Rate of improvement (ROI) calculation

Rate of improvement, usually shortened to ROI, is how much a student's score changes per week on the same curriculum-based measurement probe. A student who goes from 18 to 29 digits correct over 9 weeks has an ROI of about 1.1 to 1.2 digits per week, depending on how you calculate it. That one number answers the question every team asks: is the gap closing fast enough?

This guide walks through the calculation with one fictional student, shows three methods side by side and lists the errors that make ROI misleading. For drawing the aimline and trend line on the graph, see the guide on graphing IEP data with aimlines. For the wider monitoring cycle, start at the IEP progress monitoring pillar.

What ROI tells you and what it does not

ROI is a slope. It describes growth, not level. A student can have a strong ROI and still score far below grade level, or a weak ROI while scoring close to it. Teams need both numbers, which is why a report should give the current score and the ROI together.

ROI is only as good as the probes behind it. The forms must be of equal difficulty, given and scored the same way every time, and spaced at regular intervals. Repeated brief measures of this kind are the basis of progress monitoring as the National Center on Intensive Intervention describes it.^[1] If the forms vary in difficulty, the slope measures the forms as much as the student.

What you need before you start

• At least 8 weekly scores on one measure, such as digits correct per minute on a grade 3 mixed computation probe. Fewer points give a slope that can swing a lot when one score changes.
• The week number for each score. Count calendar weeks from the first probe, not probe numbers. If school was closed for a week, that week still counts.
• The goal or aimline, with the baseline, the target and the date. The aimline slope is the ROI the goal requires.
• A comparison ROI if you have one, from peers on the same probes or from the tool's published growth figures.
• A spreadsheet or a calculator. A spreadsheet's SLOPE function does the least-squares math for you.

Step by step

Step 1: Line up weeks and scores

Make two columns. Column A is the week number (1, 2, 3 and so on, with gaps if a week had no probe). Column B is the score. Use the same unit throughout, such as digits correct per minute. If a probe was given under different conditions, such as with a calculator, leave it out and note why.

Step 2: Check that the phase is clean

ROI should describe one phase of instruction. If the intervention changed in week 6, calculate one ROI for weeks 1 to 5 and another from week 6 on. A slope that runs across a change blends two different answers into one meaningless number.

Step 3: Calculate the slope

Pick one method and use it every time for this student. The three common methods are below, from roughest to most precise.

• Two-point: last score minus first score, divided by the weeks between them. Fast, but one odd day at either end changes everything.
• Median of thirds: split the scores into first, middle and last thirds. Take the median score and median week of the first and last thirds. ROI is the difference in scores divided by the difference in weeks. Good for hand graphs.
• Least squares (OLS): the slope of the best-fitting straight line through every point. In a spreadsheet, type =SLOPE(B2:B11, A2:A11). This uses all the data and is the usual choice when 8 or more points exist.

Step 4: Find the ROI the goal needs

Subtract the baseline from the goal and divide by the number of weeks until the goal date. A baseline of 17 and a goal of 45 in 32 weeks needs 28 divided by 32, or 0.875 per week. That is the aimline slope.

Step 5: Compare and decide

Divide the student's ROI by the ROI the goal needs. A ratio of 1.0 or higher means the student is growing fast enough to reach the goal. Below 1.0 means the goal will be missed at this pace unless something changes. If you have a peer ROI from the same probes, divide the student's ROI by it too. A ratio below 1.0 against peers means the gap is widening, even if the goal is on track.

Step 6: Report it with units

Write ROI as a number with its unit and time base: "1.09 digits correct per minute per week." Name the method and the weeks covered. A team reading "ROI = 1.1" in a report has no way to tell what it means.

Worked example: Marcus, grade 3 math computation

Marcus is a fictional grade 3 student with a math computation goal. All numbers below are illustrations, not benchmarks.

Baseline: three probes in early September scored 16, 17 and 19 digits correct per minute. Median: 17.

Goal: 45 digits correct per minute on grade 3 mixed computation probes in 32 weeks. Required ROI: (45 minus 17) divided by 32 equals 0.875 digits per week.

Ten weekly probes:

Two-point ROI: (29 minus 18) divided by 9 weeks equals 1.22 digits per week.

Median of thirds: first three scores 18, 21, 19 have a median of 19 at week 2. Last three scores 27, 26, 29 have a median of 27 at week 9. ROI is (27 minus 19) divided by 7, or 1.14 digits per week.

Least squares: the mean week is 5.5 and the mean score is 23.4. The sum of the cross products of the deviations is 90.0, and the sum of the squared week deviations is 82.5. The slope is 90.0 divided by 82.5, or 1.09 digits per week. A spreadsheet SLOPE formula gives the same answer.

Against the goal: 1.09 divided by 0.875 is 1.25. Marcus is growing about a quarter faster than his goal requires. If the trend holds, he would pass 45 before the goal date, so the team should look at raising the goal at the next review.

Against peers: suppose the grade 3 classes took the same probes, and the median classmate gained 1.4 digits per week over the same weeks. Marcus's ratio is 1.09 divided by 1.4, or about 0.78. He is on track for his own goal but still falling slightly further behind his classmates. That is worth saying plainly at the meeting, because it can shape the next goal and the intensity of service.

The methods agree here because the data are steady. With bumpier data the two-point answer drifts much more than the others.

Using ROI in eligibility decisions

When a team considers a specific learning disability, the regulations ask for data-based documentation of repeated assessments of achievement at reasonable intervals, shared with parents.^[2] ROI is a common way to condense that documentation into one figure. Each state sets its own criteria for identifying a specific learning disability, and some states define how ROI or response to intervention data must be used.^[3] Check your state manual before writing a gap or ratio cut point into a report. For how this plays out in the IEP itself, see the guide on the specific learning disability IEP.

Common mistakes

• Weak: ROI from the first and last probe only. Better: a least-squares slope across all points in the phase, or median of thirds by hand.
• Weak: counting probes as weeks when two weeks were missed. Better: use calendar weeks, so a 10-week span with 8 probes is still 10 weeks.
• Weak: one slope across a change in instruction. Better: a separate ROI for each phase, with the change marked on the graph.
• Weak: comparing ROI on grade 3 probes with peers' ROI on grade 4 probes. Better: compare only slopes from the same measure and level.
• Weak: "ROI is 1.1, good progress." Better: "ROI is 1.09 digits correct per minute per week (least squares, weeks 1 to 10). The goal requires 0.875."
• Weak: an ROI from 4 points used to deny or confirm eligibility. Better: wait for enough points to trust the slope, and report the range of scores alongside it.

Tools for the calculation

The rate per minute measurement page explains how timed probes are scored so the unit stays the same. The guide to math CBM probes covers choosing and giving the probes that feed an ROI. For decision rules that use the slope, see the four-point rule and trend analysis guide. When you write the goal itself, the math IEP goals and the addition and subtraction goal templates give wording with a measurable target.

Frequently asked questions

Use it in IEP Atlas

• Curriculum based measurement in the IEP glossary
• Probe in the IEP glossary
• Math IEP goals
• Rate per minute measurement guide
• Goal line in the IEP glossary

Related guides

• IEP progress monitoring: how to track, graph and report goal progress
• Math CBM probes
• Curriculum-based measurement vs mastery measurement
• Graphing IEP data: aimlines and trend lines
• Decision rules: the four-point rule and trend analysis
• IEP progress report comments for math

Sources

1. Progress Monitoring: Data & Goal Setting, National Center on Intensive Intervention
2. 34 CFR §300.309: Determining the existence of a specific learning disability, U.S. Department of Education (IDEA website)
3. 34 CFR §300.307: Specific learning disabilities, U.S. Department of Education (IDEA website)

Written and checked by the IEP Atlas editorial team under our editorial policy. This guide describes general practice and federal rules. It is not legal advice; your state may add requirements, and the IEP team makes the decisions for each student.