FAST

Adaptive Math (aMath)

Cost

Technology, Human Resources, and Accommodations for Special Needs

Service and Support

Purpose and Other Implementation Information

Usage and Reporting

Initial 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.

 

Replacement Cost:

Annual rates subject to change.

 

Included in Cost:

The FAST™ application is a fully cloud-based system, and therefore computer and internet access are required for full use of the application. Teachers will require less than one hour of training on the administration of the assessment. A paraprofessional can administer the assessment as a Group Proctor in FAST™.

Technology Requirements:

  • Computer or Tablet
  • Internet connection

 

Training Requirements:

  • Less than 1 hour of training

 

Qualified Administrators:

  • No minimum qualifications

 

Accommodations:

The application allows for the following accommodations to support accessibility for culturally and linguistically diverse populations:

  • Text magnification.
  • Sound amplification.
  • Enlarged and printed paper materials are available upon request.
  • 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.
  • Extra breaks as needed.
  • Preferential seating and use of quiet space.
  • Proxy responses.
  • Use of scratch paper.
  • As part of item development, all items were reviewed for bias and fairness.

Where to Obtain:

Website: www.fastbridge.org

Address: 520 Nicollet Mall, Suite 910, Minneapolis, MN 55402

Phone number: 612-254-2534

Email address: info@fastbridge.org


Access to Technical Support:

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

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.

 

 

Assessment Format:

  • Direct: Computerized
  • One-to-one

 

 

Administration Time:

  • 20-30 minutes per student

 

Scoring Time:

  • Scoring is automatic

 

Scoring Method:

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.

 

Scores Generated:

  • Percentile score            
  • IRT-based score            
  • Developmental benchmarks

 

 

Classification Accuracy

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Primary Sample

 

Criterion 1: GMADE

Time of Year: Spring

 

Grade K

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Cut points

187 (10th percentile)

190 (10th percentile)

202 (10th percentile)

201 (10th percentile)

206 (10th percentile)

218 (10th percentile)

Base rate in the sample for children requiring intensive intervention

Not Provided

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Base rate in the sample for children considered at-risk, including those with the most intensive needs

Not Provided

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False Positive Rate

Not Provided

Not Provided

Not Provided

Not Provided

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False Negative Rate

Not Provided

Not Provided

Not Provided

Not Provided

Not Provided

Not Provided

Sensitivity

0.71

0.95

0.88

0.95

0.95

0.84

Specificity

0.75

0.83

0.80

1.00

0.75

0.80

Positive Predictive Power

0.12

0.62

0.53

0.33

0.50

0.40

Negative Predictive Power

0.98

0.98

0.96

1.00

0.99

0.97

Overall Classification Rate

Not Provided

Not Provided

Not Provided

Not Provided

Not Provided

Not Provided

Area Under the Curve (AUC)

0.75

0.83

0.92

0.98

0.88

0.88

AUC 95% Confidence Interval Lower

0.67

0.76

0.87

0.96

0.82

0.80

AUC 95% Confidence Interval Upper

0.83

0.90

0.97

1.00

0.94

0.96

At 90% Sensitivity, specificity equals

Not Provided

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At 80% Sensitivity, specificity equals

Not Provided

Not Provided

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Not Provided

Not Provided

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At 70% Sensitivity, specificity equals

Not Provided

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Not Provided

Not Provided

Not Provided

 

Reliability

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  1. 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.  

 

  1. Description of the sample(s), including size and characteristics, for each reliability analysis conducted:

The reliability results presented below are based on the 2017-2018 norming sample.    

 

  1. Description of the analysis procedures for each reported type of reliability:

Given the adaptive nature of FASTjTM aMath tests, a model-based reliability estimate based on the standard error of measurement and test information function of an instrument was computed following Samejima (1994).

 

  1. Reliability of performance level score (e.g., model-based, internal consistency, inter-rater reliability).

Type of Reliability

Age or Grade

n

Coefficient

Confidence Interval

Model-based

K

10,000

0.97

0.96, 0.98

Model-based

1

10,000

0.96

0.95, 0.97

Model-based

2

10,000

0.96

0.95, 0.97

Model-based

3

10,000

0.96

0.95, 0.97

Model-based

4

10,000

0.96

0.95, 0.97

Model-based

5

10,000

0.96

0.95, 0.97

Model-based

6

10,000

0.96

0.95, 0.97

Model-based

7

10,000

0.97

0.96, 0.98

Model-based

8

10,000

0.96

0.95, 0.97

 

Disaggregated Reliability

The following disaggregated reliability data are provided for context and did not factor into the Reliability rating.

Type of Reliability

Subgroup

Age or Grade

n

Coefficient

Confidence Interval

None

 

 

 

 

 

 

Validity

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1.Description of each criterion measure used and explanation as to 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.  

 

2.Description of 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.  

 

3.Description of 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.  

 

4.Validity for the performance level score (e.g., concurrent, predictive, 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 Validity

Age or Grade

Test or Criterion

n

Coefficient

Confidence Interval

Concurrent

K

GMADE

81

0.62

0.46, 0.74

Concurrent

1

GMADE

72

0.66

0.50, 0.78

Concurrent

2

GMADE

67

0.67

0.51, 0.79

Concurrent

3

GMADE

86

0.76

0.65, 0.84

Concurrent

4

GMADE

60

0.67

0.50, 0.79

Concurrent

5

GMADE

65

0.84

0.75, 0.90

Construct

K

MAP

89

0.76

0.65, 0.84

Construct

1

MAP

77

0.71

0.57, 0.81

Construct

2

MAP

91

0.81

0.72, 0.87

Construct

3

MAP

89

0.76

0.65, 0.84

Construct

4

MAP

74

0.84

0.75, 0.90

Construct

5

MAP

76

0.88

0.81, 0.92

 

5.Results for other forms of validity (e.g. factor analysis) not conducive to the table format:

None provided

 

6.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.  

 

 

Disaggregated Validity

The following disaggregated validity data are provided for context and did not factor into the Validity rating.

Type of Validity

Subgroup

Age or Grade

Test or Criterion

n

Coefficient

Confidence Interval

None

 

 

 

 

 

 

 

Results for other forms of disaggregated validity (e.g. factor analysis) not conducive to the table format:

None provided 

Sample Representativeness

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Primary Classification Accuracy Sample

Representation: Large local sample from a single state (Minnesota).

Date: 2010-11

Size: 432

Male

49%

Female

51%

Unknown

NA

FRPL

8%

White

88%

Black or African American

6%

Hispanic

3%

American Indian or Alaskan

1%

American Indian/Alaska Native

2%

Asian/Pacific Islander

2%

Other

Not provided

Unknown

Not provided

Disability classification

15% special education

First language

Not provided

ELL

Not provided

 

Bias Analysis Conducted

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  1. Description of the method used to determine the presence or absence of bias:

None provided

 

  1. Description of the subgroups for which bias analyses were conducted:

None provided

 

  1. Description of the results of the bias analyses conducted, including data and interpretative statements:

None provided

 

Administration Format

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Data
  • Individual
  • Individual
  • Individual
  • Individual
  • Individual
  • Individual
  • Administration & Scoring Time

    GradeK12345
    Data
  • 20-30 minutes
  • 20-30 minutes
  • 20-30 minutes
  • 20-30 minutes
  • 20-30 minutes
  • 20-30 minutes
  • Scoring Format

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    Data
  • Automatic
  • Automatic
  • Automatic
  • Automatic
  • Automatic
  • Automatic
  • Types of Decision Rules

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    Data
  • None
  • None
  • None
  • None
  • None
  • None
  • Evidence Available for Multiple Decision Rules

    GradeK12345
    Data
  • No
  • No
  • No
  • No
  • No
  • No