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Number Sense Fluency
Cost 
Technology, Human Resources, and Accommodations for Special Needs 
Service and Support 
Purpose and Other Implementation Information 
Usage and Reporting 
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. 
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 Sense Fluency—the combined measures of Mental Computation Fluency (MCF) and Number Comparison Fluency–Triads (NCF–T)—is a computeradministered, timed test that employs strict time limits, in part, 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 accommodation is allowed for Number Sense Fluency during screening and progress monitoring: modifying the environment (e.g., special lighting, adaptive furniture). 
NCS Pearson, Inc. Training manuals are included and should provide all implementation information. Pearson provides phone and emailbased ongoing technical support, as well as a user group forum that facilitates the asking and answering of questions. 
aimswebPlus is a brief and valid assessment system for monitoring reading and math skills. Normative data were collected in 201314 on a combination of fluency measures that are sensitive to growth as well as new standardsbased assessments of classroom skills. The resulting scores and reports inform instruction and help improve student performance in Grades 2 through 8, while the Early Literacy and Early Numeracy measures provide ecologically valid and developmentally appropriate information about foundational reading and math abilities for students in Kindergarten and Grade 1. Number Sense Fluency (NSF) measures a student’s automaticity with comparing numbers within and across number systems and mentally solving one and twostep computation problems and math expressions. NSF is divided into two sections: Number Comparison Fluency–Triads (NCF–T) and Mental Computation Fluency (MCF). NCFT has a 3 minute time limit. MCF has a 4 minute time limit. Students answer as many items as they can within the time limit for each given section. 
While the Kindergarten and Grade 1 measures are administered individually, most of the Grades 2 through 8 measures can be taken online by entire classes. Once testing is complete, summary or detailed reports for students, classrooms, and districts can be immediately generated, and the math and reading composite scores can be used to estimate the risk to students or classes for meeting endofyear goals. aimswebPlus reports also offer score interpretation information based on foundational skills for college and career readiness, learning standards and other guidelines, Lexile® and Quantile® information, and recommendations for appropriate teaching resources. Raw score and percentiles scores (based on grade norms) are provided. Local norms are also available. Number Sense Fluency (NSF) comprises two sections, which are always administered together: Mental Computation Fluency (MCF): a timed measure that assesses fluency through solving 1and 2step computation expressions. Number Comparison Fluency–Triads (NCF–T): a timed measure that assesses fluency through number comparison. Both NCF–T and MCF employ a correction for guessing when calculating the total score. The corrected total score is: NC – NW/2, where NC is the number of items correctly answered and NW is the number of items answered incorrectly. Scores are then rounded to the nearest whole number. Corrected total scores can range from 0 to 40 (NCF–T) or 42 (MCF). Items not attempted and items not reached are ignored in the calculation of the corrected total score. Together, these measures combine into a Number Sense Fluency score, which is the simple sum of the NCF–T and MCF corrected scores. This NSF score is the basis for progress monitoring decisions. 
Reliability of the Performance Level Score
Grade  2  3  4  5  6  7  8 

Rating 
Reliability Coefficients for Number Sense Fluency*, Grades 2 Through 8
Type of Reliability 
Grade 
n (range) 
Coefficient Range 
Coefficient Median 
SEM 
Alternate Form 
2 
113 
0.90–0.93 
0.92 
2.86 
Alternate Form 
3 
131 
0.92–0.94 
0.93 
2.46 
Alternate Form 
4 
137 
0.91–0.94 
0.93 
2.41 
Alternate Form 
5 
132 
0.91–0.92 
0.91 
2.58 
Alternate Form 
6 
115 
0.83–0.87 
0.86 
4.19 
Alternate Form 
7 
77 
0.87–0.89 
0.88 
3.60 
Alternate Form 
8 
123 
0.89–0.91 
0.90 
3.92 
*Note. Number Sense Fluency comprises Number Comparison Fluency–Triads and Mental Computation Fluency. The Number Sense Fluency score (the simple sum of the NCF–T and MCF corrected scores) is the basis for progress monitoring decisions.
Reliability of the Slope
Grade  2  3  4  5  6  7  8 

Rating 
Validity of the Performance Level Score
Grade  2  3  4  5  6  7  8 

Rating 
aimswebPlus Math NSF Score Predictive Validity Coefficient, by Grade and Criterion Measure
Criterion 
Grade 
N 
Correlation 
Gender Percentage 
Race Percentage 

Unadjusted 
Adjusted^{1} 
F 
M 
B 
H 
O 
W 

ITBS 
2 
178 
0.65 
0.76 
61 
39 
24 
35 
1 
31 

ISAT 
3 
69 
0.75 
0.73 
49 
51 
1 
25 
13 
61 

ISAT 
4 
175 
0.68 
0.66 
51 
49 
4 
28 
9 
58 

ISAT 
5 
189 
0.81 
0.79 
53 
47 
2 
21 
9 
68 

ISAT 
6 
273 
0.7 
0.77 
59 
41 
22 
6 
8 
64 

ISAT 
7 
130 
0.82 
0.85 
45 
55 
13 
2 
3 
82 

ISAT 
8 
122 
0.51 
0.59 
37 
63 
5 
1 
3 
91 

STAAR 
3 
146 
0.72 
0.75 
55 
45 
10 
39 
14 
37 

STAAR 
4 
207 
0.72 
0.72 
51 
49 
8 
46 
14 
32 

STAAR 
5 
91 
0.55 
0.65 
47 
53 
2 
52 
6 
41 

STAAR 
6 
61 
0.64 
0.76 
55 
45 
5 
44 
3 
48 

STAAR 
7 
61 
0.72 
0.85 
40 
60 
5 
43 
4 
49 

STAAR 
8 
75 
0.65 
0.86 
61 
39 
15 
53 
0 
32 

NWEA  MAP 
2 
218 
0.57 
0.47 
48 
52 
5 
31 
12 
53 

NWEA  MAP 
3 
129 
0.76 
0.70 
46 
54 
1 
40 
14 
44 

NWEA  MAP 
4 
150 
0.67 
0.60 
59 
41 
5 
35 
10 
49 

NWEA  MAP 
5 
125 
0.82 
0.77 
47 
53 
3 
43 
11 
43 

NWEA  MAP 
6 
141 
0.7 
0.61 
55 
45 
22 
9 
10 
59 

NMSBA 
6 
206 
0.66 
0.75 
51 
49 
3 
63 
1 
32 

NMSBA 
7 
216 
0.74 
0.86 
47 
53 
2 
62 
0 
36 

NMSBA 
8 
219 
0.79 
0.86 
45 
55 
6 
70 
1 
24 

aimswebPlus CA 
2 
1484 
0.58 
0.58 
50 
50 
14 
23 
10 
53 

aimswebPlus CA 
3 
1497 
0.61 
0.61 
50 
50 
14 
23 
10 
53 

aimswebPlus CA 
4 
1482 
0.55 
0.55 
50 
50 
14 
22 
10 
54 

aimswebPlus CA 
5 
1492 
0.59 
0.59 
50 
50 
14 
23 
10 
53 

aimswebPlus CA 
6 
737 
0.73 
0.73 
50 
50 
13 
24 
9 
53 

aimswebPlus CA 
7 
959 
0.77 
0.77 
50 
50 
14 
23 
5 
58 

aimswebPlus CA 
8 
1026 
0.69 
0.69 
50 
50 
12 
22 
8 
58 
^{1} correlation adjusted for range restriction
aimswebPlus Math NSF Score Concurrent Validity Coefficient, by Grade and Criterion Measure
Criterion 
Grade 
N 
Correlation 
Gender Percentage 
Race Percentage 

Unadjusted 
Adjusted^{1} 
F 
M 
B 
H 
O 
W 

ITBS 
2 
178 
0.66 
0.75 
61 
39 
24 
35 
1 
31 

ISAT 
3 
69 
0.77 
0.75 
49 
51 
1 
25 
13 
61 

ISAT 
4 
175 
0.75 
0.73 
51 
49 
4 
28 
9 
58 

ISAT 
5 
189 
0.79 
0.77 
53 
47 
2 
21 
9 
68 

ISAT 
6 
273 
0.73 
0.75 
59 
41 
22 
6 
8 
64 

ISAT 
7 
130 
0.77 
0.81 
45 
55 
13 
2 
3 
82 

ISAT 
8 
122 
0.54 
0.59 
37 
63 
5 
1 
3 
91 

STAAR 
3 
146 
0.69 
0.73 
55 
45 
10 
39 
14 
37 

STAAR 
4 
207 
0.74 
0.71 
51 
49 
8 
46 
14 
32 

STAAR 
5 
91 
0.68 
0.76 
47 
53 
2 
52 
6 
41 

STAAR 
6 
61 
0.7 
0.76 
55 
45 
5 
44 
3 
48 

STAAR 
7 
61 
0.72 
0.79 
40 
60 
5 
43 
4 
49 

STAAR 
8 
75 
0.54 
0.77 
61 
39 
15 
53 
0 
32 

NWEA  MAP 
2 
218 
0.67 
0.68 
48 
52 
5 
31 
12 
53 

NWEA  MAP 
3 
129 
0.77 
0.78 
46 
54 
1 
40 
14 
44 

NWEA  MAP 
4 
150 
0.74 
0.77 
59 
41 
5 
35 
10 
49 

NWEA  MAP 
5 
125 
0.77 
0.80 
47 
53 
3 
43 
11 
43 

NWEA  MAP 
6 
141 
0.71 
0.85 
55 
45 
22 
9 
10 
59 

NMSBA 
6 
206 
0.71 
0.79 
51 
49 
3 
63 
1 
32 

NMSBA 
7 
216 
0.76 
0.83 
47 
53 
2 
62 
0 
36 

NMSBA 
8 
219 
0.8 
0.87 
45 
55 
6 
70 
1 
24 

aimswebPlus CA 
2 
1484 
0.63 
0.63 
50 
50 
14 
23 
10 
53 

aimswebPlus CA 
3 
1497 
0.65 
0.65 
50 
50 
14 
23 
10 
53 

aimswebPlus CA 
4 
1482 
0.63 
0.63 
50 
50 
14 
22 
10 
54 

aimswebPlus CA 
5 
1492 
0.64 
0.64 
50 
50 
14 
23 
10 
53 

aimswebPlus CA 
6 
737 
0.76 
0.76 
50 
50 
13 
24 
9 
53 

aimswebPlus CA 
7 
959 
0.78 
0.78 
50 
50 
14 
23 
5 
58 

aimswebPlus CA 
8 
1026 
0.74 
0.74 
50 
50 
12 
22 
8 
58 
^{1} correlation adjusted for range restriction
Predictive Validity of the Slope of Improvement
Grade  2  3  4  5  6  7  8 

Rating 
The predictive validity of the Number Sense Fluency (NSF) slope was assessed using the correlation of the annual NSF ROI (NSFROI) with spring Concepts & Applications (CASpring) test scores, after controlling for fall NSF (NSFFall) performance. The model used is shown here:
〖CA〗_spring= Intercept+ (β_1 )×〖NSF〗_Fall+ (β_2 )×〖NSF〗_ROI+ ε
A positive and statistically significant β_2 indicates that for a given fall NSF score, students with higher NSF ROIs had higher spring CA scores.
Concepts & Applications (CA) is an online, untimed (nonspeeded) math measure that assesses conceptual knowledge and math problem solving skills. It is standards based, with items that align to the Common Core State Standards of Mathematics. CA is used exclusively for screening (benchmarking) and is not part of the progress monitoring system. There are three CA benchmark forms (fall, winter, and spring), each with between 29 and 31 items. Scores are reported on a developmental scale that spans Grades 2 through 8.
Predictive validity of the fall to spring rate of improvement, Number Sense Fluency
Grade 
n 
b_{2} 
SE 
T 
p 
2 
1515 
16.7 
1.18 
14.3 
<0.01 
3 
1502 
14.0 
1.00 
14.0 
<0.01 
4 
1507 
14.8 
0.98 
16.0 
<0.01 
5 
1507 
11.2 
0.86 
13.1 
<0.01 
6 
1262 
14.2 
0.95 
15.0 
<0.01 
7 
1040 
12.2 
0.97 
12.5 
<0.01 
8 
973 
13.0 
0.97 
13.4 
<0.01 
Bias Analysis Conducted
Grade  2  3  4  5  6  7  8 

Rating  No  No  No  No  No  No  No 
Disaggregated Reliability and Validity Data
Grade  2  3  4  5  6  7  8 

Rating  No  No  No  No  No  No  No 
Alternate Forms
Grade  2  3  4  5  6  7  8 

Rating 
What is the number of alternate forms of equal and controlled difficulty? 20 per grade
To maximize the equivalency of the alternate test forms used for progress monitoring, each form was developed from the same set of test specifications (i.e., test blueprints). The specifications indicate which skills to measure, the number of items per skill, and how to sequence the skills on each form. Test blueprint information for each measure, including item counts by skill, is presented in Section II of this document.
Twentyfour alternate NCF–T and MCF forms per grade were developed from these specifications and administered to a students from across the U.S. For this study, each student completed three NCF–T forms and three MCF forms. Twentyfour sets of forms were defined per grade, with each form appearing in two sets. Each set included the winter benchmark form for that grade and two alternate forms. In half of the sets, the same forms were presented but in reverse order. For example, Set 1A = Winter, PM1, PM2 forms, while Set 1B = Winter, PM2, PM1 forms. The winter form was used as an anchor form and to control for sampling differences across sets. Counterbalancing controlled for order effects.
Sets were randomly assigned to students by spiraling sets within grade at each testing site.
Form equivalency is further evaluated by comparing the mean difficulty of each form. Two methods are used here to describe comparability of form difficulty: effect size and percentage of total score variance attributable to form.
The effect size (ES) for each form is the mean of the form minus the weighted average across all forms divided by the pooled SD.
Effect sizes less than 0.30 are considered small. Most effect sizes were less than 0.10 for the NCF–T and MCF forms, across grades.
The percentage of the total score variance attributable to test form was computed by dividing the between form variance by the pooled within form variance plus between form variance. In each grade, the percentage of test score variance attributable to forms was less than 1%.
Grade 
Measure 
Form 
n range 
Mean 
SD 
ES 
2 
NSF 
4 
59–63 
17.4 
16.97 
0.02 
2 
NSF 
5 
58–59 
17.5 
18.75 
0.03 
2 
NSF 
6 
57–60 
18.9 
18.53 
0.11 
2 
NSF 
7 
51–56 
15.8 
15.16 
0.07 
2 
NSF 
8 
59 
16.7 
17.00 
0.02 
2 
NSF 
9 
57–61 
17.3 
16.40 
0.02 
2 
NSF 
10 
56–63 
17.8 
17.70 
0.05 
2 
NSF 
11 
59–62 
16.1 
15.44 
0.05 
2 
NSF 
12 
58 
16.8 
17.36 
0.01 
2 
NSF 
13 
50–58 
15.9 
15.04 
0.06 
2 
NSF 
14 
51–58 
18.7 
15.08 
0.10 
2 
NSF 
15 
59–60 
17.1 
15.70 
0.01 
2 
NSF 
16 
57–58 
17.0 
19.29 
0.00 
2 
NSF 
17 
58–61 
16.7 
17.91 
0.02 
2 
NSF 
18 
57–58 
16.4 
20.76 
0.03 
2 
NSF 
19 
59–60 
17.2 
15.57 
0.01 
2 
NSF 
20 
50–62 
15.6 
16.97 
0.08 
2 
NSF 
21 
57–58 
16.5 
15.97 
0.03 
2 
NSF 
22 
56–59 
18.4 
15.26 
0.08 
2 
NSF 
23 
56–59 
15.8 
16.57 
0.07 
Mean 
17.0 
16.9 
0.04 

SD 
0.96 
1.58 





Percentage variance: 0.29% 

Grade 
Measure 
Form 
n range 
Mean 
SD 
ES 
3 
NSF 
4 
52–59 
24.6 
19.77 
0.02 
3 
NSF 
5 
63–64 
25.5 
18.60 
0.06 
3 
NSF 
6 
58–64 
25.7 
20.22 
0.07 
3 
NSF 
7 
51–62 
23.9 
20.14 
0.02 
3 
NSF 
8 
53–62 
23.8 
16.01 
0.03 
3 
NSF 
9 
54 
24.3 
23.13 
0.00 
3 
NSF 
10 
55–57 
25.5 
19.17 
0.06 
3 
NSF 
11 
54–57 
24.0 
18.40 
0.02 
3 
NSF 
12 
54 
24.1 
23.42 
0.01 
3 
NSF 
13 
55–63 
22.4 
18.01 
0.10 
3 
NSF 
14 
51–62 
26.2 
20.21 
0.10 
3 
NSF 
15 
55–61 
24.6 
17.40 
0.02 
3 
NSF 
16 
58–70 
24.1 
18.63 
0.01 
3 
NSF 
17 
52–67 
23.4 
20.17 
0.05 
3 
NSF 
18 
61–63 
23.5 
16.06 
0.04 
3 
NSF 
19 
53–60 
24.9 
20.81 
0.03 
3 
NSF 
20 
53–63 
23.7 
16.79 
0.03 
3 
NSF 
21 
56–62 
24.0 
16.42 
0.02 
3 
NSF 
22 
55–60 
25.1 
17.81 
0.04 
3 
NSF 
23 
57–61 
22.7 
17.28 
0.08 
Mean 
24.3 
18.9 
0.04 

SD 
0.98 
2.10 





Percentage variance: 0.25% 

Grade 
Measure 
Form 
n range 
Mean 
SD 
ES 
4 
NSF 
4 
58–68 
27.6 
19.90 
0.02 
4 
NSF 
5 
58–70 
29.2 
17.98 
0.07 
4 
NSF 
6 
63–66 
30.2 
19.72 
0.12 
4 
NSF 
7 
65 
27.1 
18.79 
0.04 
4 
NSF 
8 
58–63 
26.6 
17.97 
0.07 
4 
NSF 
9 
58–68 
28.6 
20.48 
0.04 
4 
NSF 
10 
67–70 
29.1 
18.55 
0.06 
4 
NSF 
11 
61–67 
27.7 
18.93 
0.01 
4 
NSF 
12 
57–70 
28.4 
22.13 
0.03 
4 
NSF 
13 
65–67 
25.8 
18.41 
0.11 
4 
NSF 
14 
61–67 
31.1 
22.57 
0.16 
4 
NSF 
15 
66–72 
27.2 
18.62 
0.04 
4 
NSF 
16 
57–70 
27.7 
21.70 
0.01 
4 
NSF 
17 
66–68 
26.4 
18.10 
0.08 
4 
NSF 
18 
58–64 
27.3 
20.62 
0.03 
4 
NSF 
19 
67–68 
27.8 
20.49 
0.01 
4 
NSF 
20 
58–72 
26.7 
16.91 
0.06 
4 
NSF 
21 
61–67 
28.2 
17.59 
0.02 
4 
NSF 
22 
61–65 
29.2 
20.64 
0.07 
4 
NSF 
23 
65–74 
26.1 
18.28 
0.09 
Mean 
27.9 
19.4 
0.06 

SD 
1.37 
1.59 





Percentage variance: 0.49% 

Grade 
Measure 
Form 
n range 
Mean 
SD 
ES 
5 
NSF 
4 
57–67 
29.0 
18.19 
0.02 
5 
NSF 
5 
57–60 
29.9 
17.74 
0.06 
5 
NSF 
6 
57–64 
31.0 
18.83 
0.12 
5 
NSF 
7 
70–71 
27.9 
19.76 
0.04 
5 
NSF 
8 
59–70 
27.2 
18.41 
0.08 
5 
NSF 
9 
61–62 
29.4 
22.14 
0.04 
5 
NSF 
10 
63–71 
30.1 
20.10 
0.07 
5 
NSF 
11 
63–64 
27.6 
20.17 
0.06 
5 
NSF 
12 
64–70 
30.0 
22.05 
0.07 
5 
NSF 
13 
61–62 
26.6 
19.08 
0.11 
5 
NSF 
14 
58–63 
32.6 
20.54 
0.20 
5 
NSF 
15 
61–64 
28.4 
20.20 
0.01 
5 
NSF 
16 
57–67 
28.1 
19.69 
0.03 
5 
NSF 
17 
58–68 
27.9 
18.74 
0.04 
5 
NSF 
18 
64–66 
28.2 
18.38 
0.03 
5 
NSF 
19 
66 
28.6 
19.91 
0.00 
5 
NSF 
20 
58–63 
26.9 
18.12 
0.09 
5 
NSF 
21 
60–71 
27.9 
19.40 
0.04 
5 
NSF 
22 
59–60 
29.8 
19.71 
0.06 
5 
NSF 
23 
61–66 
26.6 
16.77 
0.11 
Mean 
28.7 
19.4 
0.06 

SD 
1.55 
1.33 





Percentage variance: 0.59% 

Grade 
Measure 
Form 
n range 
Mean 
SD 
ES 
6 
NSF 
4 
65–75 
25.2 
20.28 
0.02 
6 
NSF 
5 
53–70 
26.0 
17.82 
0.06 
6 
NSF 
6 
51–80 
26.5 
19.78 
0.09 
6 
NSF 
7 
48–49 
23.9 
16.89 
0.06 
6 
NSF 
8 
52–77 
24.0 
17.16 
0.05 
6 
NSF 
9 
47–51 
25.8 
15.47 
0.05 
6 
NSF 
10 
48–80 
26.2 
18.18 
0.07 
6 
NSF 
11 
79–80 
23.8 
19.67 
0.06 
6 
NSF 
12 
69–86 
25.0 
19.18 
0.01 
6 
NSF 
13 
43–80 
23.3 
17.54 
0.09 
6 
NSF 
14 
51–52 
27.3 
17.30 
0.14 
6 
NSF 
15 
56–86 
24.7 
16.25 
0.01 
6 
NSF 
16 
56–73 
24.9 
20.08 
0.00 
6 
NSF 
17 
43–58 
24.1 
15.15 
0.04 
6 
NSF 
18 
69–77 
25.0 
19.66 
0.01 
6 
NSF 
19 
56–82 
25.6 
16.10 
0.04 
6 
NSF 
20 
65–82 
23.4 
19.14 
0.08 
6 
NSF 
21 
49–73 
24.0 
19.45 
0.05 
6 
NSF 
22 
46–47 
25.8 
15.81 
0.05 
6 
NSF 
23 
51–75 
23.2 
16.75 
0.09 
Mean 
24.9 
17.9 
0.05 

SD 
1.16 
1.67 





Percentage variance: 0.37% 

Grade 
Measure 
Form 
n range 
Mean 
SD 
ES 
7 
NSF 
4 
51–66 
21.4 
18.25 
0.05 
7 
NSF 
5 
60–68 
22.0 
19.89 
0.08 
7 
NSF 
6 
35–68 
22.5 
18.25 
0.11 
7 
NSF 
7 
60–71 
20.0 
16.40 
0.03 
7 
NSF 
8 
64–66 
19.9 
17.41 
0.03 
7 
NSF 
9 
42–54 
20.8 
17.45 
0.02 
7 
NSF 
10 
62–66 
21.9 
19.51 
0.08 
7 
NSF 
11 
62–71 
19.4 
17.56 
0.06 
7 
NSF 
12 
42–61 
20.1 
16.83 
0.02 
7 
NSF 
13 
41–61 
18.1 
16.92 
0.13 
7 
NSF 
14 
39–66 
23.0 
18.87 
0.14 
7 
NSF 
15 
54–59 
20.9 
17.53 
0.02 
7 
NSF 
16 
51–64 
20.8 
19.93 
0.02 
7 
NSF 
17 
39–45 
19.8 
17.60 
0.04 
7 
NSF 
18 
41–49 
19.2 
18.36 
0.07 
7 
NSF 
19 
39–64 
21.2 
18.98 
0.04 
7 
NSF 
20 
39–54 
19.3 
18.43 
0.07 
7 
NSF 
21 
50–60 
19.8 
17.82 
0.04 
7 
NSF 
22 
59–61 
21.9 
17.28 
0.08 
7 
NSF 
23 
49–64 
18.2 
17.81 
0.13 
Mean 
20.5 
18.1 
0.06 

SD 
1.36 
0.99 





Percentage variance: 0.50% 

Grade 
Measure 
Form 
n range 
Mean 
SD 
ES 
8 
NSF 
4 
64–65 
20.6 
21.05 
0.02 
8 
NSF 
5 
55–73 
21.0 
20.80 
0.04 
8 
NSF 
6 
61–67 
21.8 
21.62 
0.08 
8 
NSF 
7 
55–72 
19.7 
21.45 
0.02 
8 
NSF 
8 
53–64 
19.5 
22.21 
0.03 
8 
NSF 
9 
52–67 
20.7 
18.78 
0.03 
8 
NSF 
10 
59–67 
21.3 
19.12 
0.06 
8 
NSF 
11 
58–72 
19.3 
19.59 
0.04 
8 
NSF 
12 
61–74 
20.3 
18.61 
0.01 
8 
NSF 
13 
58–64 
18.9 
20.31 
0.06 
8 
NSF 
14 
53–64 
22.1 
19.20 
0.10 
8 
NSF 
15 
58–59 
20.3 
19.44 
0.01 
8 
NSF 
16 
58–65 
20.2 
19.75 
0.00 
8 
NSF 
17 
53–64 
19.8 
18.98 
0.02 
8 
NSF 
18 
61–62 
19.6 
18.29 
0.03 
8 
NSF 
19 
62–64 
20.3 
20.99 
0.01 
8 
NSF 
20 
55–74 
18.5 
21.02 
0.08 
8 
NSF 
21 
55–62 
19.3 
19.05 
0.04 
8 
NSF 
22 
65 
21.4 
22.44 
0.06 
8 
NSF 
23 
52–73 
18.7 
18.63 
0.07 
Mean 
20.2 
20.1 
0.04 

SD 
1.02 
1.29 





Percentage variance: 0.24% 

Rates of Improvement Specified
Grade  2  3  4  5  6  7  8 

Rating 
Are benchmarks for minimum acceptable endofyear performance specified in your manual or published materials?
Yes
Specify the endofyear performance standards:
aimswebPlus allows users to select from a range of endofyear targets the one that is most appropriate for their instructional needs. The targets are based on spring reading or math composite national percentiles by grade level. Twelve national percentile targets ranging from the 15th through the 70th percentile are provided, in increments of 5.
For Grades 3 through 8, it is recommended that users select the spring percentile that most closely aligns to the overall percentage of students below proficient on state reading/math tests. This is the percentage considered at risk. For example, if the percentage of students below proficient on the state test is 20%, the recommended endofyear benchmark is the 20th percentile. Likewise, if the percentage of students below proficient on the state test is 60%, the recommended endofyear benchmark is the 60th percentile.
Because passing rates on state assessments are fairly consistent across grades, the percentage of students at risk in Kindergarten through Grade 2 is likely to be very similar to the percentage at risk in Grade 3. As such, aimswebPlus recommends using the percentage of students below proficient on the Grade 3 state reading/math tests as the endofyear benchmark for students in Kindergarten through Grade 2. For example, if the percentage of students below proficient on the state test in Grade 3 is 30%, the recommended endofyear benchmark for students in Kindergarten through Grade 2 is the 30th percentile.
If these percentages are not available, aimswebPlus recommends using the 25th percentile as the endofyear benchmark.
Fall and winter benchmark cut scores are derived automatically by the aimswebPlus system. The cut scores are based on empirical research of the relationship between fall/winter scores and spring benchmarks. Two cutscores are provided: one corresponding to a 50% probability of exceeding the spring benchmark, and the other corresponding to an 80% probability of exceeding the spring benchmark. Fall or winter scores above the 80% probability cut score are deemed low risk; fall or winter scores between the 50% and 80% cut scores are deemed moderate risk; and fall or winter scores below the 50% probability cut score are deemed high risk. These three levels correspond to the RTI tiers reported in the aimswebPlus system.
What is the basis for specifying minimum acceptable endofyear performance?
Normreferenced
Specify the benchmarks:
Percentage of students below proficient level on state test.
What is the basis for specifying these benchmarks?
Normreferenced
If normreferenced, describe the normative profile:
Demographic Characteristics of the aimswebPlus Norm Sample, Grades 2 Through 8

Sex 
Race 
SES (F/R lunch) 

Subject 
Grade 
Measure 
F 
M 
B 
H 
O 
W 
Low 
Mod 
High 
Math 
2 
NSF 
0.50 
0.50 
0.14 
0.23 
0.10 
0.53 
0.30 
0.40 
0.30 
Math 
3 
NSF 
0.50 
0.50 
0.14 
0.23 
0.10 
0.53 
0.30 
0.40 
0.30 
Math 
4 
NSF 
0.50 
0.50 
0.14 
0.22 
0.10 
0.54 
0.30 
0.40 
0.30 
Math 
5 
NSF 
0.50 
0.50 
0.14 
0.23 
0.10 
0.53 
0.30 
0.40 
0.30 
Math 
6 
NSF 
0.50 
0.50 
0.13 
0.24 
0.09 
0.53 
0.30 
0.40 
0.30 
Math 
7 
NSF 
0.50 
0.50 
0.14 
0.23 
0.05 
0.58 
0.30 
0.40 
0.30 
Math 
8 
NSF 
0.50 
0.50 
0.12 
0.22 
0.08 
0.58 
0.30 
0.40 
0.30 
Representation: National
Date: 2013–2014
Number of States: 18
Regions: 5
Gender: 50% Male 50%Female
SES: Low, middle, high, free and reduced lunch
ELL: 10%
EndofYear Benchmarks
Grade  2  3  4  5  6  7  8 

Rating 
Sensitive to Student Improvement
Grade  2  3  4  5  6  7  8 

Rating 
Describe evidence that the monitoring system produces data that are sensitive to student improvement (i.e., when student learning actually occurs, student performance on the monitoring tool increases on average).
Sensitivity to improvement was assessed by demonstrating that annual performance gains were statistically significant and moderate in size as expressed in fall standard deviation units. A gain expressed in SD units that exceeds 0.3 can be considered moderate (see Cohen, J., 1988. Statistical Power Analysis for the Behavioral Sciences (Second Edition). Lawrence Erlbaum Associates.)
Fall and spring benchmark mean, SD, pairedsample t, and annual gain represented as fall standard deviation units, Number Sense Fluency by grade
Mean 
SD 
N 
Paired t 
p 
Gain/SD 

Grade 
Fall 
Spring 
Fall 
Spring 

2 
16.0 
25.7 
14.02 
17.16 
2000 
48.2 
<.01 
0.69 
3 
24.8 
33.5 
16.18 
18.46 
2000 
42.0 
<.01 
0.54 
4 
25.8 
34.1 
15.08 
17.81 
2000 
41.9 
<.01 
0.55 
5 
25.8 
31.3 
15.93 
18.23 
2000 
26.6 
<.01 
0.34 
6 
22.3 
30.0 
15.16 
20.35 
2000 
29.6 
<.01 
0.51 
7 
20.9 
25.1 
16.82 
18.79 
2000 
17.5 
<.01 
0.25 
8 
23.1 
25.6 
18.56 
20.62 
2000 
11.7 
<.01 
0.13 
Decision Rules for Changing Instruction
Grade  2  3  4  5  6  7  8 

Rating 
Does your manual or published materials specify validated decision rules for when changes to instruction need to be made?
Yes
Specify the decision rules:
aimswebPlus applies a statistical procedure 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 aimsweb Progress Monitoring Guide (Pearson, 2012). 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. “The student is projected to not reach the goal.” This statement appears if the confidence interval is completely below the goal score.
B. “The student is projected to exceed the goal.” This statement appears if the confidence interval is completely above the goal score.
C. “The student is projected to be near the goal. The projected score at the goal date is between X and Y” (where X and Y are the bottom and top of the confidence interval). This statement appears if the confidence interval includes the goal score.
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_iy ́_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?
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: The student’s progress 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 aimsweb Progress Monitoring Guide about the need for users to take nonlinearity into account when interpreting progressmonitoring data. The student will continue to progress at the same rate as they have been progressing to that time. This is an unavoidable assumption for a decision system based on extrapolating from past growth.
Even though the rules are not derived from data, it is useful to observe how they work in a sample of real data. For this purpose, we selected random samples of students in the aimsweb 2010–2011 database who were progressmonitored on either Reading CurriculumBased Measurement (RCBM) or Math Computation (MCOMP). All students selected scored below the 25th percentile in the fall screening administration of RCBM or MCOMP. The RCBM sample consisted of 1,000 students (200 each at of Grades 2 through 6) who had at least 30 monitoring scores, and the MCOMP sample included 500 students (100 per Grades 2 through 6) with a minimum of 28 monitoring scores. This analysis was only a rough approximation, because we did not know each student’s actual goal or whether the intervention or goal was changed during the year.
To perform the analyses, we first set an estimated goal for each student by using the ROI at the 85th percentile of aimsweb national ROI norms to project their score at their 30th monitoring administration. Next, we defined “meeting the goal” as having a mean score on the last three administrations (e.g., the 28th through 30th administrations of RCBM) that was at or above the goal score. At each monitoring administration for each student, we computed the projected score at the goal date and the 75% confidence interval for that score, and recorded which of the three decision statements was generated (projected not to meet goal, projected to exceed goal, or ontrack/nochange).
In this analysis, accuracy of guidance to change (that is, accuracy of projections that the student will not reach the goal or will exceed the goal) reached a high level (80%) by about the 13th to 15th monitoring administration, on average. The percentage of students receiving guidance to not change (i.e., their trendline was not far from the aimline) would naturally tend to decrease over administrations as the size of the confidence interval decreased. At the same time, however, there was a tendency for the trendline to become closer to the aimline over time as it became more accurately estimated, and this worked to increase the percentage of students receiving the “no change” guidance.
Decision Rules for Increasing Goals
Grade  2  3  4  5  6  7  8 

Rating 
Does your manual or published materials specify validated decision rules for when changes to increase goals?
Yes
Specify the decision rules:
The same statistical approach described under Decision Rules for Changing Instruction (GOM 9 above) applies to the decisions about increasing a goal. aimswebPlus provides the following guidance for deciding whether to increase a performance goal:
If the student is projected to exceed the goal and there are at least 12 weeks remaining in the schedule, consider raising the goal.
What is the evidentiary basis for these decision rules?
See GOM 9 evidentiary basis information above.
Improved Student Achievement
Grade  2  3  4  5  6  7  8 

Rating 
Improved Teacher Planning
Grade  2  3  4  5  6  7  8 

Rating 