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:
  • Direct: Computerized
  • One-to-one
Scoring Time:
  • Scoring is automatic
Scores Generated:
  • Percentile score
  • IRT-based score
  • Developmental benchmarks
Administration Time:
  • 25 minutes per student
Scoring Method:
  • Automatically (computer-scored)
Technology Requirements:
  • 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.
The tool is intended for use with the following grade(s).
not selected Preschool / Pre - kindergarten
selected Kindergarten
selected First grade
selected Second grade
selected Third grade
selected Fourth grade
selected Fifth grade
selected Sixth grade
selected Seventh grade
selected Eighth grade
not selected Ninth grade
not selected Tenth grade
not selected Eleventh grade
not selected Twelfth grade

The tool is intended for use with the following age(s).
not selected 0-4 years old
selected 5 years old
selected 6 years old
selected 7 years old
selected 8 years old
selected 9 years old
selected 10 years old
selected 11 years old
selected 12 years old
selected 13 years old
not selected 14 years old
not selected 15 years old
not selected 16 years old
not selected 17 years old
not selected 18 years old

The tool is intended for use with the following student populations.
not selected Students in general education
not selected Students with disabilities
not selected English language learners

ACADEMIC ONLY: What skills does the tool screen?

Reading
Phonological processing:
not selected RAN
not selected Memory
not selected Awareness
not selected Letter sound correspondence
not selected Phonics
not selected Structural analysis

Word ID
not selected Accuracy
not selected Speed

Nonword
not selected Accuracy
not selected Speed

Spelling
not selected Accuracy
not selected Speed

Passage
not selected Accuracy
not selected Speed

Reading comprehension:
not selected Multiple choice questions
not selected Cloze
not selected Constructed Response
not selected Retell
not selected Maze
not selected Sentence verification
not selected Other (please describe):


Listening comprehension:
not selected Multiple choice questions
not selected Cloze
not selected Constructed Response
not selected Retell
not selected Maze
not selected Sentence verification
not selected Vocabulary
not selected Expressive
not selected Receptive

Mathematics
Global Indicator of Math Competence
selected Accuracy
not selected Speed
selected Multiple Choice
not selected Constructed Response

Early Numeracy
not selected Accuracy
not selected Speed
not selected Multiple Choice
not selected Constructed Response

Mathematics Concepts
not selected Accuracy
not selected Speed
not selected Multiple Choice
not selected Constructed Response

Mathematics Computation
not selected Accuracy
not selected Speed
not selected Multiple Choice
not selected Constructed Response

Mathematic Application
not selected Accuracy
not selected Speed
not selected Multiple Choice
not selected Constructed Response

Fractions/Decimals
not selected Accuracy
not selected Speed
not selected Multiple Choice
not selected Constructed Response

Algebra
not selected Accuracy
not selected Speed
not selected Multiple Choice
not selected Constructed Response

Geometry
not selected Accuracy
not selected Speed
not selected Multiple Choice
not selected Constructed Response

not selected Other (please describe):

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

Where to obtain:
Email Address
info@fastbridge.org
Address
520 Nicollet Mall, Suite 910, Minneapolis, MN 55402
Phone Number
612-254-2534
Website
www.fastbridge.org
Initial cost for implementing program:
Cost
$7.00
Unit of cost
student
Replacement cost per unit for subsequent use:
Cost
$7.00
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.
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.
Provide information about special accommodations for students with disabilities.
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.

Administration

BEHAVIOR ONLY: What type of administrator is your tool designed for?
not selected General education teacher
not selected Special education teacher
not selected Parent
not selected Child
not selected External observer
not selected Other
If other, please specify:

What is the administration setting?
not selected Direct observation
not selected Rating scale
not selected Checklist
not selected Performance measure
not selected Questionnaire
selected Direct: Computerized
selected One-to-one
not selected 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)
selected Computer or tablet
selected Internet connection
not selected 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?
selected Individual
not selected Small group   If small group, n=
not selected Large group   If large group, n=
not selected Computer-administered
not selected 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?
not selected No discontinue rules provided
not selected Basals
not selected Ceilings
selected Other
If other, please specify:
CAT stop criteria where standard error of measurement equals 0.20.


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.
selected 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?
not selected Manually (by hand)
selected Automatically (computer-scored)
not selected 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?
not selected Age norms
selected Grade norms
not selected Classwide norms
not selected Schoolwide norms
not selected Stanines
not selected Normal curve equivalents

What types of performance level scores are available?
not selected Raw score
not selected Standard score
selected Percentile score
not selected Grade equivalents
selected IRT-based score
not selected Age equivalents
not selected Stanines
not selected Normal curve equivalents
selected Developmental benchmarks
not selected Developmental cut points
not selected Equated
not selected Probability
not selected Lexile score
not selected Error analysis
not selected Composite scores
not selected Subscale/subtest scores
not selected 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.
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

Grade Kindergarten
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Classification Accuracy for Criterion 1 Fall Data unavailable Data unavailable Data unavailable Data unavailable Data unavailable Data unavailable
Classification Accuracy for Criterion 1 Winter Data unavailable Data unavailable Data unavailable Data unavailable Data unavailable Data unavailable
Classification Accuracy for Criterion 1 Spring Unconvincing evidence Partially convincing evidence Convincing evidence Convincing evidence Partially convincing evidence Convincing evidence
Classification Accuracy for Criterion 2 Fall Data unavailable Data unavailable Data unavailable Data unavailable Data unavailable Data unavailable
Classification Accuracy for Criterion 2 Winter Data unavailable Data unavailable Data unavailable Data unavailable Data unavailable Data unavailable
Classification Accuracy for Criterion 2 Spring Data unavailable Data unavailable Data unavailable Data unavailable Data unavailable Data unavailable
Legend
Full BubbleConvincing evidence
Half BubblePartially convincing evidence
Empty BubbleUnconvincing evidence
Null BubbleData unavailable
dDisaggregated data available

Classification Accuracy - Criterion 1 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)
Male
Female
Other
Gender Unknown
White, Non-Hispanic
Black, Non-Hispanic
Hispanic
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
Rating Convincing evidence Convincing evidence Convincing evidence Convincing evidence Convincing evidence Convincing evidence
Legend
Full BubbleConvincing evidence
Half BubblePartially convincing evidence
Empty BubbleUnconvincing evidence
Null BubbleData unavailable
dDisaggregated 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
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Rating Partially convincing evidence Unconvincing evidence Partially convincing evidence Convincing evidence Partially convincing evidence Convincing evidence
Legend
Full BubbleConvincing evidence
Half BubblePartially convincing evidence
Empty BubbleUnconvincing evidence
Null BubbleData unavailable
dDisaggregated 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
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Rating 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:
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.

Disclaimer

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.