FAST earlyMath
Number Sequence

Descriptive Information

Please provide a description of your tool:

FAST™ earlyMath Number Sequence is used to monitor student progress in early mathematics in the early primary grades and assesses oral counting and comprehension 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(14 for grade 1) items separated by the type of question (count sequence, number after, number before, and number between). 13 number sequence items involving counting on from a given number, counting backward from a given number; identifying the number that comes before, after, or between; and determine one or two more or less than a number, or 5 or 10 more or less than a number (grade 1). The resulting score is the number of items responded to correctly out of 13 (or 14).

Is your tool designed to measure progress towards an end-of-year goal (e.g., oral reading fluency) or progress towards a short-term skill (e.g., letter naming fluency)?

End-year goal
Short-term skill

The tool is intended for use with the following grade(s).

Preschool / Pre - kindergarten
Kindergarten
First grade
Second grade
Third grade
Fourth grade
Fifth grade
Sixth grade
Seventh grade
Eighth grade
Ninth grade
Tenth grade
Eleventh grade
Twelfth grade

The tool is intended for use with the following age(s).

0-4 years old
5 years old
6 years old
7 years old
8 years old
9 years old
10 years old
11 years old
12 years old
13 years old
14 years old
15 years old
16 years old
17 years old
18 years old

The tool is intended for use with the following student populations.

Students in general education
Students with disabilities
English language learners

ACADEMIC ONLY: What dimensions does the tool assess?

Reading

Global Indicator of Reading Competence
Listening Comprehension
Vocabulary
Phonemic Awareness
Decoding
Passage Reading
Word Identification
Comprehension

Spelling & Written Expression

Global Indicator of Spelling Competence
Global Indicator of Writting Expression Competence

Mathematics

Global Indicator of Mathematics Comprehension
Early Numeracy
Mathematics Concepts
Mathematics Computation
Mathematics Application
Fractions
Algebra

Other

Please describe specific domain, skills or subtests:

Number Sequence

BEHAVIOR ONLY: Please identify which broad domain(s)/construct(s) are measured by your tool and define each sub-domain or sub-construct.

BEHAVIOR ONLY: Which category of behaviors does your tool target?

Acquisition and Cost Information

Administration

BEHAVIOR ONLY: What type of administrator is your tool designed for?

General education teacher
Special education teacher
Parent
Child
External observer
Other

If other, please specify:

BEHAVIOR ONLY: What is the administration format?

Direct observation
Rating scale
Checklist
Performance measure
Other

If other, please specify:

BEHAVIOR ONLY: What is the administration setting?

General education classroom
Special education classroom
School office
Recess
Lunchroom
Home
Other

If other, please specify:

Does the program require technology?

Yes

If yes, what technology is required to implement your program? (Select all that apply)

Computer or tablet
Internet connection
Other technology (please specify)

What is the administration context?

Individual

Small group   If small group, n=

Large group   If large group, n=

Computer-administered
Other

If other, please specify:

The stimulus material is presented in paper form and responses are recorded by the administrator on a digital record form in the FAST system.

ACADEMIC ONLY: What are the discontinue rules?

No discontinue rules provided
Basals
Ceilings
Other

If other, please specify:

If the student incorrectly responds to all items 1-5, discontinue the task.

Training & Scoring

Training

Is training for the administrator required?

Yes

Describe the time required for administrator training, if applicable:

Less than one hour of training.

Please describe the minimum qualifications an administrator must possess.

No minimum qualifications

Are training manuals and materials available?

Yes

Are training manuals/materials field-tested?

No

Are training manuals/materials included in cost of tools?

Yes

If No, please describe training costs:

Can users obtain ongoing professional and technical support?

Yes

If Yes, please describe how users can obtain support:

Users have access to ongoing technical support.

Scoring

BEHAVIOR ONLY: What types of scores result from the administration of the assessment?

Score

Observation	Behavior Rating
Frequency Duration Interval Latency	Raw score

Conversion

Observation	Behavior Rating
Rate Percent	Standard score Subscale/ Subtest Composite Stanine Percentile ranks Normal curve equivalents IRT based scores

Interpretation

Observation	Behavior Rating
Error analysis Peer comparison Rate of change	Dev. benchmarks Age-Grade equivalent

How are scores calculated?

Manually (by hand)
Automatically (computer-scored)
Other

If other, please specify:

What is the basis for calculating performance level and percentile scores?

Age norms
Grade norms
Classwide norms
Schoolwide norms
Stanines
Normal curve equivalents

What types of performance level scores are available?

Raw score
Standard score
Percentile score
Grade equivalents
IRT-based score
Age equivalents
Stanines
Normal curve equivalents
Developmental benchmarks
Developmental cut points
Equated
Probability
Lexile score
Error analysis
Composite scores
Subscale/subtest scores
Other

If other, please specify:

Please describe the scoring structure. Provide relevant details such as the scoring format, the number of items overall, the number of items per subscale, what the cluster/composite score comprises, and how raw scores are calculated.

Raw scores are calculated as the number of items correct.

Do you provide basis for calculating slope (e.g., amount of improvement per unit in time)?

Yes

ACADEMIC ONLY: Do you provide benchmarks for the slopes?

Yes

ACADEMIC ONLY: Do you provide percentile ranks for the slopes?

Yes

What is the basis for calculating slope and percentile scores?

Age norms
Grade norms
Classwide norms
Schoolwide norms
Stanines
Normal curve equivalents

Describe the tool’s approach to progress monitoring, behavior samples, test format, and/or scoring practices, including steps taken to ensure that it is appropriate for use with culturally and linguistically diverse populations and students with disabilities.

Users define a progress monitoring schedule that includes frequency of administration, an end goal date, and target score. For each data point, a single form is administered. Accuracy and rate scores are computed and plotted across time. Scores and trends are compared to a performance target to determine student response to instruction and intervention.

Rates of Improvement and End of Year Benchmarks

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

Yes

If yes, specify the growth standards:

National growth norms, representing average weekly rates of improvement (ROI) from fall to spring , and derived from the full population of students are used as the basis for acceptable growth. Using the median ROI growth rate for each measure and grade, the FAST system computes growth rate benchmarks based on 80% , 100%, 120% and 150% of the median. The 120% rate, called "Ambitious" in the system serves as the FAST recommended growth target. This target was chosen because research show that Tier 2 and Tier 3 students receiving appropriate, research-based intensive intervention should expect to growth about 20% faster than the general population.

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

Yes

If yes, specify the end-of-year performance standards:

Minimum acceptable end-of-year performance are based on a national percentile threshold. For all grades and assessments the spring 40th national percentile is used.

What is the basis for specifying minimum acceptable growth and end of year benchmarks?

Norm-referenced
Criterion-referenced
Other

If other, please specify:

False

National representation (check all that apply):

Northeast:

New England

Middle Atlantic

Midwest:

East North Central

West North Central

South:

South Atlantic

East South Central

West South Central

West:

Mountain

Pacific

Local representation (please describe, including number of states)

We have national demographically matched norms based on data obtained in 20 states.

Date

2017-2018

Size

36417

Gender (Percent)

Male

50.1

Female

49.9

Unknown

SES indicators (Percent)

Eligible for free or reduced-price lunch

48%

Other SES Indicators

Race/Ethnicity (Percent)

White, Non-Hispanic

45.2

Black, Non-Hispanic

13.7

Hispanic

26.6

American Indian/Alaska Native

Asian/Pacific Islander

8.2

Other

6.2

Unknown

Disability classification (Please describe)

Not reported

First language (Please describe)

Not reported

Language proficiency status (Please describe)

Not reported

Do you provide, in your user’s manual, norms which are disaggregated by race or ethnicity? If so, for which race/ethnicity?

White, Non-Hispanic
Black, Non-Hispanic
Hispanic
American Indian/Alaska Native
Asian/Pacific Islander
Other
Unknown

If criterion-referenced, describe procedure for specifying criterion for adequate growth and benchmarks for end-of-year performance levels.

Describe any other procedures for specifying adequate growth and minimum acceptable end of year performance.

Reliability

Grade	Kindergarten	Grade 1
Rating

Legend

Convincing evidence

Partially convincing evidence

Unconvincing evidence

Data unavailable

^dDisaggregated data available

*Offer a justification for each type of reliability reported, given the type and purpose of the tool.

Inter-rater reliability is an appropriate measure of form reliability because it demonstrates the stability of scores across administrators. Because earlyMath Number Sequence uses fixed forms for progress monitoring, it is important to demonstrate that alternate forms provide consistent measurement of students' basic math computation skills. Alternate form reliability was calculated to demonstrate consistency between progress monitoring forms. This reliability coefficient was calculated from actual progress monitoring data using scores from forms administered no more than two weeks apart.

*Describe the sample(s), including size and characteristics, for each reliability analysis conducted.

For alternate form reliability, the data file consisted of all scores collected during the 2018-2019 school year. The sample demographics represent at least 15 states in each grade, all race/ethnicity categories, urban, suburban, and rural school districts, and the full range of socio-economic status. See results below for specific sample sizes by tool, grade, and analysis. Data for the inter-rater reliability analysis came from administrations done in 2014 by experienced graduate students who attended a 2-hour training collected the data. After the first testing session. Subtests were administered to students in nine elementary schools within three school districts in a metropolitan area in the Midwest. Students were administered five randomly selected progress monitoring forms. District A was about 56% White, 14% Black, 10% Hispanic, and 19% Asian/Pacific Islander. About 45% of students were eligible to receive free/reduced lunch and 13% were eligible for special education services. District B was about 93% White, 4% Black, 3% Hispanic, and 4% Asian/Pacific Islander. About 17% of students were eligible to receive free/reduced lunch and 10% were eligible for special education services. District C was about 80% White, 7% Black, 5% Hispanic, and 11% Asian/Pacific Islander. About 45% of students were eligible to receive free/reduced lunch and 10% were eligible for special education services.

*Describe the analysis procedures for each reported type of reliability.

For alternate form reliability the reliability coefficient was calculated from actual progress monitoring data using scores from forms administered no more than two weeks apart. Inter-rater reliability is a measure of the extent to which student scores are consistent across different examiners or scorers. Estimates of inter-rater reliability are based on two independent scorers, and the coefficients represent the level of agreement between examiners or raters.

*In the table(s) below, report the results of the reliability analyses described above (e.g., model-based evidence, internal consistency or inter-rater reliability coefficients). Include detail about the type of reliability data, statistic generated, and sample size and demographic information.

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Do you have reliability data that are disaggregated by gender, race/ethnicity, or other subgroups (e.g., English language learners, students with disabilities)?

No

If yes, fill in data for each subgroup with disaggregated reliability data.

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Validity

Grade	Kindergarten	Grade 1
Rating

Legend

Convincing evidence

Partially convincing evidence

Unconvincing evidence

Data unavailable

^dDisaggregated data available

*Describe each criterion measure used and explain why each measure is appropriate, given the type and purpose of the tool.

FAST earlyMath Decomposing is an appropriate criterion measure for earlyMath Number Sequence. The criterion tool is part of the FAST progress monitoring system; but, measures a different skill from earlyMath Number Sequence. The measures have no overlapping items. earlyMath Number Sequence assesses student counting and number line understanding, which is a prerequisite skill for the development of early and later math skills. Math skills exist on a continuum from recognizing magnitude and number identification skills to math computation and mathematical thinking. Number Sequence measures the early math skill of counting and number line understanding and it is reasonable to compare it to the nearly adjacent, but distinct, skill of breaking numbers into parts as measured by Decomposing.

*Describe the sample(s), including size and characteristics, for each validity analysis conducted.

The data file consisted of all scores collected during the 2018-2019 school year. The sample demographics represent at least 15 states in each grade, all race/ethnicity categories, urban, suburban, and rural school districts, and the full range of socio-economic status. See results below for specific sample sizes by tool, grade, and analysis.

*Describe the analysis procedures for each reported type of validity.

Concurrent validity was calculated by correlating student scores during the same season administration of the earlyMath Number Sequence tool and the FAST aMath criterion measure. Predictive validity was calculated by correlating student scores adjacent season administrations (for example, Fall to Winter) of the earlyMath Number Sequence tool and the FAST earlyMath Decomposing criterion measure.

*In the table below, report the results of the validity analyses described above (e.g., concurrent or predictive validity, evidence based on response processes, evidence based on internal structure, evidence based on relations to other variables, and/or evidence based on consequences of testing), and the criterion measures.

Results from other forms of validity analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Describe the degree to which the provided data support the validity of the tool.

earlyMath Number Sequence is designed to measure foundational math computation skills that are critical to overall success in mathematics, and are sensitive to interventions delivered through MTSS. As such demonstrating the relationship between scores on earlyMath Number Sequence and a broader measure of math ability reflects this purpose. Concurrent and predictive validity are both reasonable metrics for evaluating the validity of a progress monitoring tool. The results provide strong evidence of the value and validity of using earlyMath Number Sequence to predict more general math outcomes.

Do you have validity data that are disaggregated by gender, race/ethnicity, or other subgroups (e.g., English language learners, students with disabilities)?

No

If yes, fill in data for each subgroup with disaggregated validity data.

Results from other forms of validity analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Bias Analysis

Have you conducted additional analyses related to the extent to which your tool is or is not biased against subgroups (e.g., race/ethnicity, gender, socioeconomic status, students with disabilities, English language learners)? Examples might include Differential Item Functioning (DIF) or invariance testing in multiple-group confirmatory factor models.

No

If yes,

a. Describe the method used to determine the presence or absence of bias:

b. Describe the subgroups for which bias analyses were conducted:

c. Describe the results of the bias analyses conducted, including data and interpretative statements. Include magnitude of effect (if available) if bias has been identified.

Sensitivity: Reliability of Slope

Grade	Kindergarten	Grade 1
Rating

Legend

Convincing evidence

Partially convincing evidence

Unconvincing evidence

Data unavailable

^dDisaggregated data available

Describe the sample, including size and characteristics. Please provide documentation showing that the sample was composed of students in need of intensive intervention. A sample of students with intensive needs should satisfy one of the following criteria: (1) all students scored below the 30th percentile on a local or national norm, or the sample mean on a local or national test fell below the 25th percentile; (2) students had an IEP with goals consistent with the construct measured by the tool; or (3) students were non-responsive to Tier 2 instruction. Evidence based on an unknown sample, or a sample that does not meet these specifications, may not be considered.

The data file consisted of all scores collected during the 2018-2019 school year in which the students were below the 30th national percentile or lower. The sample demographics represent at least 15 states in each grade, all race/ethnicity categories, urban, suburban, and rural school districts, and the full range of socio-economic status. See results below for specific sample sizes by tool, grade, and analysis.

Describe the frequency of measurement (for each student in the sample, report how often data were collected and over what span of time).

Data for this analysis was comprised of students for whom there was data for at least 10 data points collected over at least 20 weeks.

Describe the analysis procedures.

The split-half method, in which the slope from all odd administrations was correlated with the slope from all even administrations was used to compute the reliability of slope. The sample was limited to at-risk students with a national percentile below the 30th percentile, and those who had at least 10 observations over a 20 week span.

In the table below, report reliability of the slope (e.g., ratio of true slope variance to total slope variance) by grade level (if relevant).

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Do you have reliability of the slope data that is disaggregated by subgroups (e.g., race/ethnicity, gender, socioeconomic status, students with disabilities, English language learners)?

No

If yes, fill in data for each subgroup with disaggregated reliability of the slope data.

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Sensitivity: Validity of Slope

Grade	Kindergarten	Grade 1
Rating

Legend

Convincing evidence

Partially convincing evidence

Unconvincing evidence

Data unavailable

^dDisaggregated data available

Describe each criterion measure used and explain why each measure is appropriate, given the type and purpose of the tool.

Describe the sample(s), including size and characteristics. Please provide documentation showing that the sample was composed of students in need of intensive intervention. A sample of students with intensive needs should satisfy one of the following criteria: (1) all students scored below the 30th percentile on a local or national norm, or the sample mean on a local or national test fell below the 25th percentile; (2) students had an IEP with goals consistent with the construct measured by the tool; or (3) students were non-responsive to Tier 2 instruction. Evidence based on an unknown sample, or a sample that does not meet these specifications, may not be considered.

Describe the frequency of measurement (for each student in the sample, report how often data were collected and over what span of time).

Describe the analysis procedures for each reported type of validity.

In the table below, report predictive validity of the slope (correlation between the slope and achievement outcome) by grade level (if relevant).
NOTE: The TRC suggests controlling for initial level when the correlation for slope without such control is not adequate.

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published validity studies:

No

Provide citations for additional published studies.

Describe the degree to which the provided data support the validity of the tool.

Do you have validity of the slope data that is disaggregated by subgroups (e.g., race/ethnicity, gender, socioeconomic status, students with disabilities, English language learners)?

No

If yes, fill in data for each subgroup with disaggregated validity of the slope data.

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published validity studies:

No

Provide citations for additional published studies.

Alternate Forms

Grade	Kindergarten	Grade 1
Rating

Legend

Convincing evidence

Partially convincing evidence

Unconvincing evidence

Data unavailable

^dDisaggregated data available

Describe the sample for these analyses, including size and characteristics:

Forms were developed carefully to achieve content balance. Thus, each form was derived from a common blueprint. To demonstrate empirically the equivalence of forms, we used progress monitoring data. After selecting students who scored below the 30th percentile and had at least 10 observations over 20 weeks, we calculated a mean score for each form adjusted for typical growth. The form means were subtracted for the grand mean for all forms within the grade of interest. That difference was converted to standard deviation units. Comparability of the entire set of 20 forms is also summarized using analysis of variance where Form is treated as a fixed factor. The results indicate that Form accounts for a very small amount of the total score variance (between 0% and 2%). This is a very small percent and will have a trivial effect on the growth slope over the 20 or so administrations that are common for progress monitoring. The data file consisted of all scores collected during the 2018-2019 school year in which the students were below the 30th national percentile or lower. The sample demographics represent at least 15 states in each grade, all race/ethnicity categories, urban, suburban, and rural school districts, and the full range of socio-economic status. See results below for specific sample sizes by tool, grade, and analysis.

What is the number of alternate forms of equal and controlled difficulty?

20

If IRT based, provide evidence of item or ability invariance

If computer administered, how many items are in the item bank for each grade level?

N/A

If your tool is computer administered, please note how the test forms are derived instead of providing alternate forms:

N/A

Decision Rules: Setting & Revising Goals

Grade	Kindergarten	Grade 1
Rating

Legend

Convincing evidence

Partially convincing evidence

Unconvincing evidence

Data unavailable

^dDisaggregated data available

In your manual or published materials, do you specify validated decision rules for how to set and revise goals?

No

If yes, specify the decision rules:

What is the evidentiary basis for these decision rules?
NOTE: The TRC expects evidence for this standard to include an empirical study that compares a treatment group to a control and evaluates whether student outcomes increase when decision rules are in place.

Decision Rules: Changing Instruction

Grade	Kindergarten	Grade 1
Rating

Legend

Convincing evidence

Partially convincing evidence

Unconvincing evidence

Data unavailable

^dDisaggregated data available

In your manual or published materials, do you specify validated decision rules for when changes to instruction need to be made?

No

If yes, specify the decision rules:

What is the evidentiary basis for these decision rules?
NOTE: The TRC expects evidence for this standard to include an empirical study that compares a treatment group to a control and evaluates whether student outcomes increase when decision rules are in place.