FAST: earlyMath

Decomposing (1)

Rating Summary

Classification Accuracyfull bubble
GeneralizabilityModerate High
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 Decomposing-One 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 Decomposing-One measure is part of earlyMath in the FAST assessment suite.

This tool assesses the student’s ability to put together (compose) and take apart (decompose) numbers by using “parts” and a “whole.” Composing and decomposing is a vital step for students towards understanding base-ten reasoning and form strategies for addition facts summing greater than 10 (Baroody, 2006). As the student verbalizes the number that represents the missing “part,” the examiner marks any errors on his/her copy of the score form. The resulting score is the total number of items responded to correctly per 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 Decomposing-One measure is intended for use in grade 1 or with ages 6–7.

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                                       

 

20th Percentile Spring

n = 154

False Positive Rate

0.10

False Negative Rate

0.18

Sensitivity

0.82

Specificity

0.90

Positive Predictive Power

0.38

Negative Predictive Power

0.98

Overall Classification Rate

0.89

AUC (ROC)

0.93

Base Rate

0.07

Cut Points:

5

At XX% Sensitivity, Specificity equals

93% sensitivity, 0.48 specificity

At XX% Sensitivity, Specificity equals

82% sensitivity, 0.64 specificity

At XX% Sensitivity, Specificity equals

68% sensitivity, 0.86 specificity

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Generalizability

Description of study sample:

·         Number of States: 1 Minnesota

·         Regions: 1

·         Gender

o   57.9% Male

o   42.2% 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

36

 

0.83

 

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

Inter-rater

1

45

0.67 – 1.00

1.00

 

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

Alternate Form

1

39-43

0.75 - 0.87

0.83

 

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

Coefficient alpha

1

573

 

0.79 for first 6 items

0.87 for first 10 items

0.88 for first 13 items

 

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

Split-Half

1

573

 

0.82 for first 6 items

0.88 for first 10 items

0.90 for first 13 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

 

0.57

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

1

MAP

192

 

0.51

Data collected in Winter. See above.

Predictive

1

MAP

188

 

0.59

Fall to Winter prediction. See above.

Predictive

1

MAP

192

 

0.58

Fall to Spring prediction. See above.

Predictive

1

MAP

187

 

0.55

Winter to Spring prediction. See above.

Concurrent

1

MAP

203

 

0.51

Data Collected in Spring. See above.

Predictive

1

GMADE composite Level 1

155

 

0.59

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

161

 

0.56

Winter to Spring prediction. See above.

Concurrent

1

GMADE composite Level 1

166

 

0.63

Data collected in Spring. See above.

Concurrent 1 aMath 471   0.77

Late Spring

Students from 7 schools in Minnesota

1% American Indian, 1% Asian, 25% Hispanic, 10% Black, 51% White, and 11% Not Specified

53% Female, 9 % Eligible for Special Education Services

Predictive 1 aMath 257   0.71

Fall to Late Spring

Students from 7 schools in Minnesota

6% Hispanic, 1% Black, 47% White, and 46% Not Specified

56% Female, 12% Eligible for Special Education Services

Predictive 1 aMath 410   0.75

Early Spring to Late Spring

Students from 7 schools in Minnesota

7% Hispanic, 1% Black, 51% White, and 11% Not Specified

55% Female, 13% Eligible for Special Education Services

Predictive 1 aMath 85   0.73

Late Spring to End of Year

Students from 5 schools in Minnesota

1% American Indian, 2% Asian, 20% Hispanic, 13% Black, 8% White, and 55% Not Specified

54% Female, 7% Eligible for Special Education Services

 

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
(Winter to Spring; 20th Percentile; White)
n = 120

1st Grade
(Winter to Spring; 20th Percentile; Hispanic)
n = 10

1st Grade
(Winter to Spring; 20th Percentile; Black)
n = 23

False Positive Rate

0.29

0.17

0.05

False Negative Rate

0.35

0.25

0.75

Sensitivity

0.65

0.75

0.94

Specificity

0.71

0.83

0.75

Positive Predictive Power

0.27

0.75

0.75

Negative Predictive Power

0.92

0.83

0.92

Overall Classification Rate

0.70

0.80

0.91

AUC (ROC)

0.78

0.85

0.90

Base Rate

0.14

0.40

0.17

Cut Points:

6

6

6

 

Disaggregated Reliability

Type of Reliability

Age or Grade

n (range)

Coefficient Range

Coefficient Median

Information (including normative data)/Subjects

Alpha

1

10

 

0.87

American Indian or Alaskan Native

Alpha

1

16

 

0.92

Asian or Pacific Islander

Alpha

1

14

 

0.87

Hispanic

Alpha

1

29

 

0.89

Black

Alpha

1

221

 

0.86

White

Split Half

1

10

 

0.85

American Indian or Alaskan Native

Split Half

1

16

 

0.89

Asian or Pacific Islander

Split Half

1

14

 

0.75

Hispanic

Split Half

1

29

 

0.65

Black

Split Half

1

221

 

0.67

White