FAST™
Adaptive Math (aMath)
Summary
FAST™ aMath (FAST™ Adaptive Math) is a fully automated computer adaptive measure of broad math skills. It is individualized for each student, but may be group administered. Items tap a variety of Common Core State Standards math skills and domains including counting and cardinality, operations and algebraic thinking, number and operations in base ten, numbers and operations, measurement and data, and geometry. Students typically complete the assessment in 20-30 minutes. The type of questions and response format is similar to many state-wide assessments (i.e., multiple choice, fill in the blank). There are both auditory and visual stimuli presented for each question.
- Where to Obtain:
- Theodore J. Christ & Colleagues, LLC
- info@fastbridge.org
- 520 Nicollet Mall, Suite 910, Minneapolis, MN 55402
- 612-254-2534
- www.fastbridge.org
- Initial Cost:
- $7.00 per student
- Replacement Cost:
- $7.00 per student per year
- Included in Cost:
- FAST™ assessments are accessed through an annual subscription offered by FastBridge Learning, priced on a “per student assessed” model. The subscription rate for school year 2017–18 is $7.00 per student. There are no additional fixed costs. FAST subscriptions are all inclusive providing access to: all FAST reading and math assessments for universal screening, progress monitoring and diagnostic purposes including Computer Adaptive Testing and Curriculum-Based Measurement; Behavior and Developmental Milestones assessment tools; the FAST data management and reporting system; embedded online system training for staff; and basic implementation and user support. In addition to the online training modules embedded within the FAST application, FastBridge Learning offers onsite training options. One, two, and three day packages are available. Packages are determined by implementation size and which FAST assessments (e.g., reading, math, and/or behavior) a district intends to use: 1-day package: $3,000.00; 2-day package: $6,000.00; 3-day package: $9,000.00. Any onsite training purchase also includes a complimentary online Admin/Manager training session (2 hours) for users who will be designated as District Managers and/or School Managers in FAST. Additionally, FastBridge offers web-based consultation and training delivered by certified FAST trainers. The web-based consultation and training rate is $200.00/hour.
- The application allows for the following accommodations to support accessibility for culturally and linguistically diverse populations: o Text magnification. o Sound amplification. o Enlarged and printed paper materials are available upon request. o Students with differing needs or disabilities may take computer-adaptive tests such as aMath via a tablet-type device to facilitate screen optimization, magnification, sound amplification, and standard accommodations. o Extra breaks as needed. o Preferential seating and use of quiet space. o Proxy responses. o Use of scratch paper. 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:
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- Computer or tablet
- Internet connection
- Accommodations:
- The application allows for the following accommodations to support accessibility for culturally and linguistically diverse populations: o Text magnification. o Sound amplification. o Enlarged and printed paper materials are available upon request. o Students with differing needs or disabilities may take computer-adaptive tests such as aMath via a tablet-type device to facilitate screen optimization, magnification, sound amplification, and standard accommodations. o Extra breaks as needed. o Preferential seating and use of quiet space. o Proxy responses. o Use of scratch paper. o As part of item development, all items were reviewed for bias and fairness.
Descriptive Information
- Please provide a description of your tool:
- FAST™ aMath (FAST™ Adaptive Math) is a fully automated computer adaptive measure of broad math skills. It is individualized for each student, but may be group administered. Items tap a variety of Common Core State Standards math skills and domains including counting and cardinality, operations and algebraic thinking, number and operations in base ten, numbers and operations, measurement and data, and geometry. Students typically complete the assessment in 20-30 minutes. The type of questions and response format is similar to many state-wide assessments (i.e., multiple choice, fill in the blank). There are both auditory and visual stimuli presented for each question.
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?
- September, December, and May
- 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.
- FAST™ aMath is a computer-adaptive test (CAT), and therefore yields scores based on an IRT logit scale. This type of scale is not useful to most school professionals; in addition, it is difficult to interpret scores on a scale for which everything below the mean value yields a negative number. Therefore, it was necessary to create a FAST aMath scale more similar to existing educational measures. The FAST aMath scale yields scores that are transformed from logits using the following formula: y = 200 + (15*Logit Score) where y is the new FAST aMath scaled score, and Logit Score is the initial FAST aMath theta estimate. Scores were scaled with a lower bound of 150 and a higher bound of 250. 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.
- FAST™ aMath is designed to address issues of instructional relevance. FAST aMath is a simple, efficient, computer-adaptive measure of both broad and component math skills from Kindergarten through Fifth Grade (K-5). FAST aMath is highly researched and based on the recommendations of the National Math Panel (2008) and National Common Core Standards (2010). FAST aMath is designed to identify those students with deficits in math achievement in need of additional instruction and predict performance on state accountability measures. FAST aMath includes fully automated administration and scoring of individualized assessments for purposes of universal screening and instructional leveling. Improved assessments that inform math early intervention and math instruction are necessary to identify students who struggle with math and prevent long term failure among students with disabilities (Geary, 1999). The objective of FAST aMath is to extend and improve on the quality of currently available assessments. At present, research and validation of early intervention measures to screen for student proficiency in math is in its infancy (Gersten, Jordan, & Flojo, 2005). While some measures do show promise (i.e., Oral Counting, Number Identification, Quantity Discrimination, and Missing Numbers), these measures have insufficient reported reliability and validity evidence for use in early identification and formative assessment. The ultimate goal of FAST aMath is instructional efficacy. As the measure fully develops, subsequent efficacy projects will examine its use and impact to improve outcomes for individual students. FAST aMath provides an option with greater flexibility, increased efficiency, higher quality, and broader applications with students across primary and secondary schools.
Technical Standards
Classification Accuracy & Cross-Validation Summary
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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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| Classification Accuracy Fall |
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| Classification Accuracy Winter |
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| Classification Accuracy Spring |
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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?
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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?
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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 - Spring
| Evidence | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 |
|---|---|---|---|---|---|---|
| Criterion measure | GMADE | GMADE | GMADE | GMADE | GMADE | GMADE |
| Cut Points - Percentile rank on criterion measure | 10 | 10 | 10 | 10 | 10 | 10 |
| Cut Points - Performance score on criterion measure | 187.00 | 190.00 | 202.00 | 201.00 | 206.00 | 218.00 |
| Cut Points - Corresponding performance score (numeric) on screener measure | ||||||
| Classification Data - True Positive (a) | 20 | 18 | 18 | 9 | 14 | 13 |
| Classification Data - False Positive (b) | 11 | 9 | 9 | 12 | 8 | 25 |
| Classification Data - False Negative (c) | 6 | 4 | 5 | 1 | 7 | 1 |
| Classification Data - True Negative (d) | 44 | 41 | 35 | 64 | 31 | 25 |
| Area Under the Curve (AUC) | 0.75 | 0.83 | 0.92 | 0.98 | 0.88 | 0.88 |
| AUC Estimate’s 95% Confidence Interval: Lower Bound | 0.67 | 0.76 | 0.87 | 0.96 | 0.82 | 0.80 |
| AUC Estimate’s 95% Confidence Interval: Upper Bound | 0.83 | 0.90 | 0.97 | 1.00 | 0.94 | 0.96 |
| Statistics | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 |
|---|---|---|---|---|---|---|
| Base Rate | 0.32 | 0.31 | 0.34 | 0.12 | 0.35 | 0.22 |
| Overall Classification Rate | 0.79 | 0.82 | 0.79 | 0.85 | 0.75 | 0.59 |
| Sensitivity | 0.77 | 0.82 | 0.78 | 0.90 | 0.67 | 0.93 |
| Specificity | 0.80 | 0.82 | 0.80 | 0.84 | 0.79 | 0.50 |
| False Positive Rate | 0.20 | 0.18 | 0.20 | 0.16 | 0.21 | 0.50 |
| False Negative Rate | 0.23 | 0.18 | 0.22 | 0.10 | 0.33 | 0.07 |
| Positive Predictive Power | 0.65 | 0.67 | 0.67 | 0.43 | 0.64 | 0.34 |
| Negative Predictive Power | 0.88 | 0.91 | 0.88 | 0.98 | 0.82 | 0.96 |
| Sample | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 |
|---|---|---|---|---|---|---|
| Date | 2010-11 | 2010-11 | 2010-11 | 2010-11 | 2010-11 | 2010-11 |
| Sample Size | 81 | 72 | 67 | 86 | 60 | 64 |
| Geographic Representation | West North Central (MN) | West North Central (MN) | West North Central (MN) | West North Central (MN) | West North Central (MN) | West North Central (MN) |
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| 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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| 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.
- FAST™ aMath is an IRT-based CAT test; as such, a single model-based approach to reliability will be presented.
- *Describe the sample(s), including size and characteristics, for each reliability analysis conducted.
- The analyses presented are based on over 2,000 students in grades K-5 from one state.
- *Describe the analysis procedures for each reported type of reliability.
- Given the adaptive nature of FAST™ aMath tests, a reliability estimate provided by Samejima (1994), based on the standard error of measurement and test information function of an instrument was computed. The figure below presents conditional standard errors of measurement across grade levels.
*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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| 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.
- 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
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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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| Rating | Provided | Provided | Provided | Provided | Provided | Provided |
- 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:
- Bias was assessed using the logistic regression procedure for detection of uniform and non-uniform differential item functioning (DIF). The advantages of using the logistic regression procedure for DIF detection include being a model-based approach and having the capability to detect both uniform and non-uniform DIF with adequate and equal power; however, the procedure also tends to inflate Type I error rates. As such, an effect size measure developed by Jodoin and Gierl (2001) was computed and evaluated in addition to statistical significance. Jodoin and Gierl present a four-category framework for interpreting the effect size measure, where the four categories are indicative of no, negligible, moderate, and severe DIF.
- b. Describe the subgroups for which bias analyses were conducted:
- There were sufficient data to examine bias in relation to race/ethnicity. The race/ethnicity group comparisons examined were White versus Black, White versus Hispanic, White versus Asian, and White versus Native American.
- 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.
- The results indicate that there is no or negligible DIF for all items examined in all the race/ethnicity comparisons. The items displaying negligible DIF had effect sizes less than or equal to 0.015.
Data Collection Practices
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