FAST: earlyMath

Decomposing (K)

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-KG 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, 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-KG measure is part of earlyMath in the FAST assessment suite. This tool assesses the student’s ability to automatically decompose (take apart) fives and tens. The student is presented with eight items (four decomposing from five, and four decomposing from ten). Each item presented to the student is a series of five or ten frames filled with photos of food (e.g., cookies, bananas, apples). The examiner asks “I ate 2, how many are left?” The resulting score is the number of items answered correctly (out of 8). Students are asked to answer each item without using any counting strategies (e.g., counting on from one, counting dots with fingers). This is an untimed measure.

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-KG measure is intended for use in Kindergarten or with ages 5-6.

The assessment is individually administered in 1–2 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 Winter

n = 143

45th Percentile Winter

n = 143

False Positive Rate

0.23

0.25

False Negative Rate

0.19

0.24

Sensitivity

0.81

0.76

Specificity

0.77

0.75

Positive Predictive Power

0.38

0.59

Negative Predictive Power

0.96

0.57

Overall Classification Rate

0.78

0.76

AUC (ROC)

0.83

0.79

Base Rate

0.15

0.32

Cut Points:

3

4

At XX% Sensitivity, Specificity equals

91% sensitivity, 0.67 specificity

89% sensitivity, 0.34 specificity

At XX% Sensitivity, Specificity equals

81% sensitivity, 0.77 specificity

76% sensitivity, 0.75 specificity

At XX% Sensitivity, Specificity equals

53% sensitivity, 0.86 specificity

65% sensitivity, 0.74 specificity

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Generalizability

Description of study sample:

·         Number of States: 1 Minnesota

·         Regions: 1

·         Gender

o   50.69% 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 cross validation study sample:

·         Number of States: 12 (CO, IA, IL, IN, MA, MT, VT, OR, PA, WI) 

·         Regions: Midwest, Northeast, West

·         Gender

o   51% Male

o   48% Female

·         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

K

38

 

0.68

 

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

Inter-rater

K

45

0.75 – 1.00

1.00

 

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

Split-half

K

605

 

0.83

 

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

Cronbach’s alpha

K

605

 

0.80

 

The same sample used to calculate split-half 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)

223

 

0.47

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

Concurrent

K

MAP

231

 

0.46

Data collected in Spring. See above.

Predictive

K

MAP

221

 

0.52

Winter to Spring prediction. See above.

Predictive

K

GMADE composite Level R

143

 

0.43

Winter to Spring prediction. 3% American Indian, 4% Asian, 8% Black, 6% Hispanic, 80% White, 29% Free and reduced lunch, 8% IEP eligible.

Concurrent

K

GMADE composite Level R

157

 

0.44

Data collected in Spring. 3% American Indian, 4% Asian, 8% Black, 6% Hispanic, 80% White, 29% Free and reduced lunch, 8% IEP eligible.

Concurrent K AIMSweb Quantity Discrimination 58   0.72 See description below

Note. Correlations were disattenuated based on reported reliabilities.

The validity evidence study coefficient for Decomposing K 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.

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). Discriminating the quantity or size of numbers is identified as a key skill in early numeracy development by both educational, and cognitive research, and is often used as a screener of early mathematics development (Gersten, 2012). 

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 = 14

False Positive Rate

0.32

0.38

False Negative Rate

0.21

0.33

Sensitivity

0.79

0.67

Specificity

0.68

0.63

Positive Predictive Power

0.23

0.57

Negative Predictive Power

0.96

0.71

Overall Classification Rate

0.69

0.64

AUC (ROC)

0.79

0.77

Base Rate

0.11

0.43

Cut Points:

5

3

 

Disaggregated Reliability

 

Type of Reliability

Age or Grade

n (range)

Coefficient Range

Coefficient Median

Information (including normative data)/Subjects

Alpha

K

14

 

0.87

American Indian or Alaskan Native

Alpha

K

23

 

0.79

Asian or Pacific Islander

Alpha

K

22

 

0.82

Hispanic

Alpha

K

46

 

0.80

Black

Alpha

K

506

 

0.73

White