Star
Mathematics

Descriptive Information

Please provide a description of your tool:

Star Math is a computer-adaptive assessment of general mathematics achievement for students in grades 1 to 12. Star Math provides information on student performance on hundreds of skills within 32 domains. Mathematics computation, mathematic application, and mathematics concepts can be assessed. The difficulty of items is adjusted automatically to reflect the skill level of all students.

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 skills does the tool screen?

Reading

Phonological processing:

RAN
Memory
Awareness
Letter sound correspondence
Phonics
Structural analysis

Word ID

Accuracy
Speed

Nonword

Accuracy
Speed

Spelling

Accuracy
Speed

Passage

Accuracy
Speed

Reading comprehension:

Multiple choice questions
Cloze
Constructed Response
Retell
Maze
Sentence verification
Other (please describe):

Listening comprehension:

Multiple choice questions
Cloze
Constructed Response
Retell
Maze
Sentence verification
Vocabulary
Expressive
Receptive

Mathematics

Global Indicator of Math Competence

Accuracy
Speed
Multiple Choice
Constructed Response

Early Numeracy

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematics Concepts

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematics Computation

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematic Application

Accuracy
Speed
Multiple Choice
Constructed Response

Fractions/Decimals

Accuracy
Speed
Multiple Choice
Constructed Response

Algebra

Accuracy
Speed
Multiple Choice
Constructed Response

Geometry

Accuracy
Speed
Multiple Choice
Constructed Response

Other (please describe):

Please describe specific domain, skills or subtests:

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

Internalizing
Externalizing
Internalizing and Externalizing

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

Acquisition and Cost Information

Where to obtain:

Email Address

answers@renaissance.com

Address

Renaissance Learning, PO Box 8036, Wisconsin Rapids, WI 54495

Phone Number

(800) 338-4204

Website

http://www.renaissance.com

Initial cost for implementing program:

Cost

Unit of cost

Replacement cost per unit for subsequent use:

Cost

Unit of cost

Duration of license

Additional cost information:

Describe basic pricing plan and structure of the tool. Provide information on what is included in the published tool, as well as what is not included but required for implementation.

There is a one-time setup fee along with a per student subscription fee. Total cost will depend on the number of schools and students. Please contact: answers@renaissance.com or (800) 338-4204 for specific details on pricing for your district. Star Math is cloud-based and purchase includes the tool, software/technical manual, installation guide, testing instructions, and remote installation and setup.

Provide information about special accommodations for students with disabilities.

Star Math is a computer-adaptive assessment, and the difficulty of items is adjusted automatically to reflect the skill level of the student. Students can use either the keyboard or the mouse, accommodating students with limited motor skills. Star Math offers several accommodations for students with disabilities through the accessibility options built into a computer’s operating system. For students with limited vision, the introductory screens of Star Math respond to the “high contrast” accessibility feature within Windows and the “switch to black and white” accessibility feature in MAC OS. Star Math is compatible with Mac’s “zoom in” accessibility feature, which allows users to magnify nearly all Star Math screens.

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:

What is the administration setting?

Direct observation
Rating scale
Checklist
Performance measure
Questionnaire
Direct: Computerized
One-to-one
Other

If other, please specify:

Group administered

Does the tool require technology?

Yes

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

Computer or tablet
Internet connection
Other technology (please specify)

If your program requires additional technology not listed above, please describe the required technology and the extent to which it is combined with teacher small-group instruction/intervention:

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:

What is the administration time?

Time in minutes

20

per (student/group/other unit)

student/group

Additional scoring time:

Time in minutes

per (student/group/other unit)

ACADEMIC ONLY: What are the discontinue rules?

No discontinue rules provided
Basals
Ceilings
Other

If other, please specify:

Are norms available?

Yes

Are benchmarks available?

Yes

If yes, how many benchmarks per year?

Unlimited

If yes, for which months are benchmarks available?

All

BEHAVIOR ONLY: Can students be rated concurrently by one administrator?

If yes, how many students can be rated concurrently?

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?

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:

Renaissance Technical Support Staff

Scoring

How are scores calculated?

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

If other, please specify:

Do you provide basis for calculating performance level scores?

Yes

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:

scale score

Does your tool include decision rules?

If yes, please describe.

Can you provide evidence in support of multiple decision rules?

No

If yes, please describe.

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.

All scores are calculated automatically by the software. The software calculates a maximum likelihood Rasch ability estimate based on the calibrated difficulty of the items that were administered to the student, and the pattern of the student’s right and wrong responses to those items. Star Math uses a proprietary, Rasch-based, 1-parameter logistic response model to calculate scores. The scaled score is a non-linear, monotonic transformation of the Rasch ability estimate resulting from the adaptive test. From the scaled scores and the student’s current grade placement are derived grade equivalent, percentile, and normal curve equivalent scores. No clusters, composite, or raw scores are reported.

Describe the tool’s approach to screening, samples (if applicable), and/or test format, including steps taken to ensure that it is appropriate for use with culturally and linguistically diverse populations and students with disabilities.

Each Star Math test contains 34 items in a multiple-choice format. Aligned to state-specific standards and the Common Core State Standards, the test blueprint specifies operational item counts from each of the four domains: Numbers and Operations, Algebra, Geometry and Measurements and Data Analysis, Statistics and Probability. The items are administered to ensure that a balance of content is administered at each grade, appropriate to the typical curriculum for that grade. The assessments’ computer-adaptive structure matches students to items of appropriate difficulty, which in turn may help to reduce student frustration during testing. The assessments can also provide accommodations for students with hearing and visual impairments. This skill measurement provides a crucial component in progress monitoring. As students learn new skills in the state standards or growth within a response to intervention plan, Star Math can assess the level of achievement as often as weekly. As a screener, Star Math can provide accurate and reliable scores to place a student on a continuum of skills aligned to the state standards, which creates the foundation for a personalized learning environment. The frequency with which a student is assessed, therefore, can be either as often as weekly or at key milestones throughout the year without overexposure to the test items. For this reason, the Star Math assessment has a large item bank, containing thousands of unique items. Each item has been designed to measure a skill at a specific grade level. All items have been calibrated, so that the difficulty of each item is expressed on a Rasch difficulty scale that spans the range of math proficiency from grade 1 through grade 12.

Classification Accuracy & Cross-Validation Summary

Grade	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10	Grade 11
Classification Accuracy Fall
Classification Accuracy Winter
Classification Accuracy Spring

Smarter Balanced Mathematics

Classification Accuracy

Select time of year

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

The Smarter Balanced Mathematics assessment is an external outcome measure administered at least 90 days after each student’s Star assessment.

Do the classification accuracy analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the classification analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

The Star cut-point for students at risk was determined to be at the 25th percentile of Star scores. This point aligns with students in need of intervention, as indicated in Star default benchmarks. Students scoring below the 25th percentile were placed into the at-risk category and students scoring above the 25th percentile were placed into the no-risk category. Consistent with the TRC guidelines, we selected the 20th PR on the outcome measure as the point aligned with students in need of intensive intervention.

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

No

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

Cross-Validation

Has a cross-validation study been conducted?

No

If yes,

Select time of year.

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

Do the cross-validation analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the cross-validation analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

---

Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics

Classification Accuracy

Select time of year

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

The PARCC assessment is an external outcome measure administered at least 90 days after each student’s Star assessment.

Do the classification accuracy analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the classification analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

The Star cut-point for students at risk was determined to be at the 25th percentile of Star scores. This point aligns with students in need of intervention, as indicated in Star default benchmarks. Students scoring below the 25th percentile were placed into the at-risk category and students scoring above the 25th percentile were placed into the no-risk category. Consistent with the TRC guidelines, we selected the 20th PR on the outcome measure as the point aligned with students in need of intensive intervention.

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

No

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

Cross-Validation

Has a cross-validation study been conducted?

Yes

If yes,

Select time of year.

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

The PARCC Mathematics assessment is an external outcome measure administered at least 90 days after each student’s Star assessment.

Do the cross-validation analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the cross-validation analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

The Star cut-point for students at risk was determined to be at the 25th percentile of Star scores. This point aligns with students in need of intervention, as indicated in Star default benchmarks. Students scoring below the 25th percentile were placed into the at-risk category and students scoring above the 25th percentile were placed into the no-risk category. Consistent with the TRC guidelines, we selected the 20th PR on the outcome measure as the point aligned with students in need of intensive intervention.

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

No

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

---

PARCC Algebra I

Classification Accuracy

Select time of year

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

The PARCC Algebra I assessment is an external outcome measure administered at least 90 days after each student’s Star assessment.

Do the classification accuracy analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the classification analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

The Star cut-point for students at risk was determined to be at the 25th percentile of Star scores. This point aligns with students in need of intervention, as indicated in Star default benchmarks. Students scoring below the 25th percentile were placed into the at-risk category and students scoring above the 25th percentile were placed into the no-risk category. Consistent with the TRC guidelines, we selected the 20th PR on the outcome measure as the point aligned with students in need of intensive intervention.

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

No

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

Cross-Validation

Has a cross-validation study been conducted?

Yes

If yes,

Select time of year.

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

The PARCC Algebra I assessment is an external outcome measure administered at least 90 days after each student’s Star assessment.

Do the cross-validation analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the cross-validation analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

The Star cut-point for students at risk was determined to be at the 25th percentile of Star scores. This point aligns with students in need of intervention, as indicated in Star default benchmarks. Students scoring below the 25th percentile were placed into the at-risk category and students scoring above the 25th percentile were placed into the no-risk category. Consistent with the TRC guidelines, we selected the 20th PR on the outcome measure as the point aligned with students in need of intensive intervention.

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

No

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

---

ACT Mathematics

Classification Accuracy

Select time of year

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

The ACT Mathematics assessment is an external outcome measure administered at least 90 days after each student’s Star assessment.

Do the classification accuracy analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the classification analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

The Star cut-point for students at risk was determined to be at the 25th percentile of Star scores. This point aligns with students in need of intervention, as indicated in Star default benchmarks. Students scoring below the 25th percentile were placed into the at-risk category and students scoring above the 25th percentile were placed into the no-risk category. Consistent with the TRC guidelines, we selected the 20th PR on the outcome measure as the point aligned with students in need of intensive intervention.

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

No

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

Cross-Validation

Has a cross-validation study been conducted?

No

If yes,

Select time of year.

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

Do the cross-validation analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the cross-validation analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

---

Classification Accuracy - Fall

Evidence	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10	Grade 11
Criterion measure	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	ACT Mathematics	ACT Mathematics	ACT Mathematics
Cut Points - Percentile rank on criterion measure	20	20	20	20	20	20	20	20	20	20
Cut Points - Performance score on criterion measure
Cut Points - Corresponding performance score (numeric) on screener measure	<339	<457	<542	<613	<661	<694	<692	<776	<797	<809
Classification Data - True Positive (a)
Classification Data - False Positive (b)
Classification Data - False Negative (c)
Classification Data - True Negative (d)
Area Under the Curve (AUC)	0.86	0.92	0.92	0.91	0.93	0.93	0.85	0.87	0.85	0.89
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.84	0.91	0.92	0.91	0.92	0.92	0.84	0.85	0.83	0.88
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.87	0.93	0.93	0.92	0.93	0.93	0.87	0.90	0.87	0.91

Statistics	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10	Grade 11
Base Rate
Overall Classification Rate
Sensitivity
Specificity
False Positive Rate
False Negative Rate
Positive Predictive Power
Negative Predictive Power

Sample	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10	Grade 11
Date	Fall 2013	Fall 2013	Fall 2014	Fall 2014	Fall 2014	Fall 2014	Fall 2014	Fall 2005-2012	Fall 2006-2013	Fall 2007-2014
Sample Size
Geographic Representation	East North Central (IL) Middle Atlantic (NJ) Mountain (CO, NM) New England (RI) West South Central (AR)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)	East North Central (IL, OH) Middle Atlantic (NJ) Mountain (CO) New England (RI) West South Central (AR)	East South Central (AL, KY) West South Central (AR)	East South Central (AL, KY, TN) South Atlantic (NC) West South Central (AR)	East North Central (WI) East South Central (AL, KY, TN) South Atlantic (NC) West South Central (AR)
Male
Female
Other
Gender Unknown
White, Non-Hispanic
Black, Non-Hispanic
Hispanic
Asian/Pacific Islander
American Indian/Alaska Native
Other
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability
English Language Learner

Classification Accuracy - Winter

Evidence	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10	Grade 11
Criterion measure	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	Smarter Balanced Mathematics	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics
Cut Points - Percentile rank on criterion measure	20	20	20	20	20	20	20	20	20	20	20
Cut Points - Performance score on criterion measure
Cut Points - Corresponding performance score (numeric) on screener measure	<269	<416	<495	<584	<646	<678	<712	<714	<741	<777	<799
Classification Data - True Positive (a)
Classification Data - False Positive (b)
Classification Data - False Negative (c)
Classification Data - True Negative (d)
Area Under the Curve (AUC)	0.88	0.91	0.91	0.94	0.93	0.93	0.92	0.85	0.84	0.87	0.87
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.84	0.90	0.90	0.94	0.92	0.93	0.91	0.82	0.82	0.86	0.85
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.92	0.92	0.92	0.95	0.94	0.94	0.93	0.87	0.86	0.89	0.89

Statistics	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10	Grade 11
Base Rate
Overall Classification Rate
Sensitivity
Specificity
False Positive Rate
False Negative Rate
Positive Predictive Power
Negative Predictive Power

Sample	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10	Grade 11
Date	Winter 2012-13	Winter 2013-14	Winter 2014-15	Winter 2014-15	Winter 2014-15	Winter 2014-15	Winter 2014-15	Winter 2014-15	Winter 2013-2016	Winter 2013-2017	Winter 2014-2018
Sample Size
Geographic Representation	East North Central (IL) Mountain (CO)	New England (CT) Pacific (CA, OR, WA)	East North Central (IL) Middle Atlantic (NJ) Mountain (CO, NM) New England (RI) West South Central (AR)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)	East North Central (IL, OH) Middle Atlantic (NJ) Mountain (CO) New England (RI) West South Central (AR)	Pacific (CA, WA)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)
Male
Female
Other
Gender Unknown
White, Non-Hispanic
Black, Non-Hispanic
Hispanic
Asian/Pacific Islander
American Indian/Alaska Native
Other
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability
English Language Learner

Classification Accuracy - Spring

Evidence	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10
Criterion measure	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Smarter Balanced Mathematics	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	PARCC Algebra I	Smarter Balanced Mathematics	ACT Mathematics
Cut Points - Percentile rank on criterion measure	20	20	20	20	20	20	20	20	20	20
Cut Points - Performance score on criterion measure
Cut Points - Corresponding performance score (numeric) on screener measure	<382	<460	<554	<623	<662	<708	<711	<712	<768	<813
Classification Data - True Positive (a)
Classification Data - False Positive (b)
Classification Data - False Negative (c)
Classification Data - True Negative (d)
Area Under the Curve (AUC)	0.88	0.92	0.93	0.91	0.93	0.93	0.85	0.81	0.85	0.86
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.84	0.91	0.92	0.90	0.92	0.92	0.83	0.76	0.83	0.84
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.92	0.93	0.94	0.92	0.94	0.93	0.86	0.85	0.86	0.89

Statistics	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10
Base Rate
Overall Classification Rate
Sensitivity
Specificity
False Positive Rate
False Negative Rate
Positive Predictive Power
Negative Predictive Power

Sample	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10
Date	Spring 2013	Spring 2014	Spring 2014	Spring 2014	Spring 2014	Spring 2014	Spring 2014	Spring 2014	Spring 2013-2016	Spring 2007-2014
Sample Size
Geographic Representation	East North Central (IL) Mountain (CO) West South Central (AR)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)	New England (CT) Pacific (CA, OR, WA)	East North Central (IL, OH) Middle Atlantic (NJ) Mountain (CO) New England (RI) Pacific (CA, OR, WA) West South Central (AR)	East North Central (OH) Mountain (CO, NM) West South Central (AR)	Pacific (CA, WA)	East South Central (AL, KY, TN) West South Central (AR)
Male
Female
Other
Gender Unknown
White, Non-Hispanic
Black, Non-Hispanic
Hispanic
Asian/Pacific Islander
American Indian/Alaska Native
Other
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability
English Language Learner

Cross-Validation - Fall

Evidence	Grade 2	Grade 7	Grade 8
Criterion measure	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics
Cut Points - Percentile rank on criterion measure	20	20	20
Cut Points - Performance score on criterion measure
Cut Points - Corresponding performance score (numeric) on screener measure	<339	<657	<692
Classification Data - True Positive (a)
Classification Data - False Positive (b)
Classification Data - False Negative (c)
Classification Data - True Negative (d)
Area Under the Curve (AUC)	0.94	0.93	0.94
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.92	0.91	0.94
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.97	0.96	0.97

Statistics	Grade 2	Grade 7	Grade 8
Base Rate
Overall Classification Rate
Sensitivity
Specificity
False Positive Rate
False Negative Rate
Positive Predictive Power
Negative Predictive Power

Sample	Grade 2	Grade 7	Grade 8
Date	Fall 2013	Fall 2014	Fall 2014
Sample Size
Geographic Representation	Middle Atlantic (NJ)	Middle Atlantic (NJ)	Middle Atlantic (NJ)
Male
Female
Other
Gender Unknown
White, Non-Hispanic
Black, Non-Hispanic
Hispanic
Asian/Pacific Islander
American Indian/Alaska Native
Other
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability
English Language Learner

Cross-Validation - Winter

Evidence	Grade 1	Grade 3	Grade 7	Grade 8
Criterion measure	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics
Cut Points - Percentile rank on criterion measure	20	20	20	20
Cut Points - Performance score on criterion measure
Cut Points - Corresponding performance score (numeric) on screener measure	<269	<495	<708	<714
Classification Data - True Positive (a)
Classification Data - False Positive (b)
Classification Data - False Negative (c)
Classification Data - True Negative (d)
Area Under the Curve (AUC)	0.89	0.96	0.93	0.92
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.84	0.94	0.90	0.88
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.96	0.98	0.96	0.95

Statistics	Grade 1	Grade 3	Grade 7	Grade 8
Base Rate
Overall Classification Rate
Sensitivity
Specificity
False Positive Rate
False Negative Rate
Positive Predictive Power
Negative Predictive Power

Sample	Grade 1	Grade 3	Grade 7	Grade 8
Date	Winter 2012-13	Winter 2014-15	Winter 2014-15	Winter 2014-15
Sample Size
Geographic Representation	Middle Atlantic (NJ)	Middle Atlantic (NJ)	Middle Atlantic (NJ)	Middle Atlantic (NJ)
Male
Female
Other
Gender Unknown
White, Non-Hispanic
Black, Non-Hispanic
Hispanic
Asian/Pacific Islander
American Indian/Alaska Native
Other
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability
English Language Learner

Cross-Validation - Spring

Evidence	Grade 1	Grade 7	Grade 8
Criterion measure	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics	PARCC Algebra I
Cut Points - Percentile rank on criterion measure	20	20	20
Cut Points - Performance score on criterion measure
Cut Points - Corresponding performance score (numeric) on screener measure	<382	<711	<712
Classification Data - True Positive (a)
Classification Data - False Positive (b)
Classification Data - False Negative (c)
Classification Data - True Negative (d)
Area Under the Curve (AUC)	0.89	0.94	0.86
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.84	0.91	0.81
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.94	0.97	0.91

Statistics	Grade 1	Grade 7	Grade 8
Base Rate
Overall Classification Rate
Sensitivity
Specificity
False Positive Rate
False Negative Rate
Positive Predictive Power
Negative Predictive Power

Sample	Grade 1	Grade 7	Grade 8
Date	Spring 2013	Spring 2014	Spring 2014
Sample Size
Geographic Representation	Middle Atlantic (NJ)	Middle Atlantic (NJ)	Middle Atlantic (NJ)
Male
Female
Other
Gender Unknown
White, Non-Hispanic
Black, Non-Hispanic
Hispanic
Asian/Pacific Islander
American Indian/Alaska Native
Other
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability
English Language Learner

Reliability

Grade	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10	Grade 11
Rating

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

The internal consistency reliability coefficient estimates the proportion of variability within a single administration of a test that is due to inconsistency among the items that comprise the test.

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

For each grade, a large sample (n = 131,103) of students completed Star Math assessments throughout the 2012–2013 and 2013–2014 school year.

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

Reliability was defined as the proportion of test score variance that is attributable to true variation in the trait the test measures.The variance of the test scores was calculated from Scaled Score data. The variance of the errors of measurement was estimated from the conditional standard error of measurement (CSEM) statistics that accompany each of the IRT-based test scores, including the Scaled Scores. The conditional standard error of measurement (CSEM) was calculated along with the IRT ability estimate and Scaled Score. Squaring and summing the CSEM values yielded an estimate of total squared error; dividing by the number of observations yielded an estimate of error variance. Generic reliability was calculated by subtracting the ratio of error variance to Scaled Score variance from 1.

*In the table(s) below, report the results of the reliability analyses described above (e.g., internal consistency or inter-rater reliability coefficients).

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

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.

Renaissance Learning (2016). Star Assessments™ for Math Abridged Technical Manual. Wisconsin Rapids, WI: Author. Available by request to research@renaissance.com.

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.

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

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	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10	Grade 11
Rating

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

All criterion measures were external to the screening tool system and represent widely used assessments of general math ability. • CAT-5. The California Achievement Test, is a nationally normed standardized test that measures achievement in mathematics. • NWEA MAP. Measures of Academic Progress offers an adaptive computerized test for Mathematics. • PARCC. The Partnership for Assessment of Readiness for College and Careers end-of-year assessment covers mathematics and is intended to be used as an indicator of student needs and progress. • SBA. Smarter Balanced assessments are summative tests designed to measure student achievement and growth in math to support teaching and learning. • ACT. The American College Testing college readiness assessment is a national standardized test for high school achievement and college admissions. • IA. Iowa Assessments provide standardized mathematics tests as a service to schools by the College of Education of the University of Iowa. • SAT. The SAT Math Test is a standardized test widely used for college admissions in the United States that covers a range of math practices, including problem solving, modeling, using tools strategically, and using algebraic structure. • M-CAP. The aimsweb Mathematics Concepts and Applications is a brief, standardized test of problem solving skills and elements included in typical math curriculum.

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

Samples included students who had taken both Star Math and the criterion measure. The sample sizes varied across criterion and grades, ranging from 17 to 10,800 students.

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

Concurrent and predictive correlations were calculated. A criterion assessment was considered concurrent if it was taken during the same school year as the Star Math assessment. The correlation was considered predictive if the criterion assessment was one school year or more after the Star Math assessment.

*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.

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

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.

Renaissance Learning (2016). Star Assessments™ for Math Abridged Technical Manual. Wisconsin Rapids, WI: Author. Available by request to research@renaissance.com.

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

The provided data indicate that Star Math results correspond to other various respected measures of general mathematics ability.

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.

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

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

Grade	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8	Grade 9	Grade 10	Grade 11
Rating	Provided	Provided	Provided	Provided	Provided	Provided	Provided	Provided	Provided	Provided	Provided

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:

Describe the method used to determine the presence or absence of bias. Logistic regression analyses conditional on ability, group membership, and ability by group interaction were conducted to assess the presence of both uniform and non-uniform DIF simultaneously. Additionally, an effect size measure – Nagelkerke R-squared – was computed to quantify the magnitude of DIF where present.

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

DIF analyses were conducted for gender (males and females) and race/ethnicity (Caucasian, African American, American Indian, Asian, and Hispanic subpopulations). Due to insufficient samples sizes on English Language Learner (ELLs) and students with disabilities (SWD), DIF analyses for these two subgroups were not possible at the time of the analyses.

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.

Using a blended criterion that flagged items for uniform/non-uniform DIF if they had a p-value less than 0.01 and Nagelkerke R2 greater than or equal to 0.035, the results indicated that Star Math is sufficiently bias-free. A total of 391 items (4% of the Star Math items) were flagged for DIF. Those flagged items were removed from the item banks for review and recalibration.