Istation
Istation Math Formative Assessment

Descriptive Information

Please provide a description of your tool:

Istation Math Formative Assessment is a web-based computer adaptive formative assessment intended for students in grades PreK-8. The assessment is intended to provide teachers and administrators with student test results to answer two questions: (a) whether students are at risk of failure and (b) the degree of intensity of instructional support students need to be successful. Istation Math Formative Assessment can be administered individually or in group settings. The assessment is administered in English. Most students complete the assessment within 30 minutes. No additional scoring time is required for the assessment. Teachers can be trained on ISIP Math through either a webinar or an in-person training session. Training takes between 1 and 4 hours. All training materials are online and are created by Istation. Reports are available for both individual and groups of students indicating single administration results and comparisons of results over time. All reports include student-scaled scores and tier levels based on student percentiles.

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:

Geometry, Data Analysis, Measurement, Probablility (select locations only), Personal Financial Literacy (certain locations only)

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:

ACADEMIC ONLY: What are the discontinue rules?

No discontinue rules provided
Basals
Ceilings
Other

If other, please specify:

Adaptive test stopping criteria based on minimized standard error of measurement

Training & Scoring

Training

Is training for the administrator required?

Yes

Describe the time required for administrator training, if applicable:

1-4 hours of training

Please describe the minimum qualifications an administrator must possess.

Paraprofessional at minimum

No minimum qualifications

Are training manuals and materials available?

Yes

Are training manuals/materials field-tested?

Yes

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:

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.

Ability scores are estimated using Bayesian EAP with an informative prior under a 2 PL unidimensional IRT model. Reported scale scores are generated through a linear transformation of the raw IRT-based ability scores. An overall ability is estimated after all of the appropriate sub-contents (number and operations, geometry, algebra, measurement, ratios and proportional relationships, probability and statistics, personal financial literacy, and mathematical reasoning) are measured based on the responses from all items.

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

No

ACADEMIC ONLY: Do you provide benchmarks for the slopes?

No

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

No

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.

Ability scale scores are compared to cut-points determined from a nationally representative norming sample to classify students into one of three instructional tiers. Ongoing reviews of item parameters, score scaling, and the setting of cut points are practiced for the Istation Math Formative Assessment. The data used for the item calibration was based on an ethnically diverse regional sample, including urban and suburban students of varied abilities and backgrounds.

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 norms for Istation Math Formative Assessment enable teachers, parents, and students to know how their students’ scores compare with a nationally representative sample of children in their particular grade. Norming samples are obtained as part of Istation's ongoing research in assessing math ability. The samples were drawn from enrolled Istation Math Formative Assessment users during the 2018-2019 school year for overall scores and 2019-2020 for domain scores. Considerable attention was given to ensure the sample was nationally representative of students in pre-kindergarten through 8th grade with respect to the demographic variables of age, race/ethnicity, gender, socioeconomic status, Special education services, and English language proficiency. Norming establishes the Instructional Tier Goals used to determine Instructional Tiers for each month. Consistent with other reading assessments, Istation has defined a three-tier normative grouping based on indices associated with the 20th and 40th percentiles. Students with an index on or above the 40th percentile for their grade are placed into Tier 1. Students with an index below the 20th percentile are placed into Tier 3. These tiers are used to guide educators in determining the level of instruction for each student.

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:

Istation establishes Instruction Tier Goals to determine Instructional Tiers for each month of the year. The monthly goals for May or June (determined by each customer) are used as the end-of-year performance goal.

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)

Date

2018-2019 for Overall Scores, 2019-2020 for Domain Scores

Size

71,500 and 71,506

Gender (Percent)

Male

32%

Female

30%

Unknown

38%

SES indicators (Percent)

Eligible for free or reduced-price lunch

Other SES Indicators

Grades Prek-5: High Poverty Schools: 35.6% ; Mid High Poverty Schools: 26%; Mid Low Poverty Schools: 21%; Low Poverty Schools: 16.4%; Private and Private Charter Schools: 1.3% Grades 6-8: High Poverty Schools: 34% ; Mid High Poverty Schools: 25%; Mid Low Poverty Schools: 22.4%; Low Poverty Schools:18.1%; Private and Private Charter Schools: 1%

Race/Ethnicity (Percent)

White, Non-Hispanic

18%

Black, Non-Hispanic

7%

Hispanic

15%

American Indian/Alaska Native

unknown

Asian/Pacific Islander

2%

Other

3%

Unknown

56%

Disability classification (Please describe)

First language (Please describe)

Language proficiency status (Please describe)

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	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Rating	d	d	d	d	d	d	d	d	d

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.

Cronbach’s (1951) coefficient alpha is typically used as an indicator of reliability across test items within a testing instance. However, Cronbach’s Alpha is not appropriate for any IRT-based measure because alpha assumes that all students in the testing instance respond to a common set of items. Due to its very nature, students taking a CAT-based assessment, such as Istaton Math Formative Assessment, will receive a custom set of items based on their initial estimates of ability and response patterns. Thus, students do not respond to a common set of items. The IRT analog to classical internal consistency is marginal reliability (Bock & Mislevy, 1982). Marginal reliability is a method of combining the variability in estimating abilities at different points on the ability scale into a single index. Like Cronbach’s alpha, marginal reliability is a unitless measure bounded by 0 and 1, and it can be used with Cronbach’s alpha to directly compare the internal consistencies of classical test data to IRT-based test data. Istation Math Formative Assessment has stopping criteria based on minimizing the standard error of the ability estimate. As such, the lower limit of the marginal reliability of the data for any testing instance of Istation Math Formative Assessment will always be approximately 0.90. Test-retest Reliability: Students can take the Istation Math Formative Assessment multiple times a year. This type of evidence allows to examine how consistently students respond to the assessment over different occasions. Evidence of test-retest stability was obtained for a subset of the normed sample. Students who tested twice within a time interval of 2-21 days in the beginning, middle, and end of the year were selected in this study.

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

Samples were derived from the total population of students using the Istation Math Formative Assessment throughout the 2018-2019 school year. Sample sizes ranged from 1,766-9,932 students in K grade 8 across the United States to estimate IRT-based reliability. For test-retest, a subset of the normed sample was used for the purpose of this study. Sample sizes ranged from 1,714-52,633 across K-grade 8

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

Istation derived IRT-based reliability from Classical Test Theory standpoint to Item Response Theory. Test-retest reliability of Istation Math Formative Assessment was estimated as the Pearson correlation of student scaled scores for a set of students who took ISIP twice during the school year in 2018-19. The confidence interval (CI) for the test-retest reliability coefficient was obtained using the standard CI for a Pearson correlation (i.e., via the Fisher z-transformation).

*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:

Yes

Provide citations for additional published studies.

Istation’s Indicators of Progress (ISIP) Math: Technical Report (2021).

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

Yes

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	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Rating	d	d	d	d	d	d

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.

The criterion measure in Kindergarten through grade 5 for both types of validity analyses (concurrent and predictive) is the NWEA MAP math assessment. The measure is an appropriate criterion because it measures a construct hypothesized to be related to Istation Math Formative Assessment overall math. NWEA MAP is external as MAP and Istation Math Formative Assessment are published by separate companies. Other criterion measures used for both types of validity analyses were the Oklahoma School Testing Program (OSTP) assessment for grades 3 -8 (concurrent), the Idaho Standards Achievement Test (ISAT) for grades 3-5 (concurrent), and the STAAR assessment for grades 3-5 (predictive and concurrent). OSTP is an appropriate measure because it provides a broad indicator of overall math ability, similar to Istation Math Formative Assessment overall math scores. Istation Math Formative Assessment, OSTP, ISAT, and STAAR are independent of each other as each measure is published by different companies. The STAAR assessment is published for the Texas Education Agency.

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

Concurrent and predictive analyses of NWEA MAP data were conducted on a sample of students from Idaho. The sample sizes ranged from 220-247 across grades. STAAR data were collected from one state with sample sizes ranging from 21-613. ISAT data were collected from one state with sample sizes ranging from 194-222. OSTP data were collected from one state with sample sizes ranging from 165-192.

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

Validity coefficients were calculated by computing Pearson product-moment correlations between Istation Math Formative Assessment and the criterion measures. 95% confidence intervals were computed using the Fisher Z transformation method. Predictive validity examines associations between BOY and EOY, whereas concurrent validity considers associations between the measures at EOY.

*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:

Yes

Provide citations for additional published studies.

Patarapichayatham, C., & Locke, V. (2020a). Linking the ACT Aspire Assessments to ISIP Reading and Math. www.istation.com/studies. Patarapichayatham, C., & Locke, V. (2020b). Linking the Ohio AIR to ISIP. www.istation.com/studies.

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

The coefficients show strong support for predictive and concurrent validity evidence.

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

Yes

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.

Yes

If yes,

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

Differential Item Functioning (DIF) analysis was conducted by grade level using logistic regression DIF detection analysis by difR package in R software.

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

Two DIF factors were investigated: gender (male/female) and race/ethnicity (non-Hispanic white/all other combined).

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.

The difR obtained two DIF detection criterions: Zumbo & Thomas (ZT) and Jodoign & Gierl (JG). Both criterions had the same procedure but different cut points. There are three DIF effect sizes: A – negligible or non-significant DIF effect, B – slightly to moderate DIF effect, and C – moderate to large DIF effect. The DIF effect size under Zumbo & Thomas (ZT) is as follows: 0 < A ≤ 0.13, 0.13 < B ≤ 0.26, and 0.26 < C ≤ 1 Jodoign & Gierl (JG) is much smaller: 0 < A ≤ 0.035, 0.035 < B ≤ 0.07, and 0.07 < C ≤ 1. Results show that all items displayed as A item (negligible or non-significant DIF effect) with ZT DIF criterion. Under JG DIF criterion, results show that approximately 98% displayed as A item (negligible or non-significant DIF effect); 1% displayed as B item (slightly to moderate DIF effect); and less than 1% displayed as C item (moderate to large DIF effect) for both DIF factors.

Sensitivity: Reliability of Slope

Grade	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
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 for this study were collected in the 2018-2019 school year. The Kindergarten through grade 8 samples were constructed using Istation website data for at-risk students with at least ten observations. Sample sizes ranged from 61 to 2090. The inclusion criteria were students identified as at-risk (below the 30th percentile) and had at least ten observations starting in August of the school year (Period 0).

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 using the Spearman-Brown formula was selected due to its effectiveness in evaluating the internal consistency of the assessment tool. This method provides a robust measure of reliability without the need for repeated testing sessions. By correlating scores from split halves of the test, the method assesses the extent to which different parts of the test provide consistent results, which is crucial for determining the reliability of the slope as a measure of math progress.

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:

Provide citations for additional published studies.

Sensitivity: Validity of Slope

Grade	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
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:

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)?

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:

Provide citations for additional published studies.

Alternate Forms

Grade	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Rating

Legend

Convincing evidence

Partially convincing evidence

Unconvincing evidence

Data unavailable

^dDisaggregated data available

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

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

If IRT based, provide evidence of item or ability invariance

All items are calibrated by 2PL IRT. Item difficulties range from -3.0 to 3.0, and item discriminations range from 0.2 to 2.5. Items that did not meet these criteria are removed.

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

Because each item is calibrated using item response theory (IRT), the item bank represents the full ability continuum for each domain. Overall, more than 5,000 items are available to assess students at, below, and above grade level.

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

Because the Istation Math Formative assessment is computer-adaptive, the test forms are built at the item level with each student's response. The CAT system assigns a student an initial ability estimate based on their grade to deliver the first item. With each student's response to an item, the system then selects an item that fits best based on the student’s ability estimate using both item discrimination and item difficulty under the 2PL IRT model. This continues with each student's response to an item. Once the stopping criterion is met (reaching the maximum item per subtest), the assessment stops, and a student ability score and an overall math composite score are reported for each subtest.

Decision Rules: Setting & Revising Goals

Grade	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
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	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
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.