Assessing Student Proficiency in Early Number Sense (ASPENS)
Mathematics

Descriptive Information

Please provide a description of your tool:

Assessing Student Proficiency in Early Number Sense (ASPENS) is a series of three curriculum-based measures administered for the purposes of universal screening of students’ mathematical proficiency. ASPENS assesses number sense for both kindergarten and first-grade students using grade-appropriate Magnitude Comparison and Missing Number measures, but also adds one additional aspect of mathematical proficiency at each grade level. The Numeral Identification measure is given in kindergarten only while the Basic Arithmetic Facts and Base 10 measure is given to first-graders to efficiently assess more sophisticated aspects of mathematical proficiency. The kindergarten ASPENS measure includes the Numerical Identification, Magnitude Comparison, and Missing Number subtests. Numbers for each subtest range from 0 to 20, and the score is the number of correct responses given in one minute. For the Numeral Identification measure, students are asked to name numbers as quickly as possible. The Magnitude Comparison measure requires students to name the greater of two visually presented numbers. The Missing Number measure is comprised of pages with boxes containing strings of three numbers with the first, middle, or last number of the string missing, and students name the missing number. The first grade ASPENS measure also includes Magnitude Comparison and Missing Number subtests. The tests use the same procedures described above; however, the range of numbers is 0 to 99 for first graders. The Basic Arithmetic Facts and Base 10 measure is added in the middle of first grade to assess recall of basic arithmetic facts. Students are presented problems that contain elements that can be composed or decomposed in the Base 10 system (e.g., 5 + 9 becomes 4 + 10) to assess fact fluency. The score is the number of correct items (1 point for each problem) solved in two minutes

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):
Numerical Identification, Magnitude Comparison, Missing Number, and The Basic Arithmetic Facts and Base 10 subtests

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

ctran@inresg.org

Address

Contact Christopher Tran at Instructional Research Group

Phone Number

(714) 826-9600

Website

Instructional Research Group (www.inresg.org)

Initial cost for implementing program:

Cost

$0.00

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.

This is a not a commercial screening tool and therefore does not have a formal pricing plan. Contact Christopher Tran at Instructional Research Group (ctran@inresg.org). Costs include reproduction costs only or the minimal costs to prepare and send all the relevant electronic forms. ASPENS materials are available for benchmark and progress monitoring for students in kindergarten and first grade. A Benchmark Manual, Scoring Booklet for the Benchmark Assessments, Progress Monitoring Manual, and Scoring Booklet for the Progress Monitoring Assessments are provided for kindergarten and first grade. Training opportunities are provided by the authors of ASPENS at Instructional Research Group (www.inresg.org). Materials not included but required for implementation include a clipboard, pencil, and a digital timer/stopwatch.

Provide information about special accommodations for students with disabilities.

• The use of a marker or ruler to focus student attention on each line of the assessment materials. First try to administer the assessment without a visual aid. If it is determined that the student needs this accommodation, retest the student with an alternate form of the Progress Monitoring Materials. • Student materials that have enlarged print to accommodate students with visual impairments. • The use of colored overlays, filters, or lighting adjustments for students with visual impairments. • The use of assistive technology, such as hearing aids and assistive listening devices, for students with hearing impairments.

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:

Does the tool require technology?

No

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

7

per (student/group/other unit)

student

Additional scoring time:

Time in minutes

2

per (student/group/other unit)

student

ACADEMIC ONLY: What are the discontinue rules?

No discontinue rules provided
Basals
Ceilings
Other

If other, please specify:

Testing for each measure is discontinued after a student misses 5 items consecutively.

Are norms available?

No

Are benchmarks available?

Yes

If yes, how many benchmarks per year?

3

If yes, for which months are benchmarks available?

Beginning, middle and end of the school year.

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:

1-4 hrs of training

Please describe the minimum qualifications an administrator must possess.

Educational professionals and other school-approved personnel, provided they have received sufficient training on the administration and scoring rules and how to interpret the data.

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?

No

If No, please describe training costs:

Contact Christopher Tran at Instructional Research Group (ctran@inresg.org).

Can users obtain ongoing professional and technical support?

No

If Yes, please describe how users can obtain support:

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?

No

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:

Does your tool include decision rules?

Yes

If yes, please describe.

Testing for each measure is discontinued after a student misses 5 items consecutively

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.

Unit-weighted composite scores were created using the procedure detailed in the ASPENS Administrator’s Handbook. Users multiply the raw subtest scores by a weight and then add the weighted subtests scores together. The unit weighting is accounted for by the multiplication weights assigned to each subtest. The weights for each subtest are based on the standard deviation (SD) of the raw scores for that subtest. The subtest with the largest SD is weighted a 1. The remaining subtests with smaller SDs (i.e., those with lower means and with inherently more difficult items) are given weights greater than 1, in proportion to the subtest with the SD of 1. Details of this approach are provided by Good, Powell-Smith, and Kaminski (2011). We explain this to practitioners as indicating that “raw scores for the subtests are combined, but the subtests are weighted differently before they are combined, with more weight given to measures that are harder for students at a particular age range” (Clarke et al., 2018). Developing benchmark goals and cut-points for risk: Odds of achieving subsequent reading goals. Presentation at pre-DIBELS Summit, Albuquerque, NM. Retrieved July 15, 2011 from http://hprec.org/DIBELS/Summitt2011Presentations/Keynote.pdf Clarke, B., Gersten, R., Smolkowski, K., Haymond, K., Dimino, J. & Sutherland, M. (2018). Exploring the validity and reliability of a screening measure that focuses solely on number knowledge for students in the primary grades. Manuscript submitted for publication.

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.

The tests are administered one-to-one to help facilitate student performance. Additional approaches ensuring appropriate use of the measure for diverse populations are addressed via training.

Classification Accuracy & Cross-Validation Summary

Grade	Kindergarten	Grade 1
Classification Accuracy Fall
Classification Accuracy Winter
Classification Accuracy Spring

TerraNova, Third Edition: Math Form G (Same Year)

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 criterion outcome was mathematics achievement assessed via the TerraNova, Third Edition (CTB/McGraw Hill, 2008) in May of 2010 and May of 2011. The TerraNova is a nationally norm-referenced and standardized achievement test used in the U.S. to assess K–12 achievement in reading, language, mathematics, science, and social studies. Form G of the Mathematics subtest was used as the criterion. The criterion measure is independent and external to the screening measure.

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).

Diagnostic statistics were estimated for students at risk, defined by the 15th percentile on the TerraNova. We first generated receiver operating characteristic (ROC) curves for each of the screening measures administered in the fall, winter, and spring. ROC curves plot the proportion of true positives (sensitivity) against the proportion of false positives (1 – specificity) for all values of the screener. We next calculated the area under the curve, A. Based on a review of the literature on signal detection theory and academic outcomes, Smolkowski and Cummings (2015) considered values of A above .95 as excellent, values from .85 to .95 as very good, and values from .75 to .85 as reasonable. Estimates and confidence intervals for A were produced by SAS PROC LOGISTIC (SAS Institute, 2016). We chose decision thresholds based on the screener score with a sensitivity value closest to .90. For each measure, we reported A with confidence intervals, the selected decision threshold (i.e., recommended cut point), sensitivity and specificity with confidence bounds, negative and positive predictive values, the proportion of students who screened positive (τ), and the base rate or proportion determined to be at risk on the criterion measure. Confidence bounds around sensitivity and specificity were formed using a normal-curve approximation (Harper & Reeves, 1999), which are recommended only when cell sizes (e.g., number of false positives, number of true negatives) were greater than 10. We also defined confidence bounds around the cut scores, which represented the lowest and highest screener scores for which the sensitivity confidence intervals contained sensitivity of .90. Frequency statistics were produced with SAS PROC FREQ (SAS Institute, 2016).

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.

---

TerraNova, Third Edition: Math Form G (Next School Year)

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 criterion outcome was mathematics achievement assessed via the TerraNova, Third Edition (CTB/McGraw Hill, 2008) in May of 2010 and May of 2011. The TerraNova is a nationally norm-referenced and standardized achievement test used in the U.S. to assess K–12 achievement in reading, language, mathematics, science, and social studies. Form G of the Mathematics subtest was used as the criterion. The criterion measure is independent and external to the screening measure.

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).

Diagnostic statistics were estimated for students at risk, defined by the 15th percentile on the TerraNova. We first generated receiver operating characteristic (ROC) curves for each of the screening measures administered in the fall, winter, and spring. ROC curves plot the proportion of true positives (sensitivity) against the proportion of false positives (1 – specificity) for all values of the screener. We next calculated the area under the curve, A. Based on a review of the literature on signal detection theory and academic outcomes, Smolkowski and Cummings (2015) considered values of A above .95 as excellent, values from .85 to .95 as very good, and values from .75 to .85 as reasonable. Estimates and confidence intervals for A were produced by SAS PROC LOGISTIC (SAS Institute, 2016). We chose decision thresholds based on the screener score with a sensitivity value closest to .90. For each measure, we reported A with confidence intervals, the selected decision threshold (i.e., recommended cut point), sensitivity and specificity with confidence bounds, negative and positive predictive values, the proportion of students who screened positive (τ), and the base rate or proportion determined to be at risk on the criterion measure. Confidence bounds around sensitivity and specificity were formed using a normal-curve approximation (Harper & Reeves, 1999), which are recommended only when cell sizes (e.g., number of false positives, number of true negatives) were greater than 10. We also defined confidence bounds around the cut scores, which represented the lowest and highest screener scores for which the sensitivity confidence intervals contained sensitivity of .80. Frequency statistics were produced with SAS PROC FREQ (SAS Institute, 2016).

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	Kindergarten	Grade 1
Criterion measure	TerraNova, Third Edition: Math Form G (Same Year)	TerraNova, Third Edition: Math Form G (Same Year)
Cut Points - Percentile rank on criterion measure	15	15
Cut Points - Performance score on criterion measure	25	21
Cut Points - Corresponding performance score (numeric) on screener measure
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)	0.82	0.80
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.75	0.74
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.88	0.86

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

Sample	Kindergarten	Grade 1
Date	2009-2010; 2010-2011	2009-2010; 2010-2011
Sample Size
Geographic Representation
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	Kindergarten	Grade 1
Criterion measure	TerraNova, Third Edition: Math Form G (Same Year)	TerraNova, Third Edition: Math Form G (Same Year)
Cut Points - Percentile rank on criterion measure	15	15
Cut Points - Performance score on criterion measure	54	30
Cut Points - Corresponding performance score (numeric) on screener measure
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)	0.83	0.85
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.77	0.79
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.89	0.91

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

Sample	Kindergarten	Grade 1
Date	2009-2010; 2010-2011	2009-2010; 2010-2011
Sample Size
Geographic Representation
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	Kindergarten	Grade 1
Criterion measure	TerraNova, Third Edition: Math Form G (Same Year)	TerraNova, Third Edition: Math Form G (Same Year)
Cut Points - Percentile rank on criterion measure	15	15
Cut Points - Performance score on criterion measure	90	45
Cut Points - Corresponding performance score (numeric) on screener measure
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)	0.85	0.84
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.80	0.79
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.90	0.90

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

Sample	Kindergarten	Grade 1
Date	2009-2010; 2010-2011	2009-2010; 2010-2011
Sample Size
Geographic Representation
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	Kindergarten	Grade 1
Rating

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

Test-retest reliabilities of kindergarten and first-grade ASPENS measures are in the moderate to high range. Test-retest reliabilities provide an estimate of the stability of scores across time.

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

Kindergarten and first-grade students in six elementary schools from fours districts in California and Ohio. Data were collected from schools in Los Angeles, CA, Pasadena, CA, Springfield, OH, and Conneaut, OH. A total of 715 students (341 kindergarteners and 374 first graders) were tested during the 2009–2010 school year. The following school year sample (2010–2011) included 567 of these students (264 first graders and 303 second graders) to examine predictive validity across two years.

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

Correlational data between two points in time.

*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:

N/a

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.

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	Kindergarten	Grade 1
Rating

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

The criterion outcome was mathematics achievement assessed via the TerraNova, Third Edition (CTB/McGraw Hill, 2008) in May of 2010 and May of 2011. The TerraNova is a nationally norm referenced and standardized achievement test used in the U.S. to assess K–12 achievement in reading, language, mathematics, science and social studies. Form G of the Mathematics subtest was used as the criterion. The criterion measure is independent and external to the screening measure.

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

Kindergarten and first-grade students in six elementary schools from fours districts in California and Ohio. Data were collected from schools in Los Angeles, CA, Pasadena, CA, Springfield, OH, and Conneaut, OH. A total of 715 students (341 kindergarteners and 374 first graders) were tested during the 2009–2010 school year. The following school year sample (2010–2011) included 567 of these students (264 first graders and 303 second graders) to examine predictive validity across two years.

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

To obtain predictive validity, the fall and winter scores on the kindergarten and first grade ASPENS subtest measures were correlated with the spring scores on the TerraNova 3. To obtain concurrent validity, spring scores on the kindergarten and first grade ASPENS subtest measures were correlated with the spring scores on the TerraNova 3.

*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:

N/a

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.

The measure shows moderate correlations to a broad measure of the construct of interest (general mathematics performance). The correlations across multiple years remain at moderate levels, indicating long-term predictive value.

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	Kindergarten	Grade 1
Rating	No	No

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.