FAST: Adaptive Math

aMath

Rating Summary

Classification Accuracyfull bubble
GeneralizabilityModerate Low
Reliabilityfull bubble
Validityfull bubble
Disaggregated Reliability and Validity Datafull bubble
Efficiency
AdministrationIndividual
Administration & Scoring Time10-45 Minutes
Scoring KeyComputer Scored
Benchmarks / NormsYes
Cost Technology, Human Resources, and Accommodations for Special Needs Service and Support Purpose and Other Implementation Information Usage and Reporting

The Formative Assessment System for Teachers™ (FAST) is online software that requires no hardware or special add-ons. FAST is supported by an extensive set of materials to support teachers and students, including self-directed training modules that allow teachers to become certified to administer each of the FAST assessments. The entire FAST assessment package (i.e., reading, math, behavior, and on-line training) is provided at an annual flat rate of $6 per student.

Testers will require less than 4 hours of training.

Paraprofessionals can administer the test.

Where to Obtain: www.fastforteachers.org 

Address:

FastBridge Learning
520 Nicollet Mall, Suite 910
Minneapolis, MN 55402-1057

Phone: 612-254-2534

Website: www.fastforteachers.org

Training materials are included in the cost of the tool.  Additional, optional on-site and webinar-based training services are available for a fee.

Ongoing technical support is available by calling 612-424-3710 or emailing fast1@umn.edu

The ultimate goal of aMath is instructional efficacy. aMath directly addresses issues of instructional relevance – it is designed to optimize each assessment for each student based on their response pattern. Grade level references are just a convenience to identify the most relevant skills across the developmental range for the typically developing child.  As such, a student in third grade with substantial math deficits might receive an assessment that is similar to that of a typically developing kindergarten student. Likewise, a student in the third grade with substantial math ability might receive an assessment that is similar to that of a typically developing 5th grade student. Both assessments and instruction must be individualized for students. aMath optimizes the efficiency, precision, and utility of assessment with individualized (adaptive) assessment.

The tool is intended for use in grades K-6 or with ages 5-10+.

Administration is computerized and is 20-30 minutes per typical student. Scoring is done automatically within the software and does not require any additional time.

Available scores include: raw scores, local through national percentile scores, local through national growth norms, developmental benchmarks and cut points, accuracy rates and error analysis.

 

Classification Accuracy

GMADE Results: Summary

Grade

n

aMath Cut Score

Sensitivity

Specificity

PPP

NPP

AUC

Some Risk – 40th Percentile GMADE

K

81

187

0.72

0.80

0.65

0.98

0.81

1

72

196

0.79

0.90

0.67

0.98

0.88

2

67

206

0.80

0.92

0.67

0.98

0.82

3

86

207

0.96

1.00

0.43

1.00

0.89

4

60

215

0.67

0.80

0.64

0.97

0.74

5

42

225

0.85

0.88

0.81

0.97

0.97

High Risk: 10th Percentile

K

81

187

0.71

0.75

0.12

0.98

0.75

1

72

190

0.95

0.83

0.62

0.98

0.83

2

67

202

0.88

0.80

0.53

0.96

0.92

3

86

201

0.95

1.00

0.33

1.00

0.98

4

60

206

0.95

0.75

0.50

0.98

0.88

5

42

218

0.84

0.80

0.40

0.97

0.88

Criterion

 

 

0.70

0.70

-

-

0.85

 

MAP Results: Summary

Grade

n

aMath Cut Score

Sensitivity

Specificity

PPP

NPP

AUC

Some Risk (MAP specified cut score)

K

89

188

0.84

0.91

0.77

0.94

0.91

1

77

193

0.84

1.00

0.20

1.00

0.93

2

91

196

0.97

1.00

0.62

1.00

0.98

3

89

208

0.77

1.00

0.21

1.00

0.91

4

74

206

0.91

1.00

0.50

1.00

0.98

5

53

220

0.86

1.00

0.62

1.00

0.94

Criterion

 

 

0.70

0.70

-

-

0.85

 

Classification Accuracy in Predicting Proficiency on GMADE

 

Kindergarten

n = 81

1st Grade

n = 72

2nd Grade

n = 67

3rd Grade

n = 86

4th Grade

n = 60

5th Grade

n = 64

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

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

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

Overall Classification Rate

0.79

0.82

0.79

0.85

0.75

0.59

Observed

0.79

0.82

0.79

0.85

0.75

0.59

Chance

0.54

0.55

0.53

0.70

0.54

0.45

Base Rate

0.32

0.31

0.34

0.12

0.35

0.22

Cut Points:

40th percentile

40th percentile

40th percentile

40th percentile

40th percentile

40th percentile

 

Classification Accuracy in Predicting Proficiency on MAP

 

Kindergarten

n = 89

1st Grade

n = 77

2nd Grade

n = 91

3rd Grade

n = 89

4th Grade

n = 74

5th Grade

n = 53

False Positive Rate

0.15

0.28

0.26

0.15

0.28

0.18

False Negative Rate

0.21

0.08

0.00

0.07

0.00

0.00

Sensitivity

0.79

0.92

1.00

0.93

1.00

1.00

Specificity

0.85

0.72

0.74

0.85

0.72

0.82

Positive Predictive Power

0.86

0.38

0.43

0.54

0.52

0.76

Negative Predictive Power

0.78

0.98

1.00

0.98

1.00

1.00

Overall Classification Rate

0.82

0.75

0.78

0.87

0.78

0.89

Observed

0.82

0.75

0.78

0.87

0.78

0.89

Chance

0.50

0.58

0.58

0.66

0.53

0.51

Base Rate

0.54

0.16

0.16

0.16

0.23

0.36

Cut Points:

40th percentile

40th percentile

40th percentile

40th percentile

40th percentile

40th percentile

 

 

 

 

 

Generalizability

Description of study sample:

·         Number of States: 1 (Minnesota)

·         Size: 496

·         Grades K-5                  

·         Regions: 1

·         Gender

o   49% Male

o   51% Female

·         SES: 8% Eligible for free or reduced-price lunch

·         Race/Ethnicity:

o   88% White, Non-Hispanic

o   1% American Indian/Alaska Native

o   6% Black, Non-Hispanic

o   2% Asian, Pacific Islander

o   3% Hispanic

·         Disability status: approximately 15% students with disabilities

·         First language: It was estimated that more than 95% of participants had English as their first language.

 

 

Reliability

Type of Reliability

Age or Grade

n (range)

Coefficient

SEM

Information (including normative data)/Subjects

range

median

Test-Retest Reliability

 

 

 

 

 

Pending; however, all tests are derived from a fully calibrated item bank with IRT parameters, which supports the assumption of form equivalence.

Internal Consistency

 

Approximately 2,000 students

 

0.95

 

 

Alternate Forms Reliability

 

Approximately 2,000 students

 

0.95

 

 

Inter-rater

 

 

 

1.0

 

Computer scored so there is no “inter-rater”

 

Validity

Type of Validity

Age or Grade

Test or Criterion

n (range)

Coefficient (if applicable)

Information (including normative data)/Subjects

Range

Median

Concurrent

K

GMADE

81

 

0.62

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

1

GMADE

72

 

0.66

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

2

GMADE

67

 

0.67

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

3

GMADE

86

 

0.76

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

4

GMADE

60

 

0.67

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

5

GMADE

65

 

0.84

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

K

MAP

89

 

0.76

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

1

MAP

77

 

0.71

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

2

MAP

91

 

0.81

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

3

MAP

89

 

0.76

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

4

MAP

74

 

0.84

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

5

MAP

76

 

0.88

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

3

MCA

88

 

0.80

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

4

MCA

70

 

0.84

See table below; 2-4 week delay between aMath and criterion administration

Concurrent

5

MCA

73

 

0.85

See table below; 2-4 week delay between aMath and criterion administration

Predictive 3 MCA-III 483   0.86 2013-2014 Fall aMath to Spring prediction of the MCA. 
Predictive 4 MCA-III 486   0.85 2013-2014 Fall aMath to Spring prediction of the MCA. 
Predictive 5 MCA-III 493   0.85 2013-2014 Fall aMath to Spring prediction of the MCA. 
Concurrent 3 MCA-III 155   0.87 2014 May aMath to Spring MCA
Concurrent 4 MCA-III 90   0.87 2014 May aMath to Spring MCA
Concurrent 5 MCA-III 67   0.88 2014 May aMath to Spring MCA

Demographic Data for Spring 2013 Validity Study

Sample Demographics

 

K

1

2

3

4

5

All

n

89

77

91

89

74

76

496

Gender (Male)

40%

47%

48%

51%

53%

54%

49%

White

89%

90%

89%

85%

88%

90%

88%

Black

6%

3%

7%

6%

7%

8%

6%

Hispanic

2%

3%

2%

5%

3%

3%

3%

Asian

1%

4%

1%

5%

0%

0%

2%

American Indian

0%

0%

1%

0%

2%

0%

1%

F/R Lunch

2%

1%

0%

20%

18%

11%

8%

Special Education

5%

10%

11%

24%

22%

18%

15%

 

Disaggregated Reliability, Validity, and Classification Data for Diverse Populations

Disaggregated Classification Accuracy in Predicting Proficiency on Minnesota Comprehensive Assessment III (MCA-III)

 

3rd Grade
(Asian)
n = 110

3rd Grade
(Hispanic)
n = 65

3rd Grade
(Black)
n = 54

3rd Grade
(White)
n = 243

False Positive Rate

0.20

0.20

0.50

0.06

False Negative Rate

0.07

0.21

0.07

0.35

Sensitivity

0.93

0.79

0.93

0.65

Specificity

0.80

0.80

0.50

0.94

Positive Predictive Power

0.63

0.63

0.70

0.46

Negative Predictive Power

0.97

0.90

0.86

0.97

Overall Classification Rate

0.84

0.80

0.74

0.92

AUC (ROC)

0.95

0.91

0.90

0.94

Base Rate

0.26

0.29

0.56

0.07

Disaggregated Classification Accuracy in Predicting Proficiency on Minnesota Comprehensive Assessment III (MCA-III)

 

4th Grade
(Asian)
n = 97

4th Grade
(Hispanic)
n = 58

4th Grade
(Black)
n = 67

4th Grade
(White)
n = 254

False Positive Rate

0.24

0.23

0.14

0.06

False Negative Rate

0.10

0.13

0.22

0.32

Sensitivity

0.90

0.87

0.78

0.68

Specificity

0.76

0.77

0.86

0.94

Positive Predictive Power

0.62

0.57

0.75

0.46

Negative Predictive Power

0.95

0.94

0.88

0.97

Overall Classification Rate

0.80

0.79

0.84

0.92

AUC (ROC)

0.95

0.89

0.93

0.93

Base Rate

0.30

0.26

0.34

0.07

Disaggregated Classification Accuracy in Predicting Proficiency on Minnesota Comprehensive Assessment III (MCA-III)

 

5th Grade
(Asian)
n = 103

5th Grade
(Hispanic)
n = 62

5th Grade
(Black)
n = 72

5th Grade
(White)
n = 243

False Positive Rate

0.14

0.18

0.17

0.04

False Negative Rate

0.22

0.22

0.21

0.43

Sensitivity

0.78

0.78

0.79

0.57

Specificity

0.86

0.82

0.83

0.96

Positive Predictive Power

0.62

0.64

0.70

0.57

Negative Predictive Power

0.93

0.90

0.89

0.96

Overall Classification Rate

0.84

0.81

0.82

0.93

AUC (ROC)

0.94

0.89

0.90

0.94

Base Rate

0.22

0.29

0.33

0.09