FastBridge
Adaptive Math (aMath)
Summary
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.
- Where to Obtain:
- Renaissance Learning
- answers@renaissance.com
- Renaissance Learning, PO Box 8036, Wisconsin Rapids, WI 54495
- (800) 338-4204
- http://www.renaissance.com
- Initial Cost:
- $8.00 per student
- Replacement Cost:
- $8.00 per student per year
- Included in Cost:
- 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 2022–23 is $8.00 per student. FastBridge subscriptions are all inclusive providing access to all FastBridge reading, math, and behavior assessments, the data management and reporting system, embedded online training, 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, onsite and online training options are also offered. 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 $3250 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.
- 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.
- Training Requirements:
- Less than 1 hour of training
- Qualified Administrators:
- No minimum qualifications specified.
- Access to Technical Support:
- Users have access to professional development technicians, as well as ongoing technical support.
- Assessment Format:
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- Direct: Computerized
- One-to-one
- Scoring Time:
-
- Scoring is automatic
- Scores Generated:
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- Percentile score
- IRT-based score
- Developmental benchmarks
- Administration Time:
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- 25 minutes per student
- Scoring Method:
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- Automatically (computer-scored)
- Technology Requirements:
-
- Computer or tablet
- Internet connection
- Accommodations:
- 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.
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.
ACADEMIC ONLY: What skills does the tool screen?
- Please describe specific domain, skills or subtests:
- BEHAVIOR ONLY: Which category of behaviors does your tool target?
-
- 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
Administration
- 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
- Do you provide basis for calculating performance level scores?
-
Yes
- 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.
Technical Standards
Classification Accuracy & Cross-Validation Summary
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Legend
Convincing evidencePartially convincing evidenceUnconvincing evidenceData unavailabledDisaggregated data available
GMADE
Classification Accuracy
- 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
- 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,
- Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.
- 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
- Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.
- 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,
- Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.
- 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
- 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 program 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.
- 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,
- Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.
- 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.
Star Math
Classification Accuracy
- Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.
- Renaissance Star Math is a computer adaptive math assessment designed to monitor student growth and mastery of concepts in numeracy, algebra, geometry, and statistics in grades PreK-12. Star Math serves three purposes. First, it provides educators with quick and accurate estimates of students’ instructional math levels. Second, it assesses math levels relative to national norms. Third, it provides the means for tracking growth in a consistent manner longitudinally for all students. This is especially helpful to school- and district-level administrators. Star Math was developed completely, independent from Fastbridge earlyMath; Fastbridge was developed at the University of Minnesota and Star was developed at Renaissance Learning. Star Math serves as a good criterion measure because, like Fastbridge earlyMath, it assesses broad math achievement using content aligned to state and national learning standards and has been highly rated by NCII as a reliable and valid measure of math achievement.
- 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 criterion measure cut point was the 20th national percentile. The cut point at the 20th national percentile contrasts high risk students against some and low risk students sample.
- 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.
Cross-Validation
- Has a cross-validation study been conducted?
-
No
- If yes,
- Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.
- 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 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8 |
|---|---|---|---|---|---|---|---|---|
| Criterion measure | Star Math | 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 | 20 | |||||||
| Cut Points - Performance score on criterion measure | 475 | 475 | 475 | 475 | 475 | 475 | 475 | |
| Cut Points - Corresponding performance score (numeric) on screener measure | 123 | 196 | 198 | 206 | 209 | 212 | 216 | 218 |
| Classification Data - True Positive (a) | 10 | 494 | 1414 | 1404 | 2688 | 1834 | 1750 | 2084 |
| Classification Data - False Positive (b) | 19 | 655 | 1149 | 1482 | 1682 | 1166 | 1203 | 1237 |
| Classification Data - False Negative (c) | 2 | 119 | 306 | 284 | 531 | 416 | 348 | 519 |
| Classification Data - True Negative (d) | 92 | 3339 | 8618 | 8680 | 8444 | 8470 | 8484 | 8822 |
| Area Under the Curve (AUC) | 0.88 | 0.90 | 0.93 | 0.93 | 0.91 | 0.93 | 0.93 | 0.92 |
| AUC Estimate’s 95% Confidence Interval: Lower Bound | 0.79 | 0.89 | 0.93 | 0.92 | 0.91 | 0.92 | 0.93 | 0.92 |
| AUC Estimate’s 95% Confidence Interval: Upper Bound | 0.97 | 0.91 | 0.94 | 0.93 | 0.92 | 0.93 | 0.94 | 0.93 |
| Statistics | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8 |
|---|---|---|---|---|---|---|---|---|
| Base Rate | 0.10 | 0.13 | 0.15 | 0.14 | 0.24 | 0.19 | 0.18 | 0.21 |
| Overall Classification Rate | 0.83 | 0.83 | 0.87 | 0.85 | 0.83 | 0.87 | 0.87 | 0.86 |
| Sensitivity | 0.83 | 0.81 | 0.82 | 0.83 | 0.84 | 0.82 | 0.83 | 0.80 |
| Specificity | 0.83 | 0.84 | 0.88 | 0.85 | 0.83 | 0.88 | 0.88 | 0.88 |
| False Positive Rate | 0.17 | 0.16 | 0.12 | 0.15 | 0.17 | 0.12 | 0.12 | 0.12 |
| False Negative Rate | 0.17 | 0.19 | 0.18 | 0.17 | 0.16 | 0.18 | 0.17 | 0.20 |
| Positive Predictive Power | 0.34 | 0.43 | 0.55 | 0.49 | 0.62 | 0.61 | 0.59 | 0.63 |
| Negative Predictive Power | 0.98 | 0.97 | 0.97 | 0.97 | 0.94 | 0.95 | 0.96 | 0.94 |
| Sample | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8 |
|---|---|---|---|---|---|---|---|---|
| Date | 2021-22 | 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 | 123 | 4607 | 11487 | 11850 | 13345 | 11886 | 11785 | 12662 |
| Geographic Representation | Pacific (CA) | 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 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8 |
|---|---|---|---|---|---|---|---|---|
| Criterion measure | Star Math | 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 | 20 | |||||||
| Cut Points - Performance score on criterion measure | 475 | 475 | 475 | 475 | 475 | 475 | 475 | |
| Cut Points - Corresponding performance score (numeric) on screener measure | 192 | 198 | 201 | 208 | 211 | 213 | 216 | 219 |
| Classification Data - True Positive (a) | 13 | 558 | 1512 | 1531 | 2799 | 1906 | 1820 | 2097 |
| Classification Data - False Positive (b) | 20 | 616 | 931 | 1432 | 1450 | 979 | 994 | 1120 |
| Classification Data - False Negative (c) | 2 | 107 | 370 | 301 | 685 | 440 | 411 | 489 |
| Classification Data - True Negative (d) | 99 | 3711 | 9129 | 9112 | 8977 | 7530 | 7304 | 7164 |
| Area Under the Curve (AUC) | 0.89 | 0.92 | 0.94 | 0.94 | 0.92 | 0.93 | 0.93 | 0.92 |
| AUC Estimate’s 95% Confidence Interval: Lower Bound | 0.79 | 0.90 | 0.94 | 0.93 | 0.92 | 0.93 | 0.92 | 0.92 |
| AUC Estimate’s 95% Confidence Interval: Upper Bound | 0.98 | 0.94 | 0.95 | 0.94 | 0.93 | 0.94 | 0.93 | 0.93 |
| Statistics | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8 |
|---|---|---|---|---|---|---|---|---|
| Base Rate | 0.11 | 0.13 | 0.16 | 0.15 | 0.25 | 0.22 | 0.21 | 0.24 |
| Overall Classification Rate | 0.84 | 0.86 | 0.89 | 0.86 | 0.85 | 0.87 | 0.87 | 0.85 |
| Sensitivity | 0.87 | 0.84 | 0.80 | 0.84 | 0.80 | 0.81 | 0.82 | 0.81 |
| Specificity | 0.83 | 0.86 | 0.91 | 0.86 | 0.86 | 0.88 | 0.88 | 0.86 |
| False Positive Rate | 0.17 | 0.14 | 0.09 | 0.14 | 0.14 | 0.12 | 0.12 | 0.14 |
| False Negative Rate | 0.13 | 0.16 | 0.20 | 0.16 | 0.20 | 0.19 | 0.18 | 0.19 |
| Positive Predictive Power | 0.39 | 0.48 | 0.62 | 0.52 | 0.66 | 0.66 | 0.65 | 0.65 |
| Negative Predictive Power | 0.98 | 0.97 | 0.96 | 0.97 | 0.93 | 0.94 | 0.95 | 0.94 |
| Sample | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8 |
|---|---|---|---|---|---|---|---|---|
| Date | 2021-22 | 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 | 134 | 4992 | 11942 | 12376 | 13911 | 10855 | 10529 | 10870 |
| Geographic Representation | Pacific (CA) | 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
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Grade 1
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Grade 2
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Grade 3
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Grade 4
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Grade 5
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Grade 6
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Grade 7
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Grade 8
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|---|---|---|---|---|---|---|---|---|---|
| Rating |
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Legend
Convincing evidencePartially convincing evidenceUnconvincing evidenceData unavailabledDisaggregated data available
- *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
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Grade 1
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Grade 2
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Grade 3
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Grade 4
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Grade 5
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Grade 6
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Grade 7
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Grade 8
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|---|---|---|---|---|---|---|---|---|---|
| Rating |
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Legend
Convincing evidencePartially convincing evidenceUnconvincing evidenceData unavailabledDisaggregated data available
- *Describe each criterion measure used and explain why each measure is appropriate, given the type and purpose of the tool.
- For Kindergarten, 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. For grade 1, Renaissance Star Math acts as the criterion measure for predictive validity. Renaissance Star Math is a computer adaptive math assessment designed to monitor student growth and mastery of concepts in numeracy, algebra, geometry, and statistics in grades PreK-12. Star Math serves three purposes. First, it provides educators with quick and accurate estimates of students’ instructional math levels. Second, it assesses math levels relative to national norms. Third, it provides the means for tracking growth in a consistent manner longitudinally for all students. This is especially helpful to school- and district-level administrators. Star Math was developed completely, independent from Fastbridge aMath; Fastbridge was developed at the University of Minnesota and Star was developed at Renaissance Learning. Star Math serves as a good criterion measure because, like Fastbridge aMath, it assesses broad math achievement using content aligned to state and national learning standards and has been highly rated by NCII as a reliable and valid measure of math achievement. For grades K-1, 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. For Grades 3 – 8, the Georgia Milestones Assessment System (Georgia Milestones) was used to evaluate both predictive and concurrent validity. Georgia Milestones is a comprehensive summative assessment program used for school accountability and spanning grades 3 through high school. It 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. The test produces a scale score and achievement level for each student.
- *Describe the sample(s), including size and characteristics, for each validity analysis conducted.
- Construct, concurrent, and predictive validity analyses were conducted on a sample of students from Minnesota using MAP, GMADE, and Georgia Milestones. 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. Predictive validity was conducted on a sample of 129 students using Star Math from a single California school in grade 1.
- *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.
Data Collection Practices
Most tools and programs evaluated by the NCII are branded products which have been submitted by the companies, organizations, or individuals that disseminate these products. These entities supply the textual information shown above, but not the ratings accompanying the text. NCII administrators and members of our Technical Review Committees have reviewed the content on this page, but NCII cannot guarantee that this information is free from error or reflective of recent changes to the product. Tools and programs have the opportunity to be updated annually or upon request.
