training

Is training for the administrator required?

Yes

Describe the time required for administrator training, if applicable:

Less than 1 hour of training

Please describe the minimum qualifications an administrator must possess.

No minimum qualifications

Are training manuals and materials available?

Yes

Are training manuals/materials field-tested?

No

Are training manuals/materials included in cost of tools?

Yes

If No, please describe training costs:

Can users obtain ongoing professional and technical support?

Yes

If Yes, please describe how users can obtain support:

Users have access to professional development technicians, as well as ongoing technical support.

Scoring

How are scores calculated?

Manually (by hand)
Automatically (computer-scored)
Other

If other, please specify:

Do you provide basis for calculating performance level scores?

Yes

What is the basis for calculating performance level and percentile scores?

Age norms
Grade norms
Classwide norms
Schoolwide norms
Stanines
Normal curve equivalents

What types of performance level scores are available?

Raw score
Standard score
Percentile score
Grade equivalents
IRT-based score
Age equivalents
Stanines
Normal curve equivalents
Developmental benchmarks
Developmental cut points
Equated
Probability
Lexile score
Error analysis
Composite scores
Subscale/subtest scores
Other

If other, please specify:

Does your tool include decision rules?

No

If yes, please describe.

Can you provide evidence in support of multiple decision rules?

No

If yes, please describe.

Please describe the scoring structure. Provide relevant details such as the scoring format, the number of items overall, the number of items per subscale, what the cluster/composite score comprises, and how raw scores are calculated.

FastBridge aMath is a computer-adaptive test (CAT), that uses items calibrated with the IRT 3-PL model to yield scores based on a logit scale. The adaptive algorithm uses Bayesian scoring to estimate the student’s score after each item is administered. The item information function is used to select items that provides the most information based on the student’s current ability estimate. The process is repeated until the student has completed at least 25 items. If the ability estimate does not meet the precision criterion by the 25th item, up to five additional items are administered. The score reported in the system is a linear transformation of the logit scale as follows: Score = 200 + (15*Logit) where Score is the new aMath scale score, and Logit is the initial aMath 3-PL theta estimate. Scores range from 155 to 275. The mean value is 200 and the standard deviation is 15.

Describe the tool’s approach to screening, samples (if applicable), and/or test format, including steps taken to ensure that it is appropriate for use with culturally and linguistically diverse populations and students with disabilities.

For screening, FastBridge recommends FASTtrack Math, a tool that enables one-click access to launch online screening assessments. The computer adaptive aMath measure provides highly accurate estimates of broad math achievement for all students across the full ability continuum in K – 12. Screening scores are compared to empirically derived performance benchmarks. These benchmarks define four performance levels: high risk, some risk, low risk, and advanced. Further assessment and intervention are recommended for students in the high risk and some risk categories. In FASTtrack, aMath serves as the primary universal screener and is paired with CBMmath Automaticity to provide personalized and classroom instruction plans in the Screening-to-Intervention (S2i) report. CBMmath Automaticity assesses accuracy and automaticity on basic computation skills. The design of aMath has a strong foundation in both research and theory. Items were developed to align to national math standards; whereas the distribution of item content was guided by the 2008 National Math Advisory Panel’s recommendations indicating which concepts and skills should receive the greatest instructional focus across elementary and middle school grades. aMath was developed based on a skills hierarchy that places greater emphasis on base-ten numbers and operations in the primary grades and shifts emphasis to fractions, rational numbers, integers, and expressions in late elementary and middle school. The Kindergarten through Grade 5 items also address geometry and measurement concepts, and the application of those concepts to perimeter, area, and volume. In middle school emphasis shifts to the properties and applications of right triangles and expressions and functions. aMath assesses basic conceptual understanding, terminology, computation, and problem solving. To reduce the impact of verbal and decoding skills, aMath items are presented with audio and use a simplified English approach. Word problems also use contexts familiar to students in the targeted grades.

Classification Accuracy & Cross-Validation Summary

Grade	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Classification Accuracy Fall
Classification Accuracy Winter
Classification Accuracy Spring

GMADE

Classification Accuracy

Select time of year

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

The criterion measure for the first type of validity analysis (concurrent validity) is the GMADE. The GMADE is a comprehensive, norm-referenced assessment of mathematical skills. Students complete the GMADE using paper and pencils. The total time required to complete the GMADE varies from 60 to 90 minutes. The GMADE is an appropriate criterion for a concurrent validity study and analysis because it is a measure of a related but different construct than that measured by FAST aMath

Do the classification accuracy analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the classification analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

Cut points were selected by optimizing sensitivity, and then balancing sensitivity with specificity using methods presented in Silberglitt and Hintze (2005). The cut points were derived for the 20th percentile.

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

No

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

Cross-Validation

Has a cross-validation study been conducted?

No

If yes,

Select time of year.

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

Do the cross-validation analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the cross-validation analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

---

NWEA MAP Growth

Classification Accuracy

Select time of year

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

Do the classification accuracy analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the classification analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

Yes

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

Cross-Validation

Has a cross-validation study been conducted?

No

If yes,

Select time of year.

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

Do the cross-validation analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the cross-validation analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

---

Georgia Milestones Assessment System

Classification Accuracy

Select time of year

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

The Georgia Milestones Assessment System (Georgia Milestones) is a comprehensive summative assessment pro​gram spanning grades 3 through high school. Georgia Milestones measures how well students have learned the knowledge and skills outlined in the state-adopted content standards in English Language Arts, mathematics, science, and social studies. Students in grades 3 through 8 take an end-of-grade assessment in English Language Arts and mathematics.

Do the classification accuracy analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the classification analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

Georgia Milestones describes student performance using four achievement levels: Beginning Learner, Developing Learner, Proficient Learner, and Distinguished Learner. For the classification accuracy analyses we contrasted the Beginning Learner (Level 1) group with the remaining Levels 2 – 4. As defined by the Georgia Department of Education, Beginning Leaner students do not yet demonstrate proficiency in the knowledge and skills necessary at the grade level, as specified in Georgia’s content standards. The students need substantial academic support to be prepared for the next grade level or course and to be on track for college and career readiness. The aMath cut-points were derived by optimizing specificity and sensitivity using Youden’s J index. The analyses were repeated for each grade and season.

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

Yes

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

The data were derived from universal screening at each grade level and season in districts implementing MTSS. Although, the information regarding the specific intervention was not available for these analyses, most students scoring in the high risk range were assigned to some form of intensive intervention.

Cross-Validation

Has a cross-validation study been conducted?

No

If yes,

Select time of year.

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

Do the cross-validation analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the cross-validation analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

---

Classification Accuracy - Fall

Evidence	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System
Cut Points - Percentile rank on criterion measure
Cut Points - Performance score on criterion measure	475	475	475	475	475	475	475
Cut Points - Corresponding performance score (numeric) on screener measure	196	198	206	209	212	216	218
Classification Data - True Positive (a)	494	1414	1404	2688	1834	1750	2084
Classification Data - False Positive (b)	655	1149	1482	1682	1166	1203	1237
Classification Data - False Negative (c)	119	306	284	531	416	348	519
Classification Data - True Negative (d)	3339	8618	8680	8444	8470	8484	8822
Area Under the Curve (AUC)	0.90	0.93	0.93	0.91	0.93	0.93	0.92
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.89	0.93	0.92	0.91	0.92	0.93	0.92
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.91	0.94	0.93	0.92	0.93	0.94	0.93

Statistics	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.13	0.15	0.14	0.24	0.19	0.18	0.21
Overall Classification Rate	0.83	0.87	0.85	0.83	0.87	0.87	0.86
Sensitivity	0.81	0.82	0.83	0.84	0.82	0.83	0.80
Specificity	0.84	0.88	0.85	0.83	0.88	0.88	0.88
False Positive Rate	0.16	0.12	0.15	0.17	0.12	0.12	0.12
False Negative Rate	0.19	0.18	0.17	0.16	0.18	0.17	0.20
Positive Predictive Power	0.43	0.55	0.49	0.62	0.61	0.59	0.63
Negative Predictive Power	0.97	0.97	0.97	0.94	0.95	0.96	0.94

Sample	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19		2017-18 and 2018-19	2017-18 and 2018-19
Sample Size	4607	11487	11850	13345	11886	11785	12662
Geographic Representation	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)
Male	1.1%	0.4%	0.4%	0.4%	0.4%	0.4%	0.4%
Female	1.1%	0.4%	0.4%	0.4%	0.4%	0.4%	0.4%
Other
Gender Unknown
White, Non-Hispanic
Black, Non-Hispanic
Hispanic
Asian/Pacific Islander
American Indian/Alaska Native
Other
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability
English Language Learner

Classification Accuracy - Winter

Evidence	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System
Cut Points - Percentile rank on criterion measure
Cut Points - Performance score on criterion measure	475	475	475	475	475	475	475
Cut Points - Corresponding performance score (numeric) on screener measure	198	201	208	211	213	216	219
Classification Data - True Positive (a)	558	1512	1531	2799	1906	1820	2097
Classification Data - False Positive (b)	616	931	1432	1450	979	994	1120
Classification Data - False Negative (c)	107	370	301	685	440	411	489
Classification Data - True Negative (d)	3711	9129	9112	8977	7530	7304	7164
Area Under the Curve (AUC)	0.92	0.94	0.94	0.92	0.93	0.93	0.92
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.90	0.94	0.93	0.92	0.93	0.92	0.92
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.94	0.95	0.94	0.93	0.94	0.93	0.93

Statistics	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.13	0.16	0.15	0.25	0.22	0.21	0.24
Overall Classification Rate	0.86	0.89	0.86	0.85	0.87	0.87	0.85
Sensitivity	0.84	0.80	0.84	0.80	0.81	0.82	0.81
Specificity	0.86	0.91	0.86	0.86	0.88	0.88	0.86
False Positive Rate	0.14	0.09	0.14	0.14	0.12	0.12	0.14
False Negative Rate	0.16	0.20	0.16	0.20	0.19	0.18	0.19
Positive Predictive Power	0.48	0.62	0.52	0.66	0.66	0.65	0.65
Negative Predictive Power	0.97	0.96	0.97	0.93	0.94	0.95	0.94

Sample	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19
Sample Size	4992	11942	12376	13911	10855	10529	10870
Geographic Representation	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)
Male	1.0%	0.4%	0.4%	0.4%	0.5%	0.5%	0.5%
Female	1.0%	0.4%	0.4%	0.4%	0.5%	0.5%	0.5%
Other
Gender Unknown
White, Non-Hispanic
Black, Non-Hispanic
Hispanic
Asian/Pacific Islander
American Indian/Alaska Native
Other
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability
English Language Learner

Classification Accuracy - Spring

Evidence	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	GMADE	GMADE	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System	Georgia Milestones Assessment System
Cut Points - Percentile rank on criterion measure	10	10
Cut Points - Performance score on criterion measure	187.00	190.00	475	475	475	475	475	475	475
Cut Points - Corresponding performance score (numeric) on screener measure			199	204	208	212	214	216	219
Classification Data - True Positive (a)	20	18	596	1510	1545	2721	1549	1364	1637
Classification Data - False Positive (b)	11	9	587	915	1234	1292	701	706	830
Classification Data - False Negative (c)	6	4	107	335	273	586	339	279	355
Classification Data - True Negative (d)	44	41	3842	8070	8063	7489	6014	5374	5282
Area Under the Curve (AUC)	0.75	0.83	0.93	0.95	0.94	0.92	0.94	0.94	0.92
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.67	0.76	0.92	0.94	0.94	0.92	0.94	0.93	0.92
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.83	0.90	0.93	0.95	0.94	0.93	0.95	0.94	0.93

Statistics	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.32	0.31	0.14	0.17	0.16	0.27	0.22	0.21	0.25
Overall Classification Rate	0.79	0.82	0.86	0.88	0.86	0.84	0.88	0.87	0.85
Sensitivity	0.77	0.82	0.85	0.82	0.85	0.82	0.82	0.83	0.82
Specificity	0.80	0.82	0.87	0.90	0.87	0.85	0.90	0.88	0.86
False Positive Rate	0.20	0.18	0.13	0.10	0.13	0.15	0.10	0.12	0.14
False Negative Rate	0.23	0.18	0.15	0.18	0.15	0.18	0.18	0.17	0.18
Positive Predictive Power	0.65	0.67	0.50	0.62	0.56	0.68	0.69	0.66	0.66
Negative Predictive Power	0.88	0.91	0.97	0.96	0.97	0.93	0.95	0.95	0.94

Sample	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	2010-11	2010-11	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19	2017-18 and 2018-19
Sample Size	81	72	5132	10830	11115	12088	8603	7723	8104
Geographic Representation	West North Central (MN)	West North Central (MN)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)	South Atlantic (GA)
Male			1.0%	0.5%	0.5%	0.4%	0.6%	0.6%	0.6%
Female			1.0%	0.5%	0.4%	0.4%	0.6%	0.6%	0.6%
Other
Gender Unknown
White, Non-Hispanic
Black, Non-Hispanic
Hispanic
Asian/Pacific Islander
American Indian/Alaska Native
Other
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability
English Language Learner

Reliability

Grade	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Rating

*Offer a justification for each type of reliability reported, given the type and purpose of the tool.

As a computer-adaptive assessment used for universal screening, it is important to demonstrate the precision of the student’s score estimate. The standard error of measurement is the key index of score precision. The FastBridge adaptive algorithm uses item response theory and Bayesian scoring to administer up to 30 to achieve an SEM of 0.20 on the logit scale. In rare circumstances that level of precision is not achieved by the 30th item and the score is flagged for readministration. With IRT-based calibration the conditional SEM for each student can be aggregated into an index of reliability. The resulting coefficients yields results that are very similar to coefficient alpha and represent the consistency of the overall score stability in a population. Because FastBridge aMath is used to screen students multiple times per year, retest reliability is also an appropriate index of score stability. Test-retest reliability was computed on a subsample of students who completed two administrations of aMath within a 60-day window. The Pearson correlation coefficient of the scores from the two administrations is an index of retest stability. It is important to note that because aMath is adaptive students do not take all the same items on the two occasions. Thus, this index can be expected to fall between what would be obtained from alternate form reliability and true retest reliability.

*Describe the sample(s), including size and characteristics, for each reliability analysis conducted.

The data used to derive the IRT-based reliability coefficient represents a national sample of students in each grade across 30 states and all geographic regions. The data were obtained from universal screening administrations of FastBridge aMath and represented the demographics of the student population with 50% female, 63% white, 11% African American, 13% Hispanic, 7% Asian, and 7% from other race/ethnicities. The sample sizes were all well over 10,000 and ranged from 38,812 in Kindergarten to 97,725 in Grade 4. The test-retest reliability coefficient was derived from a sample of students who completed aMath on two occasions within a 60-day period as part of universal screening. The samples range from 271 in Kindergarten to 1,732 in Grade 4 and were distributed across 30 states.

*Describe the analysis procedures for each reported type of reliability.

aMath scores are derived from maximum likelihood estimation which produces an estimate of the error in the estimated theta (ability) score conditioned on the true score. Using the estimated theta and the conditional standard error of estimate, a reliability index that mirrors parallel form reliability can be computed as follows:: ρxx’ = Var (ϴ’)/[Var(ϴ’) + sum(CSEM(ϴ’)2)/N]. Where sum(CSEM(ϴ’)2)/N is the average error variance of the theta estimate in the sample, and Var (ϴ’) is the variance of theta scores in the sample. This ratio is akin to the ratio of true score variance to observed variance. For internal consistency reliability derived from IRT-based marginal likelihood scores, the 95% confidence interval was computed using bootstrapping approach. Onehundred samples were drawn randomly from the set of scores in each grade. Each sample used 10,000 students. The CSEM and variance of theta were computed on each sample and from those estimates, the reliability index was computed as described above. The reliability corresponding to the 2.5th percentile and the 97.5th percentile in the set of 100 replications was used to define the lower and upper bound of the reliability estimates respectively. For test-retest reliability, the 95% confidence interval was computed using the z-transformation of the correlation coefficient: Zr = 0.5*ln[(1+r)/(1-r)], and the confidence interval is Zr ± 1.96*sqrt(1/(N-3)); where r is the reliability coefficient and N is the sample size.

*In the table(s) below, report the results of the reliability analyses described above (e.g., internal consistency or inter-rater reliability coefficients).

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Do you have reliability data that are disaggregated by gender, race/ethnicity, or other subgroups (e.g., English language learners, students with disabilities)?

No

If yes, fill in data for each subgroup with disaggregated reliability data.

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Validity

Grade	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Rating

*Describe each criterion measure used and explain why each measure is appropriate, given the type and purpose of the tool.

The criterion measure for the first type of validity analysis (concurrent validity) is the GMADE. The GMADE is a comprehensive, norm-referenced assessment of mathematical skills. Students complete the GMADE using paper and pencils. The total time required to complete the GMADE varies from 60 to 90 minutes. The GMADE is an appropriate criterion for a concurrent validity study and analysis because it is a measure of a related but different construct than that measured by FAST aMath. The criterion measure for the second type of validity analysis (construct validity) is the Measures of Academic Progress (MAP). MAP is a diagnostic and computer adaptive assessment designed to measure mathematics ability and progress, which makes it an appropriate criterion to FAST aMath when considering construct validity. In addition, MAP is a known psychometrically sound assessment.

*Describe the sample(s), including size and characteristics, for each validity analysis conducted.

Validity analyses were conducted on a sample of students from Minnesota. There were 496 students in grades K-5 from a single school. Students were 88% White, 6% Black, 3% Hispanic, 2% Asian, and 1% other ethnicities. Approximately 8% of students were eligible for free or reduced price lunch and 15% were receiving special education services.

*Describe the analysis procedures for each reported type of validity.

Validity coefficients were calculated by computing Pearson product moment correlations between FAST aMath and the criterion measure. Confidence intervals represent 95% confidence intervals.

*In the table below, report the results of the validity analyses described above (e.g., concurrent or predictive validity, evidence based on response processes, evidence based on internal structure, evidence based on relations to other variables, and/or evidence based on consequences of testing), and the criterion measures.

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

Results from other forms of validity analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Describe the degree to which the provided data support the validity of the tool.

The validity coefficients provide moderate to strong evidence for the use of FAST aMath as a measure of broad mathematics ability.

Do you have validity data that are disaggregated by gender, race/ethnicity, or other subgroups (e.g., English language learners, students with disabilities)?

No

If yes, fill in data for each subgroup with disaggregated validity data.

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

Results from other forms of validity analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Bias Analysis

Grade	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Rating	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes

Have you conducted additional analyses related to the extent to which your tool is or is not biased against subgroups (e.g., race/ethnicity, gender, socioeconomic status, students with disabilities, English language learners)? Examples might include Differential Item Functioning (DIF) or invariance testing in multiple-group confirmatory factor models.

Yes

If yes,

a. Describe the method used to determine the presence or absence of bias:

Statistical bias was assessed by grade level (K-8) using data from more than 500,000 administrations from the fall of 2019. The model-based logistic regression procedure was selected for the DIF analysis because it has been shown to be sensitive to both uniform and non-uniform differential item functioning (DIF). Due to the large sample size and tendency to inflate Type I error rates, an effect size measure developed by Jodoin and Gierl (2001) based on the change in R^2 values was used to evaluate DIF. Jodoin and Gierl use a three level classification of DIF: negligible (ES <0.035), moderate (ES 0.035 - 0.07), and large (ES >0.07). These categories correlate strongly with another well-researched DIF detection model known as the SIB-Test. The analyses were conducted separately by grade level, K - 8.

b. Describe the subgroups for which bias analyses were conducted:

The data set was sufficient to examine bias in relation to race/ethnicity and gender by grade, K - 8. The race/ethnicity group comparisons examined were White versus African American, White versus Hispanic, and White versus Asian.

c. Describe the results of the bias analyses conducted, including data and interpretative statements. Include magnitude of effect (if available) if bias has been identified.

Overall, across all grades, only one item showed large DIF. By grade level the percentage of items showing moderate DIF were as follows: K = 4%; Grade 1 = 1%; Grade 2 = 2%; Grade 3 = 4%; Grade 4 = 2%; Grade 5 = 0%; Grade 6 = 1%; Grade 7 = 2%; Grade 8 = 1%. Among the items demonstrating moderate DIF, an equal percentage favored the focal group relative to the reference group. FastBridge evaluates DIF on a regular basis and items displaying moderate to large DIF are reviewed by content experts for sensitivity or bias issues. If an issue is found the item is deactivated and either revised and refield-tested or replaced.