FAST: earlyMath

Numeral Identification

Rating Summary

Classification Accuracyfull bubble
GeneralizabilityModerate Low
Reliabilityfull bubble
Validityfull bubble
Disaggregated Reliability and Validity Datafull bubble
Efficiency
AdministrationIndividual
Administration & Scoring Time1-2 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 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 1st grade.

The Formative Assessment System for Teachers (FAST™) is a cloud-based suite of assessment and reporting tools that is $6 per student/year. As a cloud-based assessment suite, there are no hardware costs or fees for additional materials. It includes a variety of assessments in reading, mathematics, and social-emotional 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 55402-1057

Phone: 612-254-2534

                                              Website: www.fastbridge.org

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

 

Ongoing technical support is available by calling 612-424-3714 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 randomly-stratified 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 one-minute 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 one-to-one 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 1st grade.

 

The Numeral Identification tool is intended for use in Kindergarten and 1st grade or with ages
5–7.

 

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

15th Percentile Spring

n = 157

Kindergarten

15th 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 reduced-price lunch: 27.8%

·         Race/Ethnicity:

o   79% White, Non-Hispanic

o   2.5% American Indian/Alaska Native

o   9.3% Black, Non-Hispanic

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 1st Grade study sample:

·         Number of States: 1 Minnesota

·         Regions: 1

·         Gender

o   57.9% Male

o   42.1% Female

·         Eligible for free or reduced-price lunch: 31.1%

·         Race/Ethnicity:

o   73.8% White, Non-Hispanic

o   1.1% American Indian/Alaska Native

o   14.8% Black, Non-Hispanic

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

Test-retest

K

38

 

0.85

 

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

Test-retest

1

36

 

0.91

 

3% American Indian, 13% Asian, 21% Black, 5% Hispanic, 59% White, 38% Free and Reduced Lunch, and 3% IEP eligible.

Inter-rater

K

45

0.83 – 1.00

0.98

 

A random sample of cases were selected from the 2013-2014 school year.

Inter-rater

1

45

0.92 – 1.00

0.98

 

A random sample of cases were selected from the 2013-2014 school year.

Split-half

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 2013-2014 school year.

Split-half

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 2013-2014 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 split-half  was used from the 2013-2014 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 split-half was used from the 2013-2014 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 test-retest reliability was reported as 0.77 and 0.85. Concurrent and predictive validity with M-CBM, 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 M-CBM, 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 randomly-stratified 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 0-9, rows three-six, and the first two spaces of row seven contain all double digit numerals 10-31. Each of the rows mentioned above contain each number within the specified range only once. The remainder of row 7 and rows 8-15 contain all numbers 0-31 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 11-19, row three contains 0, and multiples of 10, row four contains numerals 21-29, row five contains numerals 31-49, row six contains numerals 51-99, and row seven contains numerals 101-119. Each of the rows mentioned above contain each number within the specified range only once. Rows 8-16 contain all numerals 0-120 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; 20th Percentile; White)

n = 126

Kindergarten

(Spring; 20th Percentile; Black)

n = 13

1st Grade

(Winter to Spring; 20th Percentile; White)

n = 120

1st Grade

(Winter to Spring; 20th 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 Test-Retest (~13 week delay)

K

30-33

0.55-0.59

0.57

American Indian or Alaskan Native

Delayed Test-Retest

K

15-17

0.81-0.87

0.84

Asian or Pacific Islander

Delayed Test-Retest

K

16-17

0.66-0.71

0.69

Hispanic

Delayed Test-Retest

K

32-39

0.86-0.89

0.88

Black

Delayed Test-Retest

K

446-472

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 Test-Retest (~13 week delay)

1

42-44

0.81-0.82

0.82

American Indian or Alaskan Native

Delayed Test-Retest

1

14-19

0.79-0.92

0.86

Asian or Pacific Islander

Delayed Test-Retest

1

30-35

0.63-0.69

0.66

Hispanic

Delayed Test-Retest

1

47-60

0.76-0.87

0.82

Black

Delayed Test-Retest

1

407-443

0.68-0.73

0.71

White