FAST earlyMath

Numeral Identification

Cost Technology, Human Resources, and Accommodations for Special Needs Service and Support Purpose and Other Implementation Information Usage and Reporting

The Formative Assessment System for Teachers (FAST) is a cloud-based suite of assessment and reporting tools that includes earlyMath. As of 2013-14, there is a $5 per student per year charge for the system. As a cloud-based assessment suite, there are no hardware costs or fees for additional materials. 

Computer and internet access is required for full use.

Testers will require less than 1 hour of training.

Paraprofessionals can administer the test.

FastBridge Learning
520 Nicollet Mall
Suite 910
Minneapolis, MN 55402-1057
Phone: 612-254-2534

Field tested training manuals are included and should provide all implementation information.

Access to interactive online self-guided teacher training is included at no additional cost. In-person training is available at an additional cost of $300 per hour.

earlyMath is used to monitor student progress in early mathematics in the early primary grades (typically K to 1st). Most assessments provide information on both the accuracy and rate or efficiency of performance.

The appropriate progress monitoring assessment(s) is/are chosen based on screening performance and are used to diagnose and evaluate skill deficits. Those results help guide instructional and intervention development. It is recommended that Numeral Identification be used for progress monitoring throughout Kindergarten and Grade 1 depending on specific student needs.

The Numeral Identification task assesses the student’s ability and automaticity at naming numerals. Identifying numerals involves an understanding of linking numerals with names and is often considered a gateway skill for formal numeracy (Purpura & Lonigan, 2013; Mazzocco and Thompson, 2005). 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 1 minute timed assessment that also has an inventory option. An inventory option allows the teacher to find out which numerals the student has mastered, even if the student does not complete the task in 1 minute.

Each earlyMath test takes approximately 1-4 minutes to administer; additional time required for scoring is 1 minute or less.

The Numeral Identification assessment has 40 alternate forms (20 for kindergarten and 20 for first grade.)

Rate is calculated as the number of correct numerals identified per minute. Accuracy is calculated as the number of correct numerals per number of numerals attempted. Raw scores of total and correct numerals are also provided. An inventory of numerals can be generated.

 

Reliability of the Performance Level Score

GradeK1
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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.

Test-Retest

1

36

-

0.91

-

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

Interrater

K

45

0.83-1.00

0.98

-

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

Interrater

1

45

0.92-1.00

0.98

-

A random sample of cases were selected 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; 6% IEP eligible.

Alternate Form

1

42-48

0.89-0.95

0.91

-

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

Coefficient Alpha*

K

45

-

0.89 for first 25 items

0.96 for first 37 items

0.97 for first 50 items

-

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

Coefficient Alpha*

1

45

-

0.88 for first 33 items

0.90 for first 40 items

0.92 for first 46 items

-

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

-

The same sample used to calculate coefficient alpha was used 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

-

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

*Internal consistency measures, such as coefficient alpha or split-half reliability, are inflated on timed measures because of the high percentage of incomplete items at the end of the assessment, which are those for which examinees did not respond (Crocker & Algina, 1986). As a solution to both illustrate the potential inflation and also reduce it, estimates of internal consistency (reliability) were run on the items attempted by approximately 16% of students, the items completed by 50% of students, and the items completed by approximately 84% of students. Items not completed were coded as incorrect.

Reliability of the Slope

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Validity of the Performance Level Score

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Type of Validity

Age or Grade

Test or Criterion

n (range)

Coefficient

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; 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; 12% IEP eligible.

Concurrent

1

MAP

192

-

0.42

Data collected in Winter. See First grade sample above.

Predictive

K

MAP

215

-

0.64

Fall to Winter prediction. See Kindergarten sample above.

Predictive

1

MAP

188

-

0.61

Fall to Winter prediction. See First grade sample above.

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; 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; 13% IEP eligible.

Predictive

K

GMADE composite Level R

144

-

0.47

Winter to Spring prediction. See Kindergarten sample above.

Predictive

1

GMADE composite Level 1

160

-

0.51

Winter to Spring prediction. See First grade sample above.

Concurrent

K

GMADE composite Level R

150

-

0.52

Data collected in Spring. See Kindergarten sample above. 

Concurrent

1

GMADE composite Level 1

167

-

0.48

Data collected in Spring. See First grade sample above.

 

Predictive Validity of the Slope of Improvement

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Bias Analysis Conducted

GradeK1
RatingNoNo

Disaggregated Reliability and Validity Data

GradeK1
RatingNoNo

Alternate Forms

GradeK1
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1. Evidence that alternate forms are of equal and controlled difficulty or, if IRT based, evidence of item or ability invariance:

For Kindergarten, all numerals between 0 and 31 were used based on the Minnesota State Standards. Each form of the test consists of 75 items arranged in 15 rows, 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).

For First grade, 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).

To determine parallel form construction for Kindergarten progress monitoring forms, a one-way, within-subjects (or repeated measures) ANOVA was conducted to compare the effect of alternate forms (n = 5) across 41 students on the number of mean correct responses within individuals. There was a non-significant effect for form F(4, 215) = 0.29, p=0.89. This indicates that different forms did not result in significantly different mean correct responses. To determine parallel form construction for First grade progress monitoring forms, a one-way, within-subjects (or repeated measures) ANOVA was conducted to compare the effect of alternate forms (n = 5) across 46 students on the number of mean correct responses within individuals. There was a non-significant effect for form F(4, 206) = 0.115, p=0.98. This indicates that different forms did not result in significantly different mean correct responses. See Appendix C for a descriptive of study and demographics. 

2. Number of alternate forms of equal and controlled difficulty:  

40 forms (Kindergarten N = 20; First Grade N = 20)

Rates of Improvement Specified

GradeK1
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Is minimum acceptable growth (slope of improvement or average weekly increase in score by grade level) specified in manual or published materials?

Pending 2014

a. Specify the growth standards:

Percentile

Weekly Growth (K)

Weekly Growth (1)

25th

0.44

0.26

50th

0.65

0.38

75th

0.82

0.50

b. Basis for specifying minimum acceptable growth:

Norm-referenced

"Preliminary" Kindergarten Normative Profile:

Representation: Local
Date: 2013-2014
Number of States: 1
Size: 497
Region: Midwest
Gender: 51% male, 49% female
SES: 41% eligible for free or reduced lunch
Race/Ethnicity: 84% White, 5% Black, 5% American Indian/Alaska Native, 3% Hispanic, 2% Asian/Pacific Islander
Disability classification: 10% eligible to receive special education services
 
"Preliminary" First Grade Normative Profile:
 
Representation: Local
Date: 2013-2014
Number of States: 1
Size: 384
Region: Midwest
Gender: 51% male, 49% female
SES: 43% eligible for free or reduced lunch
Race/Ethnicity: 79% White, 9% Black, 6% Hispanic, 3% Asian/Pacific Islander, 2% American Indian/Alaska Native
Disability classification: 13% eligible to receive special education services

 

End-of-Year Benchmarks

GradeK1
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1. Are benchmarks for minimum acceptable end-of-year performance specified in your manual or published materials?

Pending Fall 2014

Sensitive to Student Improvement

GradeK1
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Describe evidence that the monitoring system produces data that are sensitive to student improvement (i.e., when student learning actually occurs, student performance on the monitoring tool increases on average):

Across 497 Kindergarten students, the slope for average weekly improvement (β1Week) was significantly different than 0 (β1Week = 0.66; SE = 0.02). Across 384 First grade students, the slope for average weekly improvement (β1Week) was significantly different than 0 (β1Week = 0.38; SE = 0.02). 

Decision Rules for Changing Instruction

GradeK1
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Decision Rules for Increasing Goals

GradeK1
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Improved Student Achievement

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Improved Teacher Planning

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