FAST: Adaptive Math
aMath
Rating Summary
Classification Accuracy | ![]() | |
---|---|---|
Generalizability | Moderate Low | |
Reliability | ![]() | |
Validity | ![]() | |
Disaggregated Reliability and Validity Data | ![]() | |
Efficiency | ||
Administration | Individual | |
Administration & Scoring Time | 10-45 Minutes | |
Scoring Key | Computer Scored | |
Benchmarks / Norms | Yes |
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 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 |
3rd Grade |
3rd Grade |
3rd Grade |
---|---|---|---|---|
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 |
4th Grade |
4th Grade |
4th Grade |
---|---|---|---|---|
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 |
5th Grade |
5th Grade |
5th Grade |
---|---|---|---|---|
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 |