FAST: earlyMath

Number Sequence

Rating Summary

Classification Accuracyfull bubble
GeneralizabilityModerate High
Reliabilityfull bubble
Validityfull bubble
Disaggregated Reliability and Validity Datafull bubble
Efficiency
AdministrationIndividual
Administration & Scoring Time2-3 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 Number Sequence measure is part of earlyMath om 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 for reading, mathematics, and behavior, which requires no additional costs for hardware or additional materials. FAST, developed by researchers at the University of Minnesota, 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, including online certification training and support, is provided at an annual rate of $6 per student.

 

 

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 Number Sequence measure is part of earlyMath in the FAST assessment suite. This tool assesses oral counting and the understanding of the mental number line. The test is completely verbal, and no student stimulus materials are used. As the student responds to each item, the examiner marks any errors on his/her score form. There are 13 items separated by the type of question in the kindergarten measures. The first grade measure includes 14 items of the same categories.  Types of items include: Count Sequence (measures the student’s ability to count forward from 1 to 31, and also counting backward), Number After (items of various difficulty level which assess the understanding of “number after,” “one more than,” and “two more than.”), Number Before (items of various difficulty level assess understand of “number before,” “one less than,” and “two less than.”), and Number Between (measures the student’s understanding of the concept “between”). The resulting score is the number of items responded to correctly out of 13/14.

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 Number Sequence measure is intended for use in Kindergarten and 1st grade or with ages 5–7.

The assessment is individually administered in 2–3 minutes 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                    

 

20th Percentile Spring

n = 155

45th Percentile Spring

n = 155

20th Percentile Fall

n = 155

45th Percentile Fall

n = 155

False Positive Rate

0.22

0.12

0.17

0.31

False Negative Rate

0.35

0.38

0.35

0.11

Sensitivity

0.65

0.62

0.65

0.89

Specificity

0.78

0.88

0.83

0.69

Positive Predictive Power

0.34

0.71

0.41

0.61

Negative Predictive Power

0.93

0.83

0.93

0.92

Overall Classification Rate

0.76

0.79

0.81

0.76

AUC (ROC)

0.80

0.83

0.81

0.84

Base Rate

0.15

0.32

0.15

0.35

Cut Points:

7

9

3

7

At XX% Sensitivity, Specificity equals

87% sensitivity, 0.55 specificity

89% sensitivity, 0.49 specificity

91% sensitivity, 0.56 specificity

91% sensitivity, 0.62 specificity

At XX% Sensitivity, Specificity equals

74% sensitivity, 0.68 specificity

77% sensitivity, 0.65 specificity

78% sensitivity, 0.66 specificity

78% sensitivity, 0.71 specificity

At XX% Sensitivity, Specificity equals

65% sensitivity, 0.78 specificity

66% sensitivity, 0.80 specificity

70% sensitivity, 0.79 specificity

72% sensitivity, 0.76 specificity

 

 

 

 

Classification Accuracy in Predicting Proficiency on MAP

 

 

Kindergarten

(Spring; 20th Percentile)

n = 231

1st Grade

(Fall; 20th Percentile)

n = 195

1st Grade

(Spring; 20th Percentile)

n = 203

False Positive Rate

0.22

0.19

0.23

False Negative Rate

0.20

0.16

0.22

Sensitivity

0.80

0.84

0.78

Specificity

0.78

0.81

0.77

Positive Predictive Power

0.14

0.32

0.25

Negative Predictive Power

0.99

0.98

0.97

Overall Classification Rate

0.78

0.81

0.77

AUC (ROC)

0.84

0.86

0.87

Base Rate

0.04

0.10

0.09

Cut Points:

8

4

9

 

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

 

Description of cross validation study sample:

Kindergarten

  • Number of States: 12 (CO, IA, IL, IN, MA, MT, VT, OR, PA, WI) 
  • Regions: Midwest, Northeast, West
  • Gender
    • 51% Male
    • 48% Female
  • Race/Ethnicity:
    • 52% White, Non-Hispanic
    • 1% American Indian/Alaska Native
    • 3% Black, Non-Hispanic
    • 1% Asian, Pacific Islander
    • 7% Hispanic
    • 34% Unknown

 

1st Grade

  • Number of States: 6 (IA, IN, MA, MN, NY, VT)  
  • Regions: Midwest & Northeast
  • Gender
    • 49% Male
    • 51% Female
  • Eligible for free or reduced-price lunch: 32%
  • Race/Ethnicity:
    • 52% White, Non-Hispanic
    • 1% American Indian/Alaska Native
    • 3% Black, Non-Hispanic
    • 1% Asian, Pacific Islander
    • 7% Hispanic
    • 34% Unknown

Reliability

Type of Reliability

Age or Grade

n (range)

Coefficient

SEM

Information (including normative data)/Subjects

range

median

Test-Retest

K

35

 

0.80

 

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

Test-Retest

1

36

 

0.71

 

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

Interrater

K

45

0.85 – 1.00

1.00

 

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

Interrater

1

45

0.71 – 1.00

1.00

 

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

Alternate Form

K

39 – 41

0.67 - 0.82

0.75

 

5% Asian, 23% Black, 11% Hispanic, 3% Multiracial, 58% White, and 6% IEP eligible.

Coefficient alpha

K

598

 

0.76

 

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

Coefficient alpha

1

572

 

0.85

 

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

Split-Half

K

598

 

0.87

 

The same sample used to calculate coefficient alpha was used from the 2013-2014 school year.

Split-Half

1

572

 

0.91

 

The same sample used to calculate coefficient alpha was used from the 2013-2014 school year.

 

Validity

Type of Validity

Age or Grade

Test or Criterion

n (range)

Coefficient (if applicable)

Information (including normative data)/Subjects

range

Median

Concurrent

K

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

220

 

0.54

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

Predictive

K

MAP

215

 

0.70

Fall to Winter prediction. See above.

Predictive

K

MAP

212

 

0.65

Fall to Spring prediction.

Predictive

K

MAP

221

 

0.53

Winter to Spring prediction.

Concurrent

K

MAP

231

 

0.61

Data collected in Spring

Predictive

K

GMADE composite Level R

142

 

0.49

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

K

GMADE composite Level R

144

 

0.48

Winter to Spring prediction. See above.

Concurrent

K

GMADE composite Level R

150

 

0.54

Data collected in Spring. See above.

Concurrent

1

MAP

203

 

0.64

Data collected in Fall.

Concurrent

1

MAP

189

 

0.59

Data collected in Winter.

Concurrent

1

MAP

203

 

0.58

Data collected in Spring.

Predictive

1

MAP

195

 

0.64

Fall to Winter prediction.

Predictive

1

MAP

195

 

0.64

Fall to Spring prediction.

Predictive

1

MAP

188

 

0.60

Winter to Spring prediction.

Predictive

1

GMADE composite Level R

155

 

0.59

Fall to Spring prediction.

Predictive

1

GMADE composite Level R

161

 

0.56

Winter to Spring prediction.

Concurrent

1

GMADE composite Level R

173

 

0.65

Spring to Spring prediction.

Predictive 1 MAP - Math Number Sense Strand 195   0.70

Fall to Spring

Students from one district in Minnesota.

3% American Indian, 7% Asian, 3% Black, 4% Hispanic, and 84% White.

50% Female, 7% eligible for special education services, and 35% eligible for free and reduced lunch

Predictive 1 aMath 245   0.72

Early Spring to Late Spring

Students from 7 schools in Minnesota

1% American Indian, 7% Hispanic, 1% Black, 51% White, and 40% Not Specified

56% Female, 13% Eligible for Special Education Services

Predictive 1 aMath 410   0.72

Winter to Late Spring

Students from 7 schools in Minnesota

1% American Indian, 1% Asian, 26% Hispanic, 10% Black, 53% White, and 8% Not Specified

53% Female, 8% Eligible for Special Education Services

Concurrent K FAST Numberal ID 715   0.72

Fall

Students from 8 schools in Minnesota

6% American Indian, 3% Asian, 4% Hispanic, 7% Black, 77% White, and 3% Not Specified

48% Female, 12% Eligible for Special Education Services, and 46% Eligible for free and reduced lunch

Concurrent K aMath 191   0.72

End of Year

Students from 2 schools in Minnesota

24% White, 75% Not Specified

53% Female

Predictive K aMath 198   0.76

Early Spring to Late Spring

Students from 10 schools in Minnesota, Wisconsin, and Illinois.

52% Female, 80% Race Not Specified

 

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 = 125

Kindergarten

(Spring; 20th Percentile; Black)

n = 13

1st Grade

(Fall to Spring; 20th Percentile; White)

n = 117

1st Grade

(Fall to Spring; 20th Percentile; Hispanic)

n = 8

1st Grade

(Fall to Spring; 20th Percentile; Black)

n = 20

False Positive Rate

0.29

0.29

0.30

0.33

0.29

False Negative Rate

0.38

0.33

0.19

0.67

0

Sensitivity

0.62

0.67

0.81

0.67

1.00

Specificity

0.71

0.71

0.70

0.60

0.71

Positive Predictive Power

0.20

0.67

0.30

0.50

0.38

Negative Predictive Power

0.94

0.71

0.96

0.75

1.00

Overall Classification Rate

0.70

0.78

0.72

0.63

0.75

AUC (ROC)

0.75

0.76

0.82

0.80

0.79

Base Rate

0.10

0.61

0.13

0.38

0.15

Cut Points:

9

6

6

6

6

Disaggregated Reliability

Type of Reliability

Age or Grade

n (range)

Coefficient Range

Coefficient Median

Information (including normative data)/Subjects

Alpha

K

14

 

0.76

American Indian or Alaskan Native

Alpha

K

23

 

0.77

Asian or Pacific Islander

Alpha

K

22

 

0.82

Hispanic

Alpha

K

46

 

0.81

Black

Alpha

K

506

 

0.79

White

Split-Half

K

14

 

0.65

American Indian or Alaskan Native

Split-Half

K

23

 

0.82

Asian or Pacific Islander

Split-Half

K

22

 

0.82

Hispanic

Split-Half

K

46

 

0.82

Black

Split-Half

K

506

 

0.78

White

Alpha

1

10

 

0.75

Asian or Pacific Islander

Alpha

1

16

 

0.90

Asian or Pacific Islander

Alpha

1

14

 

0.69

Hispanic

Alpha

1

29

 

0.86

Black

Alpha

1

224

 

0.76

White

Split-Half

1

10

 

0.92

American Indian or Alaskan Native

Split-Half

1

16

 

0.96

Asian or Pacific Islander

Split-Half

1

14

 

0.97

Hispanic

Split-Half

1

29

 

0.88

Black

Split-Half

1

224

 

0.73

White