FAST: earlyMath
Numeral Identification
Rating Summary
Classification Accuracy  

Generalizability  Moderate Low  
Reliability  
Validity  
Disaggregated Reliability and Validity Data  
Efficiency  
Administration  Individual  
Administration & Scoring Time  12 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 Numeral Identification measure is part of earlyMath in the FAST assessment suite from FastBridge Learning, LLC. earlyMath is designed to screen and monitor early academic readiness and achievement for students in Kindergarten and 1^{st} grade. The Formative Assessment System for Teachers (FAST™) is a cloudbased suite of assessment and reporting tools that is $6 per student/year. As a cloudbased assessment suite, there are no hardware costs or fees for additional materials. It includes a variety of assessments in reading, mathematics, and socialemotional behavior that were developed by researchers at the University of Minnesota.

Testers will require less than one hour of training. Paraprofessionals can administer the test. 
Where to Obtain: www.fastbridge.org Address:
FastBridge Learning
520 Nicollet Mall, Suite 910
Minneapolis, MN 554021057
Phone: 6122542534 Website: www.fastbridge.org Training materials are included in the cost of the tool. Additional, optional onsite and webinarbased training services are available for a fee.
Ongoing technical support is available by calling 6124243714 or emailing help@fastbridge.org. 
The Numeral Identification measure is part of earlyMath in the FAST assessment suite. This tool assesses the student’s ability and automaticity at naming numerals. The examiner and student each have the same page of numerals presented in randomlystratified order. As the student identifies the name of each numeral, the examiner marks any error on his/her copy. The resulting score is the number of numerals named correctly. This is a oneminute timed assessment that also has an inventory option. The inventory option allows the teacher to find out which numerals the student has mastered, even if the student does not complete the task in one minute.
The development of earlyMath is based on a thorough examination of the most recent research literature and professional consultation in test development and mathematics education. Each of the subtests is aligned with National Common Core State Standards (CCSS, 2010) and three domains of number sense: (a) number, (b) relations, and (c) operations (Purpura & Lonigan, 2013; National Research Council, 2009). Early numeracy skills measured within the three domains include: naming numerals, using the mental number line, counting with onetoone correspondence, understanding the relation between numerals and quantities, composing and decomposing numbers, basic verbal fact fluency, an understanding of place value, and knowledge of symbols in story problems. 
earlyMath is designed to screen and monitor early numeracy skills for students in Kindergarten and 1^{st} grade.
The Numeral Identification tool is intended for use in Kindergarten and 1^{st} grade or with ages
The assessment is individually administered in one minute per student. Scoring is automatic.
Available scores include: raw scores, percentile scores, developmental benchmarks and cut points, subscales, and error analysis. 
Classification Accuracy
Classification Accuracy in Predicting Proficiency on GMADE 


Kindergarten 15^{th} Percentile Spring n = 157 
Kindergarten 15^{th} Percentile Fall n = 133 
False Positive Rate 
0.24 
0.27 
False Negative Rate 
0.30 
0.33 
Sensitivity 
0.72 
0.67 
Specificity 
0.76 
0.73 
Positive Predictive Power 
0.28 
0.11 
Negative Predictive Power 
0.95 
0.98 
Overall Classification Rate 
0.76 
0.73 
AUC (ROC) 
0.86 
0.83 
Base Rate 
0.11 
0.05 
Cut Points: 
36 
44 
At XX% Sensitivity, Specificity equals 
8% sensitivity, 0.67 specificity 
90% sensitivity, 0.59 specificity 
At XX% Sensitivity, Specificity equals 
78% sensitivity, 0.73 specificity 
80% sensitivity, 0.67 specificity 
At XX% Sensitivity, Specificity equals 
72% sensitivity, 0.82 specificity 
73% sensitivity, 0.76 specificity 
Generalizability
Description of Kindergarten study sample:
· Number of States: 1 Minnesota
· Regions: 1
· Gender
o 50.6% Male
o 49.4% Female
· Eligible for free or reducedprice lunch: 27.8%
· Race/Ethnicity:
o 79% White, NonHispanic
o 2.5% American Indian/Alaska Native
o 9.3% Black, NonHispanic
o 3.7% Asian, Pacific Islander
o 5.6% Hispanic
· Disability status: Approximately 8% of students with disabilities
· Language proficiency status: 100% English proficient
Description of 1^{st} Grade study sample:
· Number of States: 1 Minnesota
· Regions: 1
· Gender
o 57.9% Male
o 42.1% Female
· Eligible for free or reducedprice lunch: 31.1%
· Race/Ethnicity:
o 73.8% White, NonHispanic
o 1.1% American Indian/Alaska Native
o 14.8% Black, NonHispanic
o 4.9% Asian, Pacific Islander
o 5.5% Hispanic
· Disability status: Approximately 11% of students with disabilities
· Language proficiency status: 100% English proficient
Reliability
Type of Reliability 
Age or Grade 
n (range) 
Coefficient 
SEM 
Information (including normative data)/Subjects 

range 
median 

Testretest 
K 
38 

0.85 

10% Black, 8% Hispanic, 82% White, 15% Free and reduced lunch, and 5% IEP eligible. 
Testretest 
1 
36 

0.91 

3% American Indian, 13% Asian, 21% Black, 5% Hispanic, 59% White, 38% Free and Reduced Lunch, and 3% IEP eligible. 
Interrater 
K 
45 
0.83 – 1.00 
0.98 

A random sample of cases were selected from the 20132014 school year. 
Interrater 
1 
45 
0.92 – 1.00 
0.98 

A random sample of cases were selected from the 20132014 school year. 
Splithalf 
K 
45 

0.93 for first 25 items 0.98 for first 37 items 0.98 for first 50 items 

A random sample of cases were selected from the 20132014 school year. 
Splithalf 
1 
45 

0.96 for first 33 items 0.98 for first 40 items 0.98 for first 46 items 

A random sample of cases were selected from the 20132014 school year. 
Cronbach’s alpha 
K 
45 

0.89 for first 25 items 0.96 for first 37 items 0.97 for first 50 items 

The same sample used to calculate splithalf was used from the 20132014 school year. 
Cronbach’s alpha 
1 
45 

0.88 for first 33 items 0.90 for first 40 items 0.92 for first 46 items 

The same sample used to calculate splithalf was used from the 20132014 school year. 
Alternate form 
K 
39  42 
0.88  0.95 
0.92 

5% Asian, 23% Black, 11% Hispanic, 3% Multiracial, 58% White, and 6% IEP eligible. 
Alternate form 
1 
42  48 
0.89  0.95 
0.91 

1% Asian, 15% Black, 9% Hispanic, 4% Multiracial, 71% White, and 3% IEP eligible. 
Validity
Type of Validity 
Age or Grade 
Test or Criterion 
n (range) 
Coefficient (if applicable) 
Information (including normative data)/Subjects 

range 
Median 

Concurrent 
1 
Measures of Academic Progress for Primary Grades – Math (MAP) 
194 

0.57 
Data collected in Fall. 3% American Indian, 7% Asian, 3% Black, 4% Hispanic, 84% White, 35% Free and reduced lunch, and 7% IEP eligible. 
Concurrent 
K 
MAP 
220 

0.64 
Data collected in Winter. 1% American Indian, 2% Asian, 4% Black, 2% Hispanic, 91% White, 30% Free and reduced lunch, and 12% IEP eligible. 
Concurrent 
1 
MAP 
192 

0.42 
Data collected in Winter. 
Predictive 
K 
MAP 
215 

0.64 
Fall to Winter prediction. 
Predictive 
1 
MAP 
188 

0.61 
Fall to Winter prediction. 
Predictive 
K 
MAP 
212 

0.58 
Fall to Spring prediction. 
Predictive 
1 
MAP 
192 

0.59 
Fall to Spring prediction. 
Predictive 
K 
MAP 
221 

0.57 
Winter to Spring prediction. 
Predictive 
1 
MAP 
187 

0.45 
Winter to Spring prediction. 
Predictive 
K 
GMADE composite Level R 
142 

0.46 
Fall to Spring prediction. 3% American Indian, 4% Asian, 8% Black, 6% Hispanic, 80% White, 29% Free and reduced lunch, and 8% IEP eligible. 
Predictive 
1 
GMADE composite Level 1 
154 

0.57 
Fall to Spring prediction. 1% American Indian, 5% Asian, 14% Black, 6% Hispanic, 74% White, 34% Free and reduced lunch, and 13% IEP eligible. 
Predictive 
K 
GMADE composite Level R 
144 

0.47 
Winter to Spring prediction. 
Predictive 
1 
GMADE composite Level 1 
160 

0.51 
Winter to Spring prediction. 
Concurrent 
K 
GMADE composite Level R 
150 

0.52 
Data collected in Spring. 
Concurrent 
1 
GMADE composite Level 1 
167 

0.48 
Data collected in Spring. 
Predictive  K  aMath  198  0.70 
Early Spring to End of Year 10 schools in the Midwest. 52% Female, 2% Eligible for Special Education 

Concurrent  K  AIMSweb Number ID  58  0.87  See description below  
Concurrent  K  AIMSweb Oral Counting  58  0.72  See description below  
Concurrent  K  AIMSweb Quantity Discrimination  58  0.84  See description below  
Concurrent  K  AIMSweb Missing Number  58  0.83  See description below  
Concurrent  1  AIMSweb Number ID  53  0.85  See description below  
Concurrent  1  AIMSweb Quantity Discrimination  53  0.77  See description below  
Concurrent  1  AIMSweb Missing Number  53  0.77  See description below 
Note. Correlations were disattenuated based on reported reliabilities.
The earlyMath validity evidence study Kindergarten coefficients were derived from a sample of 58 students. Approximately 47% of students were female. Reported races of students were White (53%), Hispanic (10%), Black (14%), American Indian (2%), and Asian/Pacific Islander (21%). Approximately 26% of students were English Language Learners, 40% were eligible for free or reduced lunch, and 7% received special education services.
The earlyMath validity evidence study Grade 1 coefficients were derived from a sample of 53 students. Approximately 49% of students were female. Reported races of students were White (74%), Hispanic (4%), Black (11%), and Asian/Pacific Islander (11%). Approximately 17% of students were English Language Learners, 23% were eligible for free or reduced lunch, and 13% received special education services.
AIMSweb Number Identification measure is an individually administered test that measures ability to read and orally identify numerals. The kindergarten measure requires students to identify written numbers between 1 and 10, while the first grade measure includes numbers between 1 and 20. The score is the number of numerals identified correctly in one minute. Median internal consistency reliability was 0.94 and 0.95 in kindergarten and first grade, respectively. Concurrent and predictive validity with Number Knowledge Test, and WJ Applied Problems was also reported as moderate (Median r = 0.64 to 0.70).
The AIMSweb Oral Counting is an individually administered measure that requires students to orally count starting from 1 as high as they can. The score is the number of correct counts in one minute.
AIMSweb Quantity Discrimination is an individually administered measure that requires students to orally identify the bigger number from a pair of numbers. The score is the number of correct quantity discriminations in one minute. Median testretest reliability was reported as 0.77 and 0.85. Concurrent and predictive validity with MCBM, Number Knowledge Test, and WJ Applied Problems was also reported as high (Median r = 0.73 to 0.80).
The AIMSweb Missing Number is an individually administered measure that requires students to orally identify the missing number from a string of three numbers. The placement of the missing number varies and can be at the beginning, middle, or end of the three digit string. The score is the number of missing numbers correctly identified in one minute. Median internal consistency reliability was 0.98 in kindergarten and first grade. Concurrent and predictive validity with MCBM, Number Knowledge Test, and WJ Applied Problems was also reported as high (Median r = 0.69 to 0.75).
Construct and content validity depend substantially on the development and selection of stimuli. See below for a description of the content.
The Numeral Identification task assesses the student’s ability and automaticity at naming numerals. The examiner and student each have the same page of numerals presented in randomlystratified order. As the student identifies the name of each numeral, the examiner marks any error on his/her copy. The resulting score is the number of numerals named correctly.
Kindergarten Test Construction. All numerals between 0 and 31 were used. The test consists of 75 items arranged in 15 rowss with 5 numerals per row. The first seven rows of the student sheet are stratified from easier to more difficult items in the following manner: rows one and two contain only single digits 09, rows threesix, and the first two spaces of row seven contain all double digit numerals 1031. Each of the rows mentioned above contain each number within the specified range only once. The remainder of row 7 and rows 815 contain all numbers 031 with some repetition across rows. The order of numerals within each row was determined using a random number generator, but manual changes were made if the random number generator created consecutive sequences of counting or patterns that would be recognized by the student (e.g., 4, 5, 6 or 5, 10, 15). This is a 1 minute timed assessment that also has an inventory option. An inventory option allows the teacher to find out which numerals between 0 and 31 the student has mastered, even if the student does not complete the task in 1 minute.
First Grade Test Construction. All numerals between 0 and 120 were used. The test consists of 96 items arranged in 16 rows, with 6 numerals per row. The first seven rows of the student sheet are stratified from easier to more difficult items in the following manner: row one contains only single digits, row two contains numerals 1119, row three contains 0, and multiples of 10, row four contains numerals 2129, row five contains numerals 3149, row six contains numerals 5199, and row seven contains numerals 101119. Each of the rows mentioned above contain each number within the specified range only once. Rows 816 contain all numerals 0120 with some repetition across rows. The order of numerals within each row was determined using a random number generator, but manual changes were made if the random number generator created consecutive sequences of counting or patterns that would be recognized by a student (e.g., 4, 5, 6 or 5, 10, 15). This is a 1 minute timed assessment that also has an inventory option. An inventory option allows the teacher to find out which numerals between 0 and 120 the student has mastered, even if the student does not complete the task in 1 minute.
Disaggregated Reliability, Validity, and Classification Data for Diverse Populations
Disaggregated Classification Accuracy in Predicting Proficiency on the Group Mathematics Assessment and Diagnostic Evaluation (GMADE)

Kindergarten (Spring; 20^{th} Percentile; White) n = 126 
Kindergarten (Spring; 20^{th} Percentile; Black) n = 13 
1^{st} Grade (Winter to Spring; 20^{th} Percentile; White) n = 120 
1^{st} Grade (Winter to Spring; 20^{th} Percentile; Black) n = 23 
False Positive Rate 
0.28 
0 
0.24 
0.05 
False Negative Rate 
0.29 
0.33 
0.18 
0 
Sensitivity 
0.71 
0.67 
0.82 
1.00 
Specificity 
0.72 
1.00 
0.76 
0.94 
Positive Predictive Power 
0.24 
1.00 
0.36 
0.80 
Negative Predictive Power 
0.95 
0.78 
0.96 
1.00 
Overall Classification Rate 
0.72 
0.85 
0.76 
0.96 
AUC (ROC) 
0.76 
0.87 
0.79 
0.95 
Base Rate 
0.11 
0.46 
0.14 
0.17 
Cut Points: 
35 
21 
35 
35 
Disaggregated Reliability
Type of Reliability 
Age or Grade 
n (range) 
Coefficient Range 
Coefficient Median 
Information (including normative data)/Subjects 
Alpha 
K 
14 

0.94 
American Indian or Alaskan Native 
Alpha 
K 
23 

0.97 
Asian or Pacific Islander 
Alpha 
K 
22 

0.94 
Hispanic 
Alpha 
K 
46 

0.96 
Black 
Alpha 
K 
506 

0.96 
White 
Delayed TestRetest (~13 week delay) 
K 
3033 
0.550.59 
0.57 
American Indian or Alaskan Native 
Delayed TestRetest 
K 
1517 
0.810.87 
0.84 
Asian or Pacific Islander 
Delayed TestRetest 
K 
1617 
0.660.71 
0.69 
Hispanic 
Delayed TestRetest 
K 
3239 
0.860.89 
0.88 
Black 
Delayed TestRetest 
K 
446472 
0.76 
0.76 
White 
Alpha 
1 
16 

0.96 
Asian or Pacific Islander 
Alpha 
1 
14 

0.83 
Hispanic 
Alpha 
1 
29 

0.94 
Black 
Alpha 
1 
224 

0.90 
White 
Delayed TestRetest (~13 week delay) 
1 
4244 
0.810.82 
0.82 
American Indian or Alaskan Native 
Delayed TestRetest 
1 
1419 
0.790.92 
0.86 
Asian or Pacific Islander 
Delayed TestRetest 
1 
3035 
0.630.69 
0.66 
Hispanic 
Delayed TestRetest 
1 
4760 
0.760.87 
0.82 
Black 
Delayed TestRetest 
1 
407443 
0.680.73 
0.71 
White 