aimswebPlus Math
Number Comparison FluencyPairs
Summary
aimswebPlus is a brief and valid assessment system for screening and monitoring reading and math skills for all students in Kindergarten through Grade 8. Normative data were collected in 201314 on a combination of fluency measures that are sensitive to growth and new standardsbased assessments of classroom skills. The resulting scores and reports inform instruction and help improve student performance. Number Comparison FluencyPairs is individually administered, with a teacher/examiner recording student data during the test session. Once testing is complete, summary and detailed reports for students, classrooms, and districts can be generated immediately.
 Where to Obtain:
 Pearson
 info@aimsweb.com
 NCS Pearson Inc.: San Antonio Office 19500 Bulverde Road, #201 San Antonio, TX, 78259
 18663136194
 www.aimswebplus.com
 Initial Cost:
 $8.50 per student
 Replacement Cost:
 $8.50 per student per year
 Included in Cost:
 aimswebPlus is an online solution that includes digital editions of training manuals and testing materials within the application. Cost per student for 1 Year: $8.50/student/year for access to all measures (reading and math) Cost per student for subsequent years: $8.50 Complete Kit: aimswebPlus is an online solution that includes digital editions of training manuals and testing materials within the application.
 aimswebPlus is a subscriptionbased tool. There are three subscription types available for customers: ● aimswebPlus Complete is $8.50 per student and includes all measures. ● aimswebPlus Reading is $6.50 per student and includes Early Literacy and Reading measures. ● aimswebPlus Math is $6.50 per student and includes Early Numeracy and Math measures. Note. Current aimsweb customers upgrading to aimswebPlus receive a $2/student discount off of the subscription. Test accommodations that are documented in a student’s Individual Education Plan (IEP) are permitted with aimswebPlus. However, not all measures allow for accommodations. Number Comparison Fluency–Pairs is an individually administered, timed test that employs strict time limits to generate ratebased scores. As such, valid interpretation of national norms, which are an essential aspect of decisionmaking during benchmark testing, depend on strict adherence to the standard administration procedures. The following accommodations are allowed for Number Comparison Fluency–Pairs during screening and progress monitoring: ● enlarging test forms ● modifying the environment (e.g., special lighting, adaptive furniture)
 Training Requirements:
 Less than one hour of training.
 Qualified Administrators:
 Paraprofessional or professional.
 Access to Technical Support:
 Pearson provides phone and emailbased support, as well as a user group forum that facilitates the asking and answering of questions.
 Assessment Format:

 Individual
 Computeradministered
 Scoring Time:

 Scoring is automatic OR
 0 minutes per student
 Scores Generated:

 Raw score
 Percentile score
 Administration Time:

 1 minutes per student
 Scoring Method:

 Automatically (computerscored)
 Technology Requirements:

 Computer or tablet
 Internet connection
Tool Information
Descriptive Information
 Please provide a description of your tool:
 aimswebPlus is a brief and valid assessment system for screening and monitoring reading and math skills for all students in Kindergarten through Grade 8. Normative data were collected in 201314 on a combination of fluency measures that are sensitive to growth and new standardsbased assessments of classroom skills. The resulting scores and reports inform instruction and help improve student performance. Number Comparison FluencyPairs is individually administered, with a teacher/examiner recording student data during the test session. Once testing is complete, summary and detailed reports for students, classrooms, and districts can be generated immediately.
 Is your tool designed to measure progress towards an endofyear goal (e.g., oral reading fluency) or progress towards a shortterm skill (e.g., letter naming fluency)?

ACADEMIC ONLY: What dimensions does the tool assess?
 BEHAVIOR ONLY: Please identify which broad domain(s)/construct(s) are measured by your tool and define each subdomain or subconstruct.
 BEHAVIOR ONLY: Which category of behaviors does your tool target?
Acquisition and Cost Information
Administration
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.
 Paraprofessional or professional.
 No minimum qualifications
 Are training manuals and materials available?
 Yes
 Are training manuals/materials fieldtested?
 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:
 Pearson provides phone and emailbased support, as well as a user group forum that facilitates the asking and answering of questions.
Scoring
 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.
 NCF–P is a timed measure that assesses fluency of foundational math skills. Performance is reported on the raw number correct score. Raw scores are calculated by subtracting the number of errors from the number of items attempted, resulting in a total number correct raw score. For Grade 1, the raw score is calculated by counting the number of correct responses in 60 seconds.
 Do you provide basis for calculating slope (e.g., amount of improvement per unit in time)?
 Yes
 ACADEMIC ONLY: Do you provide benchmarks for the slopes?
 Yes
 ACADEMIC ONLY: Do you provide percentile ranks for the slopes?
 Yes
 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.
 Number Comparison Fluency–Pairs is an individually administered measure, with printed content shown to students via a stimulus book. The examiner records student responses during the test session via a digital record form accessed by a computer, tablet, or other mobile device. A sample item page and test blueprint information are available from the Center upon request. ● Overview: Assesses a student’s ability to accurately and efficiently determine which of two numbers is greater. Content reflects the expectations outlined in the Common Core State Standards for mathematics. ● Test Format: individual, student stimulus book (print) and examiner digital record form (online), timed ● Test Content: The student sees rows of number pairs on each test page. Starting with the first row, the student points to and names the larger number in each pair. Each NCF–P form contains 50 items, presented in 5 rows of number pairs per page. ● 23 unique forms, 3 benchmark and 20 progress monitoring; PM testing conducted at teacherdetermined intervals ● Score: 1 point for each correctly answered item ● Time limit: 1 minute An NCF–P test blueprint was developed to reflect the expectations described in the Common Core State Standards for Grade 1. This blueprint was then used to develop all 23 NCF–P forms per grade (3 screening forms, 20 progress monitoring forms). The following blueprint provided the parameters for NCF–P form development: ● Items per form: 50 ● Content: ○ Numbers 0 through 100 ○ Progressively larger numbers used in pairs ○ Mix of greatertolesser and lessertogreater ordering of pairs ○ Four number pairs are included twice, with number order reversed (e.g., 23, 37 and 37, 23) Studentfacing content contains only numbers. Instructional text spoken by the examiner was written using simple, gradeappropriate language that keeps the students’ receptive language load to a minimum.
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:
 aimswebPlus provides student growth percentiles (SGP) by grade and initial performance level (Fall and Winter) for establishing growth standards. An SGP indicates the percentage of students in the national sample whose seasonal (or annual) rate of improvement (ROI) fell at or below a specified ROI. Separate SGP distributions are computed for each of five levels of initial (Fall or Winter) performance. Goals are set in the system by selecting the measure and baseline score, the goal date, the monitoring frequency (default is weekly), and the goal score. When the user defines the goal score, the system automatically labels the ambitiousness of the goal. The rate of improvement needed to achieve the goal is computed and translated into an SGP. An SGP < 50 is considered Insufficient; an SGP between 50 and 85 is considered Closes the Gap; an SGP between 85 and 97 is considered Ambitious; and an SGP > 97 is considered Overly Ambitious. aimswebPlus recommends setting performance goals that represent rates of growth between the 85th and 97th SGP. However, the user ultimately determines what growth rate is appropriate on an individual basis.
 Are benchmarks for minimum acceptable endofyear performance specified in your manual or published materials?
 Yes
 If yes, specify the endofyear performance standards:
 aimswebPlus allows users to select a target from a range of endofyear targets the one that is most appropriate for their instructional needs. aimswebPlus defines a meaningful target as one that is objective, quantifiable, and can be linked to a criterion that has inherent meaning for teachers. To establish a meaningful performance target using aimswebPlus tiers, the account manager (e.g., a school/district administrator) is advised to choose a target that: ● is linked to a criterion, ● is challenging and achievable, ● closes the achievement gap, and ● reflects historical performance results (when available). Customers are also advised to give consideration to the availability of resources to achieve the goal. The targets are based on spring reading or math composite score national percentiles. Twelve national percentile targets ranging from the 15th through the 70th percentile, in increments of 5 are provided. This range was chosen because it covers the breadth of passing rates on state assessments and the historical range of targets our customers typically use. The system provides a default spring performance target of the 30th national percentile. Targets can be set separately for Reading and Math. The aimswebPlus Tiers Guide provides more detail to help customers define a high quality performance target. It also provides a stepbystep method to align spring performance targets to performance levels on state accountability tests. Once a target is selected, the aimswebPlus system automatically identifies the fall (or winter) cut score that divides the score distribution into three instructional Tiers. Students above the highest cut score are in Tier 1 and have a high probability (80%–95%) of meeting the performance target; students between the upper and lower cut scores are in Tier 2 and have a moderate probability (40%–70%) of meeting the performance target; and students below the lower cut score are in Tier 3 and have a low probability (10%–40%) of meeting the performance target. The system recommends that a progress monitoring schedule be defined for any student below the 25th national percentile in a given season, or in Tiers 2 or 3.
 Date
 201314
 Size
 2000
 Male
 50
 Female
 50
 Unknown
 Eligible for free or reducedprice lunch
 Other SES Indicators
 Based on schoolwide eligibility for free or reduced lunch, students were sorted into Low (132% eligible), Moderate (3366% eligible), and High (67100% eligible) SES categories. Students were distributed fairly evenly among the three SES levels.
 White, NonHispanic
 51
 Black, NonHispanic
 Hispanic
 American Indian/Alaska Native
 Asian/Pacific Islander
 Other
 Unknown
 Disability classification (Please describe)
 The norm sample includes all students in the classroom with exceptions for moderate to severe intellectual disability; blind or deaf; or moderate to severe motor coordination disability.
 First language (Please describe)
 Language proficiency status (Please describe)
 ELL (Percent): 10
Performance Level
Reliability
Grade 
Grade 1


Rating 
 *Offer a justification for each type of reliability reported, given the type and purpose of the tool.
 Alternateform reliability, where equivalent forms are administered close together in time, is highly appropriate for progress monitoring CBM measures because it shows the consistency of score from independently time administrations with different content. Internal consistency reliability is not appropriate for speeded CBM measures. The stability coefficient, where equivalent forms are administered with an interval of several months, reflects additional measurement error dude to true change over time. As a result, these reliabilities are generally lower. The alternateform stability coefficient is based on correlations between fallwinter and winterspring benchmark scores.
 *Describe the sample(s), including size and characteristics, for each reliability analysis conducted.
 The concurrent alternateform reliability sample is based on 10 schools from across the U.S. representing each of three SES levels (described above). Participating schools administered the alternate forms to all Kindergarten students in the school, with few exceptions for moderate to severe intellectual disabilities. Each student completed 2 of 3 alternate forms with forms administered in pairs: 1,2; 1,3; and 2, 3. The number of students completing each pair ranged from 206–223. The table reports the median reliability coefficient. The stability coefficient is derived from the national norm sample described above.
 *Describe the analysis procedures for each reported type of reliability.
 Pearson correlation coefficients of the scores from alternate forms.
*In the table(s) below, report the results of the reliability analyses described above (e.g., modelbased evidence, internal consistency or interrater reliability coefficients). Include detail about the type of reliability data, statistic generated, and sample size and demographic information.
Type of  Subscale  Subgroup  Informant  Age / Grade  Test or Criterion  n (sample/ examinees) 
n (raters) 
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.
 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  Subscale  Subgroup  Informant  Age / Grade  Test or Criterion  n (sample/ examinees) 
n (raters) 
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


Rating 
 *Describe each criterion measure used and explain why each measure is appropriate, given the type and purpose of the tool.
 Four validity studies are reported: a concurrent study and a predictive study for each of two outcome criteria. Both criteria are independent of the Number Comparison Fluency–Pairs measure and are unspeeded power tests rather than speeded fluency tests. Neither is used for progress monitoring. One criterion is the Math score from the Tennessee Comprehensive Assessment Program (TCAP; Tennessee’s endofyear state assessment), administered in the spring. The other is the aimswebPlus Concepts & Applications (CA), a standardsbased interim assessment of math skills that is administered at the beginning, middle, and end of the school year. This assessment consists of 25 math concepts and problem solving items aligned to Grade 1 Common Core State Standards (CCSS) in mathematics and includes at least three items from each of the Grade 1 CCSS math domains. It is an individually administered power test in which students are given the time they need to complete each item. Its content differs from and has no overlap with Number Comparison Fluency–Pairs.
 *Describe the sample(s), including size and characteristics, for each validity analysis conducted.
 For each criterion, the same sample was used for both the concurrent and predictive validity studies. The SES index is the percentage of students at the student’s school eligible for free/reduced lunch, divided into three ranges of approximately equal size in the national student population. Criterion: TCAP CA N: 55 801 Female: 53% 50% Male: 47% 50% Black: 2% 13% Hispanic: 25% 25% White: 73% 51% Other: 0% 10% ELL: 24% 9% 68–100% FRPL: 0% 36% 34–67% FRPL: 100% 33% 0–33% FRPL: 0% 32%
 *Describe the analysis procedures for each reported type of validity.
 Both criterion measures were administered in the Spring. The concurrent studies are correlations between Spring NCF–P scores and the criteria, and the predictive studies are correlations between Fall NCF–P scores and the criteria.
*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  Subscale  Subgroup  Informant  Age / Grade  Test or Criterion  n (sample/ examinees) 
n (raters) 
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.
 Describe the degree to which the provided data support the validity of the tool.
 Number Comparison Fluency–Pairs (NCF–P) is designed to measure number sense, which is a fundamental skill underlying the development of proficiency in solving math problems. These validity studies support the interpretation of NCF–P scores as measures of number sense. Furthermore, they demonstrate that performance on number sense has a moderately strong relationship with endofyear math achievement.
 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  Subscale  Subgroup  Informant  Age / Grade  Test or Criterion  n (sample/ examinees) 
n (raters) 
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


Rating  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 multiplegroup confirmatory factor models.
 No
 If yes,
 a. Describe the method used to determine the presence or absence of bias:
 Note. Number Comparison Fluency–Pairs is a numberbased assessment and does not require the same kind of bias analyses as more vocabulary and contextheavy assessments (e.g., math word problems, reading comprehension). Instructional text spoken by the examiner was written using simple, gradeappropriate language that keeps the students’ receptive language load to a minimum.
 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.
Growth Standards
Sensitivity: Reliability of Slope
Grade  Grade 1 

Rating 
 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 nonresponsive to Tier 2 instruction. Evidence based on an unknown sample, or a sample that does not meet these specifications, may not be considered.
 The sample consisted of 2,794 Grade 1 students below the 25th national percentile on the fall Number Comparison Fluency–Pairs (NCF–P) benchmark and who were assigned a math performance goal and receiving frequent progress monitoring with NCF–P. All progress monitoring schedules were at least 20 weeks in duration during the 2016–17 school year.
 Describe the frequency of measurement (for each student in the sample, report how often data were collected and over what span of time).
 The interval between the first and last administration was a minimum of 20 weeks. Most administrations occurred weekly, with a small percentage conducted twice monthly.
 Describe the analysis procedures.
 Each student’s progress monitoring administrations were sequenced by date and divided into two groups: odd numbered administrations (e.g, 1,3,5, etc) and even numbered administrations (e.g., 2,4,6, etc). Linear regression was used to compute the slope for each student by group. The following model was used: Scorei = Intercept + Datei where Date is the amount of time since the start of progress monitoring and i ranges from 1 to the number of administrations. The correlation between oddgroup and evengroup slopes across all students was computed and converted to a splithalf reliability coefficient using the SpearmanBrown Formula: 2r/(1+r)
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).
Type of  Subscale  Subgroup  Informant  Age / Grade  Test or Criterion  n (sample/ examinees) 
n (raters) 
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.
 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.
Type of  Subscale  Subgroup  Informant  Age / Grade  Test or Criterion  n (sample/ examinees) 
n (raters) 
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.
Sensitivity: Validity of Slope
Grade  Grade 1 

Rating 
 Describe each criterion measure used and explain why each measure is appropriate, given the type and purpose of the tool.
 Two criterion measures were used: ● Concepts & Applications (CA) ● Math Facts Fluency–1 Digit (MFF–1D) CA is a standardsbased interim assessment administered as a separate test in the aimswebPlus Fall, Winter, and Spring benchmark math assessment battery. This assessment consists of 25 math concepts and problem solving items aligned to Grade 1 Common Core State Standards (CCSS) in mathematics and includes at least three items from each of the Grade 1 CCSS math domains. It is an individually administered test in which students respond orally and are given the time they need to complete each item. The math CA content and approach differs from Number Comparison Fluency–Pairs. Math Facts Fluency–1 Digit (MFF–1D) measures a student’s speed and accuracy solving onedigit addition and subtraction problems. It is a timed 1minute individually administered CBM that is included as a separate test in the aimswebPlus Fall, Winter, and Spring benchmark math assessment battery. The MFF1D content differs from and has no overlap with Number Comparison Fluency–Pairs. According to the CCSS for Mathematics, key skill and conceptual development in Grade 1 includes: ● an understanding of addition and subtraction through 20 and ● an understanding of whole number relationships and place value. NCF–P measures a student’s speed and accuracy in determining which of two onedigit or twodigit numbers is greater. It represents a CCSS Math Standard (1.NBT.3) and it is a critical foundational skill that, when mastered, should improve a student’s understanding of combining and separating numbers (addition and subtraction) and learning the fundamentals of place value which form the basis for most number and operations knowledge through Grade 8. It is expected that students who improve the most on NCF–P from Fall to Spring should have greater proficiency in the Spring with addition and subtraction facts as measured by MFF–1D, as well as with other base 10 number concepts and problem solving skills, as measured by CA.
 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 nonresponsive to Tier 2 instruction. Evidence based on an unknown sample, or a sample that does not meet these specifications, may not be considered.
 The sample consisted of 2,794 Grade 1 students below the 25th national percentile on the Fall Number Comparison Fluency–Pairs (NCF–P) benchmark and who were assigned a math performance goal and receiving frequent progress monitoring with NCF–P. All progress monitoring schedules were at least 20 weeks in duration during the 2016–17 school year.
 Describe the frequency of measurement (for each student in the sample, report how often data were collected and over what span of time).
 The interval between the first and last administration was a minimum of 20 weeks. Most administrations occurred weekly, with a small percentage conducted twice monthly.
 Describe the analysis procedures for each reported type of validity.
 Spring CA and MFF–1D scores were regressed onto the Fall to Spring PM slope for NCF–P and the Fall NCF–P scores. Including Fall NCF–P scores controls for differences in initial performance, thus removing its effect on the relationship between slope and outcome. Standardized regression coefficients and associated standard errors are reported in the table below. Model 1a: CA Spring Score = Intercept + NCF–P slope + NCF–P Fall Score Model 1b: MFF–1D Spring Score = Intercept + NCF–P slope + NCF–P Fall Score
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.
Type of  Subscale  Subgroup  Informant  Age / Grade  Test or Criterion  n (sample/ examinees) 
n (raters) 
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 validity studies:
 No
 Provide citations for additional published studies.
 Describe the degree to which the provided data support the validity of the tool.
 These results support the validity of the inference that growth in the NCF  P score reflects growth in math proficiency more generally because growth in the criterion construct contributes to higher criterion in the Spring. Because NCFP is different in content from both criteria and different in administration format from CA, one would not expect a high correlation between NCFP growth and Spring criterion performance. Therefore, moderate correlations such as these are good supporting evidence.
 Do you have validity of the slope data that is disaggregated by subgroups (e.g., race/ethnicity, gender, socioeconomic status, students with disabilities, English language learners)?
 No
If yes, fill in data for each subgroup with disaggregated validity of the slope data.
Type of  Subscale  Subgroup  Informant  Age / Grade  Test or Criterion  n (sample/ examinees) 
n (raters) 
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 validity studies:
 No
 Provide citations for additional published studies.
Alternate Forms
Grade  Grade 1 

Rating 
 Describe the sample for these analyses, including size and characteristics:
 The sample consisted of 3,156 students from 255 schools each with a math performance goal and a progress monitoring schedule who scored at or below the 30th national percentile on the spring NCF–P benchmark form. Each student completed at least one of the alternate NCF–P PM forms within a window from 5 to 35 days after benchmark testing. Forms were randomly assigned to students. Because the test interval was fairly brief and students were randomly assigned to forms, comparability is based on a direct comparison of the sample means.
 What is the number of alternate forms of equal and controlled difficulty?
 20 The average performance on the forms, administered in a 30 day window is the basis of form comparability. To demonstrate comparability we calculated the effect size as the mean difference between each form and the average difficulty across all forms in standard deviations units. (X_iμ)/SD The means ES is 0.14, and 19 of 20 effect sizes are less than 0.30, which is considered small. Comparability of the entire set of 20 forms is also summarized using analysis of variance where Form is treated as a fixed factor. The results indicate that Form accounts for only 2.12% of the total score variance. This is a very small percent and will have a trivial effect on the growth slope over the 20 or so administrations that are common for progress monitoring. More detailed information about alternate form comparability is available from the Center upon request.
 If IRT based, provide evidence of item or ability invariance
 If computer administered, how many items are in the item bank for each grade level?
 If your tool is computer administered, please note how the test forms are derived instead of providing alternate forms:
Decision Rules: Setting & Revising Goals
Grade  Grade 1 

Rating 
 In your manual or published materials, do you specify validated decision rules for how to set and revise goals?
 Yes
 If yes, specify the decision rules:
 To get the most value from progress monitoring, aimswebPlus recommends the following: (1) establish a time frame, (2) determine the level of performance expected, and (3) determine the criterion for success. Typical time frames include the duration of the intervention or the end of the school year. An annual time frame is typically used when IEP goals are written for students who are receiving special education services. For example, aimswebPlus goals can be written as follows: In 34 weeks, the student will compare numbers and answer computational problems to earn a score of 30 points on Grade 4 Number Sense Fluency forms. aimswebPlus provides several ways to define a level of expected performance. The goal can be based on: ● wellestablished performance benchmarks that can be linked to aimswebPlus measures via national percentiles (e.g., the link to state test performance levels) or total score (e.g., word read per minute in Grade 2); ● a national performance norm benchmark (e.g., the 50th national percentile is often used to indicate ongrade level performance); ● a local performance norm benchmark; ● or an expected or normative rate of improvement (ROI), such as the 85th national student growth percentile. To use this last method (student growth percentile), the user begins by selecting the measure and baseline score, the goal date, the monitoring frequency (default is weekly), and a tentative goal score. The system automatically labels the ambitiousness of the goal as Insufficient (SGP below 50), Closes the Gap (SGP between 50 and 85), Ambitious (86 to 97), or Overly Ambitious (above 97). The user can then adjust the goal (or the goal date) in light of this feedback. For students in need of intensive intervention, aimswebPlus recommends setting performance goals that represent rates of growth between the 86th and 97th SGP (Ambitious). An SGP of 86 represents a growth rate achieved by just 15% of the national sample, which is why it is considered ambitious. However, it is reasonable to expect significantly higher than average growth when implementing effective, intensive intervention. If the goal is set according to a benchmark based on raw scores or national or local norms, the aimswebPlus system still labels the ambitiousness of the goal in one of the four levels described above. If the goal corresponds to an Insufficient or Overly Ambitious rate of growth, users are advised to consider adjusting the goal. However, the user ultimately determines what growth rate is required on an individual basis. With respect to the decision to revise a goal, aimswebPlus provides empiricallybased feedback about the student’s progress relative to the initial goal using the statistical tool described in our response to question B5 below. If the projected score at the goal date is fully Above Target (ie., the 75% confidence interval for the student’s projected score at the goal date is entirely above the goal score), we recommend that the user consider raising the goal if the goal date is at least 12 weeks out. Otherwise, we recommend not changing the goal. On the other hand, if the upper end of the confidence interval on the projected score lies Below Target, we recommend either changing the intervention, increasing its intensity, or lowering the goal if the initial goal was Overly Ambitious.

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.  As described above, users have flexibility in the method they use to set and revise goals in aimswebPlus. The SGPbased labeling of goals as Overly Ambitious, Ambitious, Closes the Gap, or Insufficient is intended to assist the user in choosing a goal, but is not an automatic goalsetting system. Likewise, the analytical system that generates a confidence interval for the student's predicted performance at the goal date helps the user manage progress monitoring but does not make a decision about revising the goal. Certainly a decision to lower a goal would rely primarily on the educator's judgement, since the fist consideration would be to change the intervention. No experiment has been conducted in which the aimswebPlus information related to setting and revision goals was provided form some students receiving intensive intervention but not others.
Decision Rules: Changing Instruction
Grade  Grade 1 

Rating 
 In your manual or published materials, do you specify validated decision rules for when changes to instruction need to be made?
 Yes
 If yes, specify the decision rules:
 aimswebPlus applies a statistical procedure, based on linear regression, to the student’s progress monitoring scores in order to provide empiricallybased guidance about whether the student is likely to meet, fall short of, or exceed his/her goal. The calculation procedure (presented below) is fully described in the aimswebPlus Progress Monitoring Guide (Pearson, 2017). aimswebPlus users will not have to do any calculations—the online system does this automatically. The decision rule is based on a 75% confidence interval for the student’s predicted score at the goal date. This confidence interval is studentspecific and takes into account the number and variability of progress monitoring scores and the duration of monitoring. Starting at the sixth week of monitoring (when there are at least four monitoring scores), the aimswebPlus report following each progress monitoring administration includes one of the following statements: A. Below Target. Projected to not meet the goal. This statement appears if the confidence interval is completely below the goal score. B. Above Target. Projected to meet or exceed the goal. This statement appears if the confidence interval is completely above the goal score. C. Near Target. Projected score at goal date: Between (X) and (Y). This statement appears if the confidence interval includes the goal score, with X and Y indicating the bottom and top of the confidence interval, respectively. If Statement A appears, the user has a sound basis for deciding that the current intervention is not sufficient and a change to instruction should be made. If Statement B appears, there is an empirical basis for deciding that the goal is not sufficiently challenging and should be increased. If Statement C appears, the student’s progress is not clearly different from the aimline, so there is not a compelling reason to change the intervention or the goal; however, the presentation of the confidenceinterval range enables the user to see whether the goal is near the upper limit or lower limit of the range, which would signal that the student’s progress is trending below or above the goal. A 75% confidence interval was chosen for this application because it balances the costs of the two types of decision errors. Incorrectly deciding that the goal will not be reached (when in truth it will be reached) has a moderate cost: an intervention that is working will be replaced by a different intervention. Incorrectly deciding that the goal may be reached (when in truth it will not be reached) also has a moderate cost: an ineffective intervention will be continued rather than being replaced. Because both kinds of decision errors have costs, it is appropriate to use a modest confidence level. Calculation of the 75% confidence interval for the score at the goal date Calculate the trend line. This is the ordinary leastsquares regression line through the student’s monitoring scores. Calculate the projected score at the goal date. This is the value of the trend line at the goal date. Calculate the standard error of estimate (SEE) of the projected score at the goal date, using the following formula: 〖SEE〗_(predicted score)= √((∑_i^k 〖(y_i〖ý〗_i)〗^2)/(k2))×√(1+1/k+〖(GW(∑_1^k w_i)/k)〗^2/(∑_i^k 〖(w_i(∑_1^k w_i)/k)〗^2 )) where k = number of completed monitoring administrations, w = week number of a completed administration, GW = week number of the goal date, y = monitoring score, y’ = predicted monitoring score at that week (from the student’s trendline). The means and sums are calculated across all of the completed monitoring administrations up to that date. Add and subtract 1.25 times the SEE to the projected score, and round to the nearest whole numbers.

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.  The decision rules are statistically rather than empirically based. The guidance statements that result from applying the 75% confidence interval to the projected score are correct probabilistic statements, under certain assumptions that: the student's progress to date can be described by a linear trend line. If the pattern of the student's monitoring scores is obviously curvilinear, then the projected score based on a linear trend will likely be misleading. We provide training in the aimswebPlus Progress Monitoring Guide about the need for users to take nonlinearity into account when interpreting progressmonitoring data. Another assumption is that the student will continue to progress at the same rate that they have been progressing to that time. This is an unavoidable assumption for a decision system based on extrapolating from past growth. No controlled experimental study has been conducted to support the decision rules, however, an empirical study of actual progress monitoring results was undertaken to evaluate the accuracy of the decision rules as various points during the progress monitoring schedule. aimswebPlus Number Sense Fluency (NSF) and Oral Reading Fluency (ORF) progress monitoring data collected during the 201617 school year was used to evaluate the accuracy of the decision feedback. All students on a PM schedule who scored below the 30th national percentile on the fall benchmark and who had at least 20 PM administrations were included. Grades 2 and 3 were chosen. More than 1000 student’s scores were used in each grade. Most administrations we collected about weekly. Because we did not have the student’s actual goal score we generated a goal score based on the the ROI that corresponds to a student growth percentile of 55. This level was chosen because it represents an average rate of improvement and it resulted in about 50% of the students meeting the goal. The goal score was computed as follows: Fall Benchmark Score + ROI55*Weeks. Where ROI55 is the ROI associated with the SGP of 55 and Weeks is the number of weeks from the baseline score (Fall Benchmark) and the Spring Benchmark. For each student, beginning with the 8th score and going through the last score, we computed the score feedback based on the rules described in the previous section. If the student was projected to be below target an intervention change was deemed necessary and coded 1. Otherwise, the student was assigned a score of zero for that administration (no change is needed). We computed the accuracy of the decision to change interventions by comparing the decision to whether the student ultimately did not meet the goal score by the Spring Benchmark. Accuracy was computed as the percentage of the decisions to change intervention of all students who did not ultimately meet the goal. The results showed that decision accuracy improved with each successive administration with 70%  75% accuracy by the 8th administration and 75%  80% by the 15th administration and 90% by the 20th administration. This trend was replicated in each sample and it provides evidence that the decision rules validly indicate when a change in the intervention should be made because the student is unlikely to achieve the goal with the current rate of improvement.
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