FAST: earlyMath

Grouping and Place Value

Rating Summary

Classification Accuracyfull bubble
GeneralizabilityModerate High
Reliabilityfull bubble
Validityfull bubble
Disaggregated Reliability and Validity Datafull bubble
Efficiency
AdministrationIndividual or Group
Administration & Scoring Time3-4 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 Grouping and Place Value 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 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 Grouping and Place Value measure is part of earlyMath in the FAST assessment suite. This tool assesses the student’s ability to correctly produce the numeral that corresponds with a set of base-10 blocks, and his/her ability to select the correct grouping of base-10 blocks when presented with a numeral. This test is conducted on an individual or group basis, and the examiner scores the student’s work after the test is complete. The resulting score is the total number of items responded to correctly within two minutes.

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 Grouping and Place Value measure is intended for use in 1st grade or with ages 6–7.

The assessment is individually or group administered in two minutes per student or group. Scoring requires an additional one minute.  

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 = 136

False Positive Rate

0.15

False Negative Rate

0.25

Sensitivity

0.75

Specificity

0.86

Positive Predictive Power

0.33

Negative Predictive Power

0.97

Overall Classification Rate

0.85

AUC (ROC)

0.88

Base Rate

0.09

Cut Points:

4

At XX% Sensitivity, Specificity equals

91% sensitivity, 0.73 specificity

At XX% Sensitivity, Specificity equals

77% sensitivity, 0.86 specificity

At XX% Sensitivity, Specificity equals

41% sensitivity, 0.94 specificity

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Generalizability

Description of 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:

·         Number of States: 6 (IA, IN, MA, MN, NY, VT)  

·         Regions: Midwest & Northeast

·         Gender

o   49% Male

o   51% Female

·         Eligible for free or reduced-price lunch: 32%

·         Race/Ethnicity:

o   52% White, Non-Hispanic

o   1% American Indian/Alaska Native

o   3% Black, Non-Hispanic

o   1% Asian, Pacific Islander

o   7% Hispanic

o   34% Unknown

Reliability

Type of Reliability

Age or Grade

n (range)

Coefficient

SEM

Information (including normative data)/Subjects

range

median

Test-Retest

1

57

 

0.77

 

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

Inter-scorer

1

62

0.75 – 1.00

1.00

 

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

Alternate Form

1

39 - 43

0.63 - 0.86

0.82

 

1% Asian, 15% Black, 9% Hispanic, 4% Multiracial, 71% White, and 3% IEP eligible.

Coefficient alpha*

1

91

 

0.81 for first 3 items

0.82 for first 5 items

0.85 for first 7 items

 

 

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

Split-Half*

1

91

 

0.85 for first 3 items

0.87 for first 5 items

0.90 for first 7 items

 

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

1

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

194

 

0.62

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

1

MAP

192

 

0.44

Data collected in Winter. See above.

Predictive

1

MAP

188

 

0.63

Fall to Winter prediction. See above.

Predictive

1

MAP

194

 

0.56

Fall to Spring prediction. See above.

Predictive

1

GMADE composite Level 1

155

 

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

1

GMADE composite Level 1

158

 

0.58

Winter to Spring prediction. See above.

Concurrent

1

GMADE composite Level 1

151

 

0.55

Data collected in Spring. See above.

Predictive 1 aMath 261   0.69

Winter to Spring

Students from one district in Minnesota.

2% American Indian, 16% Black, 39% Hispanic, and 42% White.

50% Female, 3% eligible for special education services

Predictive 1 aMath 37   0.73

Winter to End of Year

Students from one district in Minnesota

3% American Indian, 2% Pacific Islander, 47% Hispanic, 31% Black, and 17% White,

50% Female, 3% Eligible for Special Education Services

Concurrent 1 AIMSweb Quantity Discrimination 52   0.74 See description below.
Concurrent 1 AIMSweb Missing Number 52   0.70 See description below.

Note. Correlations were disattenuated based on reported reliabilities.

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 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).

Disaggregated Reliability, Validity, and Classification Data for Diverse Populations

Disaggregated Classification Accuracy in Predicting Proficiency on the Group Mathematics Assessment and Diagnostic Evaluation (GMADE)

 

1st Grade

(Spring; 20th Percentile; White)

n = 123

1st Grade

(Spring; 20th Percentile; Hispanic)

n = 8

1st Grade

(Spring; 20th Percentile; Black)

n = 23

False Positive Rate

0.27

0.17

0.26

False Negative Rate

0.13

0

0

Sensitivity

0.88

1.00

1.00

Specificity

0.73

0.83

0.74

Positive Predictive Power

0.33

0.67

0.44

Negative Predictive Power

0.98

1.00

1.00

Overall Classification Rate

0.75

0.86

0.78

AUC (ROC)

0.86

0.83

0.89

Base Rate

0.13

0.25

0.17

Cut Points:

5

5

5

Disaggregated Reliability

Type of Reliability

Age or Grade

n (range)

Coefficient Range

Coefficient Median

SEM

Information (including normative data)/Subjects

Split-Half

1

38

 

0.91

White

Split-Half

Split-Half

1

21

 

0.89

Other (e.g., Asian, Black, Hispanic, American Indian)

Split-Half