AIMSweb

Area: Math Computation

Cost

Technology, Human Resources, and Accommodations for Special Needs

Service and Support

Purpose and Other Implementation Information

Usage and Reporting

M-COMP 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:

  • AIMSweb assessments for universal screening and progress monitoring
  • Data management and reporting
  • Browser-based scoring
  • Training manuals
  • Administration and scoring manuals

Internet access is required for full use of this product.

Testers will require 1-2 hours of training.

Paraprofessionals can administer the test.

Alternate forms available in Spanish.

Pearson
19500 Bulverde Road
San Antonio, TX 78259
Phone: 866-313-6194
Visit AIMSweb.com

General Information:
866-313-6194 option 2
sales@aimsweb.com

Tech support:
866-313-6194 option 1 aimswebsupport@ pearson.com

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.

M-COMP is a brief (8 minute) group (or individually) administered and standardized assessment of math computation proficiency.  It uses an open-ended fill-in-the-blank response format and consists of 33 alternate forms per grade for grades 1-8.

The mathematics domains assessed include: column addition (grades 1-3), basic facts (grades 1-6), complex computation (grades 1-7), decimals (grades 4-8), fractions (grades 4-8), conversions (grade 5-8), percentages (grades 5-8), integers (grades 6-8), expressions (grade 6), reducing (grades 6-7), equations (grade 7-8), and exponents (grade 7-8).

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,  KeyMath-3 Diagnostic Assessment, and analysis of strengths and weaknesses by NCTM and Common Core domains.

 

Reliability of the Performance Level Score: Convincing Evidence

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 field-test sample, scored independently by two different raters. Intraclass correlation (Shrout & Fleiss, 1979, type 2) which reflects consistency in level as well as rank-ordering.
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: Convincing Evidence

Type of Reliability Age or Grade n (range) Coefficient SEM Information / Subjects
range median
Split-half reliability (odd & even data points) 1 3,285   0.79 0.25 Average # of month span per student = 6.4, range 3-11; Average # of data point per student = 15.6, range 10-70.
Split-half reliability (odd & even data points) 2 6,289   0.75 0.23 Average # of month span per student = 6.8, range 3-11; Average # of data point per student = 15.9, range 10-62.
Split-half reliability (odd & even data points) 3 6,687   0.75 0.29 Average # of month span per student = 7.0, range 3-11; Average # of data point per student = 15.8, range 10-51.
Split-half reliability (odd & even data points) 4 6,756   0.77 0.32 Average # of month span per student = 6.8, range 3-11; Average # of data point per student = 15.7, range 10-49.
Split-half reliability (odd & even data points) 5 6,183   0.82 0.27 Average # of month span per student = 6.9, range 3-11; Average # of data point per student = 15.8, range 10-65.
Split-half reliability (odd & even data points) 6 3,833   0.77 0.23 Average # of month span per student = 7.0, range 3-11; Average # of data point per student = 15.5, range 10-46.
Split-half reliability (odd & even data points) 7 2,534   0.76 0.23 Average # of month span per student = 6.9, range 3-11; Average # of data point per student = 15.7, range 10-41.
Split-half reliability (odd & even data points) 8 2,510   0.74 0.20 Average # of month span per student = 6.9, range 3-11; Average # of data point per student = 15.4, range 10-42.

 

Validity of the Performance Level Score: Unconvincing Evidence

Type of Validity Age or Grade Test or Criterion n (range) Coefficient Information / Subjects
range median
Construct 1 Group Mathematics Assessment and Diagnostic Evaluation (G-MADE) 98   0.84 Students participating in the national field test of M-COMP.
Construct 3 G-MADE 98   0.73
Construct 8 G-MADE 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
M-COMP 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: Data Unavailable

Disaggregated Reliability and Validity Data: Data Unavailable

Alternate Forms: Partially Convincing Evidence

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 M-COMP, 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 M-COMP 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

Sensitive to Student Improvement: Convincing Evidence

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 M-COMP 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 M-COMP) with students from the same school who did not receive interventions (i.e., did not have progress monitoring with M-COMP). Improvement during the year was measured for all students by comparing scores on Fall and Spring administrations of the benchmark M-COMP 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 M-COMP score gains of the students with and without intervention.

At each grade level, one school with a sufficient number of students being progress-monitored was selected. All data were obtained from the 2010-2011 school year.

An independent-samples 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 non-significant 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 no-PM 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 M-COMP score gains were significantly greater in the PM group than the no-PM group, it is reasonable to conclude that AIMSweb M-COMP assessment measures are sensitive to student improvement.

Table 1. Mean and SDs of the average improvement by group, independent sample t-tests results, and p-values for the effect of the number of PM administrations.

      # of month span # of PM data points Average Improvement/SD t-test # 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: M-COMP

  Grade
Fall Percentile 1 2 3 4 5 6 7 8
1-17 0.78 0.64 0.69 0.69 0.33 0.31 0.17 0.17
18-32 0.83 0.69 0.86 0.86 0.47 0.36 0.31 0.22
33-62 0.78 0.64 0.92 0.89 0.5 0.41 0.33 0.25
63-83 0.72 0.53 0.81 0.78 0.53 0.42 0.36 0.22
84-99 0.42 0.28 0.44 0.42 0.44 0.33 0.22 0.19

 

End-of-Year Benchmarks: Convincing Evidence

1. Are benchmarks for minimum acceptable end-of-year performance specified in your manual or published materials?

Yes.

a. Specify the end-of-year performance standards:

15th percentile of national norms.

b. Basis for specifying minimum acceptable end-of-year performance:

M-COMP benchmarks are established through a combination of criterion-referenced and norm-referenced methods. Empirical research was done on the relationship of scores on an AIMSweb math measure (Math Concepts & Applications, M-CAP) 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 (R-CBM) to state reading test success. It was found that the raw score that indicated only a 50% probability of state-test 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: 2010-2011
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 end-of-year performance levels:

Rates of Improvement Specified: Convincing Evidence

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: 2010-2011
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 rate-of-improvement (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).

Decision Rules for Changing Instruction: Convincing Evidence

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 empirically-based 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 data-based 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 student-specific 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 confidence-interval 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 least-squares 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 non-linearity into account when interpreting progress-monitoring 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 progress-monitored on either Reading Curriculum-Based Measurement (R-CBM) or Math Computation (M-COMP). All students scored below the 25th percentile in the fall screening administration of R-CBM or M-COMP. The R-CBM sample consisted of 1,000 students (200 each at grades 2 through 6) who had at least 30 monitoring scores, and the M-COMP 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 R-CBM) 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 on-track/no-change).

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: Convincing Evidence

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 empirically-based 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 data-based 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 student-specific 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 confidence-interval 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 least-squares 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 non-linearity into account when interpreting progress-monitoring 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 progress-monitored on either Reading Curriculum-Based Measurement (R-CBM) or Math Computation (M-COMP). All students scored below the 25th percentile in the fall screening administration of R-CBM or M-COMP. The R-CBM sample consisted of 1,000 students (200 each at grades 2 through 6) who had at least 30 monitoring scores, and the M-COMP 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 R-CBM) 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 on-track/no-change).
 
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.

Improved Student Achievement: Data Unavailable

Improved Teacher Planning Data Unavailable