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Math Computation
Cost 
Technology, Human Resources, and Accommodations for Special Needs 
Service and Support 
Purpose and Other Implementation Information 
Usage and Reporting 
MCOMP is included in a subscription to AIMSweb Pro Math and AIMSweb Pro Complete, which range from $4.00 to $6.00 per student per year. Every AIMSweb subscription provides unlimited access to the AIMSweb online system, which includes:

Internet access is required for full use of this product. Testers will require 12 hours of training. Paraprofessionals can administer the test. Alternate forms available in Spanish. 
Pearson Field tested training manuals are included with AIMSweb subscriptions which provide administration, scoring and implementation information. Ongoing technical support is provided. Professional development opportunities are available. 
MCOMP is a brief (8 minute) group (or individually) administered and standardized assessment of math computation proficiency. It uses an openended fillintheblank response format and consists of 33 alternate forms per grade for grades 18. The mathematics domains assessed include: column addition (grades 13), basic facts (grades 16), complex computation (grades 17), decimals (grades 48), fractions (grades 48), conversions (grade 58), percentages (grades 58), integers (grades 68), expressions (grade 6), reducing (grades 67), equations (grade 78), and exponents (grade 78). 
Total score, national percentiles (grades 1 – 12) and normative performance levels by grade and season, individual student growth percentiles by grade and season (based on rates of improvement, ROI), and success probability scores (cut scores that indicate a 50% or 80% probability of passing the state test). Local norms are also available. Reports that provide instructional links to enVisionMath and focusMATH, Prentice Hall Mathematics (grades 6 – 8), SuccessMaker Math, digits, KeyMath3 Diagnostic Assessment, and analysis of strengths and weaknesses by NCTM and Common Core domains. 
Reliability of the Performance Level Score
Grade  1  2  3  4  5  6  7  8 

Rating 
Type of Reliability  Age or Grade  n (range)  Coefficient  SEM  Information / Subjects  

range  median  
Alternate Form  1  919  0.86  4.8 
National field test sample:
Sex: 54% female, 46% male
Ethnicity:
1% Asian
8% African American
24% Hispanic
64% White
3% Other
SES (median family income):
36% Low
31% Medium
33% High
Region:
16% Northeast
25% Midwest
50% South
9% West


2  976  0.82  4.8  
3  971  0.89  5.8  
4  916  0.85  6.6  
5  1,048  0.89  6.7  
6  981  0.89  5.9  
7  944  0.90  6.1  
8  948  0.88  6.5  
Interrater  1  60  0.99  Cases drawn at random from the national fieldtest sample, scored independently by two different raters. Intraclass correlation (Shrout & Fleiss, 1979, type 2) which reflects consistency in level as well as rankordering.  
2  60  0.99  
3  60  0.99  
4  60  0.99  
5  60  0.98  
6  60  0.99  
7  60  0.99  
8  60  0.98 
Reliability of the Slope
Grade  1  2  3  4  5  6  7  8 

Rating 
Type of Reliability  Age or Grade  n (range)  Coefficient  SEM  Information / Subjects  

range  median  
Splithalf reliability (odd & even data points)  1  3,285  0.79  0.25  Average # of month span per student = 6.4, range 311; Average # of data point per student = 15.6, range 1070.  
Splithalf reliability (odd & even data points)  2  6,289  0.75  0.23  Average # of month span per student = 6.8, range 311; Average # of data point per student = 15.9, range 1062.  
Splithalf reliability (odd & even data points)  3  6,687  0.75  0.29  Average # of month span per student = 7.0, range 311; Average # of data point per student = 15.8, range 1051.  
Splithalf reliability (odd & even data points)  4  6,756  0.77  0.32  Average # of month span per student = 6.8, range 311; Average # of data point per student = 15.7, range 1049.  
Splithalf reliability (odd & even data points)  5  6,183  0.82  0.27  Average # of month span per student = 6.9, range 311; Average # of data point per student = 15.8, range 1065.  
Splithalf reliability (odd & even data points)  6  3,833  0.77  0.23  Average # of month span per student = 7.0, range 311; Average # of data point per student = 15.5, range 1046.  
Splithalf reliability (odd & even data points)  7  2,534  0.76  0.23  Average # of month span per student = 6.9, range 311; Average # of data point per student = 15.7, range 1041.  
Splithalf reliability (odd & even data points)  8  2,510  0.74  0.20  Average # of month span per student = 6.9, range 311; Average # of data point per student = 15.4, range 1042. 
Validity of the Performance Level Score
Grade  1  2  3  4  5  6  7  8 

Rating 
Type of Validity  Age or Grade  Test or Criterion  n (range)  Coefficient  Information / Subjects  

range  median  
Construct  1  Group Mathematics Assessment and Diagnostic Evaluation (GMADE)  98  0.84  Students participating in the national field test of MCOMP.  
Construct  3  GMADE  98  0.73  
Construct  8  GMADE  54  0.76 
Content Validity
The M–COMP revises AIMSweb’s M–CBM and –CBM II. Multiple nationally recognized RTI and mathematics experts were engaged in the development of the blueprints for each grade (1–8). Once the blueprints were finalized, anchor probes were developed for each grade; each anchor probe was then sent to the RTI and mathematics experts, along with a team of professional educators, for an additional round of input and analysis. When all of the data were aggregated, the AIMSweb content team used the collective analyses to make final adjustments to the probes that were then standardized through an extensive data collection in the Spring of 2010.
Grade  

MCOMP  1  2  3  4  5  6  7  8 
Column Addition  √  √  √  
Basic Facts  √  √  √  √  √  √  
Complex Computation  √  √  √  √  √  √  √  
Decimals  √  √  √  √  √  
Fractions  √  √  √  √  √  
Conversions  √  √  √  √  
Percentages  √  √  √  √  
Integers  √  √  √  
Expressions  √  
Reducing  √  √  
Equations  √  √  
Exponents  √  √ 
Predictive Validity of the Slope of Improvement
Grade  1  2  3  4  5  6  7  8 

Rating 
Bias Analysis Conducted
Grade  1  2  3  4  5  6  7  8 

Rating  No  No  No  No  No  No  No  No 
Disaggregated Reliability and Validity Data
Grade  1  2  3  4  5  6  7  8 

Rating  No  No  No  No  No  No  No  No 
Alternate Forms
Grade  1  2  3  4  5  6  7  8 

Rating 
1. Evidence that alternate forms are of equal and controlled difficulty or, if IRT based, evidence of item or ability invariance:
During field testing of MCOMP, several probes were administered to each student using a matrix sampling design. As shown in the table below, the probes within a grade have consistent means and standard deviations.
Means and Standard Deviations of Raw Scores on MCOMP Probes, by Grade  

Grade 1  Grade 2  Grade 3  Grade 4  Grade 5  Grade 6  Grade 7  Grade 8  
M  SD  M  SD  M  SD  M  SD  M  SD  M  SD  M  SD  M  SD  
30.9  3.7  34.1  2.2  47.1  5.7  46.6  5.5  30.3  4.8  28.2  3.9  33.0  4.7  26.2  3.9  
31.1  3.8  34.6  2.1  47.9  6.0  46.9  4.4  30.5  4.5  28.5  5.7  33.0  5.0  26.4  3.5  
31.7  3.9  35.0  2.3  48.7  6.1  47.0  4.5  30.6  6.9  28.8  4.6  33.3  4.6  26.7  3.2  
31.8  3.7  35.6  2.0  48.8  3.3  47.8  6.1  31.5  5.8  28.8  5.6  33.3  5.8  26.8  7.4  
33.8  2.7  35.9  2.5  49.7  3.9  48.1  3.9  31.8  7.5  29.0  4.7  33.5  5.6  27.4  8.7  
34.1  3.4  35.9  2.6  49.8  5.2  48.4  3.6  32.0  5.3  29.1  4.4  33.6  5.3  27.7  3.7  
34.2  3.5  36.1  2.5  50.0  4.6  48.7  3.8  32.1  4.5  30.5  3.9  33.7  4.2  27.7  3.6  
34.2  3.6  36.2  2.3  50.3  3.3  49.5  5.1  32.2  5.4  30.6  5.1  33.9  5.8  27.8  3.8  
34.3  2.9  36.3  3.7  50.3  5.6  49.8  4.7  32.6  5.5  31.4  6.5  34.0  6.3  27.9  3.6  
34.7  3.4  36.8  3.9  50.8  4.1  50.0  5.2  32.7  5.8  31.4  4.8  34.0  5.8  28.5  3.9  
35.0  2.6  37.0  3.6  51.0  4.6  50.3  4.2  32.7  5.5  31.8  5.6  34.1  5.2  28.6  4.0  
35.2  4.0  37.8  3.1  51.0  4.7  50.4  4.7  32.9  5.0  31.9  5.5  34.2  5.7  28.8  4.3  
35.4  3.7  38.1  3.2  51.1  3.1  50.9  3.8  32.9  5.2  33.2  5.1  34.4  5.1  29.6  4.6  
35.5  3.0  38.2  2.3  51.2  4.0  50.9  4.9  32.9  4.7  33.3  5.5  34.4  5.3  30.0  4.1  
35.5  3.1  38.3  3.5  51.3  3.5  51.3  4.3  33.0  5.5  33.3  5.1  34.8  6.5  30.6  7.2  
35.9  3.2  38.3  3.2  51.4  3.7  51.5  4.6  33.0  6.7  33.6  4.9  35.1  4.3  31.2  4.0  
36.0  3.0  38.4  2.1  52.1  4.0  51.7  4.5  33.2  6.4  33.6  4.1  35.2  5.3  31.2  5.0  
36.2  4.3  38.4  3.4  52.3  3.4  51.8  3.5  33.7  6.7  33.6  5.3  35.3  6.1  31.3  4.5  
36.2  2.9  38.8  3.1  52.4  4.0  51.8  4.3  34.0  7.3  33.6  3.3  35.4  4.5  31.5  7.5  
36.4  4.1  39.3  2.0  52.6  4.0  52.2  3.3  34.1  7.1  34.0  3.8  35.6  6.2  31.9  8.1  
36.6  3.0  39.3  2.2  52.6  4.0  52.4  3.7  34.3  4.8  34.0  4.4  36.1  6.3  32.8  5.2  
36.6  3.7  39.6  2.6  52.8  4.3  52.6  4.0  34.7  5.1  34.3  3.8  36.7  5.9  32.9  7.0  
36.7  3.8  39.7  2.7  53.0  3.5  52.7  4.5  35.3  4.6  34.4  3.9  36.7  4.9  33.4  7.4  
37.4  2.4  39.7  3.0  53.3  3.1  52.9  2.8  35.4  4.7  34.7  6.1  36.9  7.2  33.5  5.2  
37.6  2.8  39.8  2.2  53.3  3.0  52.9  3.3  35.8  7.0  34.8  8.0  37.5  6.1  33.9  8.1  
37.7  2.9  39.9  2.1  53.4  4.6  53.5  2.9  36.4  5.3  35.1  3.6  37.6  7.4  34.7  4.5  
37.7  2.9  40.1  2.0  53.4  3.9  53.6  2.5  36.7  5.3  35.2  8.4  40.1  8.8  36.2  6.0  
37.8  2.5  40.8  1.9  53.5  3.4  53.7  3.6  36.8  4.8  35.4  8.8  40.6  6.6  36.5  4.4  
37.9  2.6  40.9  2.2  53.6  3.1  54.1  3.1  37.4  9.6  35.5  5.5  40.9  5.5  36.8  9.6  
39.9  2.8  41.5  1.7  53.7  3.9  54.4  5.3  37.6  5.7  35.5  5.4  41.0  8.0  36.9  4.3  
Mean:  35.5  3.3  38.0  2.6  51.4  4.1  50.9  4.2  33.6  5.8  32.6  5.2  35.6  5.8  30.9  5.3 
SD:  2.1  0.5  2.0  0.6  1.8  0.9  2.3  0.8  2.0  1.2  2.4  1.4  2.4  1.1  3.3  1.8 
2. Number of alternate forms of equal and controlled difficulty:
30 per grade
Rates of Improvement Specified
Grade  1  2  3  4  5  6  7  8 

Rating 
1. Is minimum acceptable growth (slope of improvement or average weekly increase in score by grade level) specified in manual or published materials?
No, AIMSweb specifies the median value of growth by grade and score level based on the national norm sample. Users determine what growth rate is required on an individual basis.
a. Specify the growth standards:
N/A
b. Basis for specifying minimum acceptable growth:
2. Normative profile:
Representation: National
Date: 20102011
Number of States: approximately 40
Size: 80,714
Gender: 51% Male, 49% Female,
SES: 40% free/reduced lunch
Race/Ethnicity: 59% White, 16% Black, 16% Hispanic, 4% Asian/Pacific Islander, 3% Other
3. Procedure for specifying criterion for adequate growth:
To get the most value from progress monitoring, AIMSweb 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. AIMSweb goals can be written as: In 34 weeks (1 academic year), the student will write correct answers to computation problems, earning 40 points on grade 5 M–COMP probes.
The criterion for success may be set according to standards, local norms, national norms, or a normative Rate of Improvement (ROI). The team may want to compare a student’s performance to district/local norms; that is, to compare the scores to his or her peers in the context of daily learning. The last type of criterion is to use a normative rateofimprovement (ROI). Using a mathematical formula (Initial Score + [Expected ROI x Number of Weeks]), an average rate of weekly improvement attained from a normative database is multiplied by the time frame to determine the criterion for success. For detailed information and direction for setting goals, see Progress Monitoring Strategies for Writing Individual Goals in General Curriculum and More Frequent Formative Evaluation (Shinn, 2002b).
EndofYear Benchmarks
Grade  1  2  3  4  5  6  7  8 

Rating 
1. Are benchmarks for minimum acceptable endofyear performance specified in your manual or published materials?
Yes.
a. Specify the endofyear performance standards:
15th percentile of national norms.
b. Basis for specifying minimum acceptable endofyear performance:
MCOMP benchmarks are established through a combination of criterionreferenced and normreferenced methods. Empirical research was done on the relationship of scores on an AIMSweb math measure (Math Concepts & Applications, MCAP) to success on state mathematics tests (see the State Prediction User’s Guide (2011) for a description of this research), as well as on the relationship of a reading test (RCBM) to state reading test success. It was found that the raw score that indicated only a 50% probability of statetest success was consistently located at approximately the 15th percentile of national norms, across grades, seasons, and measures (math and reading). On the basis of this consistent finding, cut scores for minimum acceptable performance for all math, reading, and language arts measures for grades 1 to 8 have been set at the 15th percentile.
c. Specify the benchmarks:
45th percentile of national norms.
d. Basis for specifying these benchmarks?
Benchmarks were established following the same procedure as described above for minimum acceptable scores, but using the criterion of 80% probability of success on state proficiency tests..Across grades, seasons, and measures (math and reading), the raw score that predicted an 80% success probability was consistently close to the 45th percentile, and so that value is used for all AIMSweb math, reading, and language arts measures for grades 1 to 8.
Normative profile:
Representation: National
Date: 20102011
Number of States: approximately 40
Size: 80,714
Gender: 51% Male, 49% Female,
SES: 40% free/reduced lunch
Race/Ethnicity: 59% White, 16% Black, 16% Hispanic, 4% Asian/Pacific Islander, 3% Other
Procedure for specifying benchmarks for endofyear performance levels:
Sensitive to Student Improvement
Grade  1  2  3  4  5  6  7  8 

Rating 
1. 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).
The sensitivity to student improvement of the AIMSWeb MCOMP monitoring system was assessed by comparing students who received instructional intervention in mathematics (as indicated by the fact that they had received progress monitoring with MCOMP) with students from the same school who did not receive interventions (i.e., did not have progress monitoring with MCOMP). Improvement during the year was measured for all students by comparing scores on Fall and Spring administrations of the benchmark MCOMP assessments, which are identical in content coverage and administration procedure to the progress monitoring assessments (but which do not share any common items with the PM measures). Sensitivity to improvement was evaluated by comparing average MCOMP score gains of the students with and without intervention.
At each grade level, one school with a sufficient number of students being progressmonitored was selected. All data were obtained from the 20102011 school year.
An independentsamples t test was computed at each grade level to compare the improvement scores of students with and without progress monitoring. The results were statistically significant (p < .05) at each grade level. More detailed information about the samples and results are presented in the table below.
To assess the possibility that group differences resulted from practice effects (as the PM group was administered from 10 to 30 probes), score gains within the PM group were regressed onto the number of administrations controlling for the span of time from initial to final administration. All but one coefficient was nonsignificant indicating that practice affects were negligible.
To address the possibility that group differences resulted from differences in initial level of performance (as baseline performance is typically used to determine who needs PM), ROI by initial score level from a nationally representative sample is presented. Table 2 below shows ROIs from the nationally representative sample by score level (defined as a percentile ranges centered on the 10th, 25th, 50th, 75th, and 90th percentile). ROIs are greatest between the 18th and 83rd percentiles, with lower ROIs in the lowest and highest scoring groups. Thus, it seems reasonable to rule out initial performance as an explanation for the PM group gains. As further evidence that the PM group experienced elevated growth rates, the ROI for the PM group in each grade is greater than the ROI for most score levels in the nationally representative sample; whereas the noPM group ROIs are about the same as the national sample.
Because the PM group would have received instructional intervention, and additional instruction is expected to lead to more learning, and MCOMP score gains were significantly greater in the PM group than the noPM group, it is reasonable to conclude that AIMSweb MCOMP assessment measures are sensitive to student improvement.
Table 1. Mean and SDs of the average improvement by group, independent sample ttests results, and pvalues for the effect of the number of PM administrations.
# of month span  # of PM data points  Average Improvement/SD  ttest  # PM administrations  
Grade  Total # of students  # of students with PM  Avg.  Min  Max  Avg.  Min  Max  no PM  PM  t  p 
Partial correlation coefficient p value 

M  SD  M  SD  
1  250  36  5.8  3  10  15.3  10  25  0.77  0.26  0.94  0.19  3.69  <.01  0.60 
2  222  30  6.4  3  10  17.8  10  30  0.46  0.28  0.64  0.25  3.33  <.01  0.33 
3  178  24  5.5  3  8  15.7  10  23  0.91  0.33  1.27  0.26  5.15  <.01  0.34 
4  221  53  4.5  3  7  16.3  10  33  0.97  0.29  1.18  0.32  4.56  <.01  <.01 
5  167  36  7.3  4  9  20.4  11  26  0.46  0.31  0.68  0.27  3.89  <.01  0.55 
6  371  68  7.7  4  9  17.7  11  29  0.33  0.26  0.43  0.26  2.56  0.01  0.90 
7  129  20  7.3  5  10  18.3  11  29  0.16  0.23  0.30  0.28  2.46  0.01  0.44 
8  352  51  7.5  4  9  15.3  10  25  0.22  0.21  0.35  0.26  3.32  <.01  0.10 
Table 2. Median ROI by initial score level: MCOMP
Grade  
Fall Percentile  1  2  3  4  5  6  7  8 
117  0.78  0.64  0.69  0.69  0.33  0.31  0.17  0.17 
1832  0.83  0.69  0.86  0.86  0.47  0.36  0.31  0.22 
3362  0.78  0.64  0.92  0.89  0.5  0.41  0.33  0.25 
6383  0.72  0.53  0.81  0.78  0.53  0.42  0.36  0.22 
8499  0.42  0.28  0.44  0.42  0.44  0.33  0.22  0.19 
Decision Rules for Changing Instruction
Grade  1  2  3  4  5  6  7  8 

Rating 
Specification of validated decision rules for when changes to instruction need to be made: The newest version of the AIMSweb online system, to be released for piloting in the fall of 2012 and made available to all users no later than the fall of 2013, applies a statistical procedure to the student’s monitoring scores in order to provide empiricallybased guidance about whether the student is likely to meet, fall short of, or exceed their goal. The calculation procedure (presented below) is fully described in the AIMSweb Progress Monitoring Guide (Pearson, 2012) and can be implemented immediately by AIMSweb users if they create a spreadsheet or simple software program. Once the new AIMSweb online system is fully distributed, the user will not have to do any calculations to obtain this databased guidance. 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 monitoring scores and the duration of monitoring. Starting at the sixth week of monitoring, when there are at least four monitoring scores, the AIMSweb report following each monitoring administration includes one of the following statements: “The student is projected to not reach the goal.” This statement appears if the confidence interval is completely below the goal score. “The student is projected to exceed the goal.” This statement appears if the confidence interval is completely above the goal score. “The student is on track to reach 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 and 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: [((1 + 1/k + (GW – mean(w)))/(k – 2))((sum(y – y’)2)/(sum(w – mean(w))2))]1/2 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.
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 20102011 database who were progressmonitored on either Reading CurriculumBased Measurement (RCBM) or Math Computation (MCOMP). All students 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 grades 2 through 6) who had at least 30 monitoring scores, and the MCOMP sample included 500 students (100 per grade) 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  1  2  3  4  5  6  7  8 

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Specification of validated decision rules for when increases in goals need to be made: The newest version of the AIMSweb online system, to be released for piloting in the fall of 2012 and made available to all users no later than the fall of 2013, applies a statistical procedure to the student’s monitoring scores in order to provide empiricallybased guidance about whether the student is likely to meet, fall short of, or exceed their goal. The calculation procedure (presented below) is fully described in the AIMSweb Progress Monitoring Guide (Pearson, 2012) and can be implemented immediately by AIMSweb users if they create a spreadsheet or simple software program. Once the new AIMSweb online system is fully distributed, the user will not have to do any calculations to obtain this databased guidance. 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 monitoring scores and the duration of monitoring. Starting at the sixth week of monitoring, when there are at least four monitoring scores, the AIMSweb report following each monitoring administration includes one of the following statements: “The student is projected to not reach the goal.” This statement appears if the confidence interval is completely below the goal score. “The student is projected to exceed the goal.” This statement appears if the confidence interval is completely above the goal score. “The student is on track to reach 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 and 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: [((1 + 1/k + (GW – mean(w)))/(k – 2))((sum(y – y’)2)/(sum(w – mean(w))2))]1/2 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.
Improved Student Achievement
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Improved Teacher Planning
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