A student's scores were 45 at baseline and 58 eight weeks later. Is that fast enough? The answer depends on a number most graphs never show: how fast it has to be.
Rate of improvement turns "a bit better" into something you can compare. This guide shows how to calculate it, what to compare it with, and where it misleads.
What ROI is
ROI is growth per unit of time. With weekly data, it is points gained per week. NCII's goal-setting guide describes it two ways: as the typical weekly growth of students in a national sample (a norm), and as a particular student's own slope of improvement.
| Norm ROI | Student's own ROI | |
|---|---|---|
| Where it comes from | Published for a tool and grade | Your data for this student |
| What it answers | What is typical growth? | How fast is this student growing now? |
| Use | Setting a goal | Judging progress, or setting a goal for some students |
Growth so far versus growth needed
Two calculations tell you most of what you need.
Growth so far = (current score minus baseline) divided by weeks between them.
Growth needed = (goal minus current score) divided by weeks left.
If growth so far is at or above growth needed, the student is on pace. If it is below, the gap will not close at the current speed. Use the calculator, which is loaded with an example.
Runs in your browser. Nothing is sent or saved. Rate of improvement here is the gain per week: (current score minus baseline) divided by weeks between the two. Use the same measure and the same level of material for both scores.
With the starting numbers, growth so far is (58 minus 45) divided by 8, or 1.63 per week. Growth needed is (90 minus 58) divided by 20, or 1.6 per week. The student is just ahead of the pace.
Setting a goal from national norms
NCII gives a three-step method. Find the ROI for your tool and grade. Multiply it by the number of weeks until the end of the year or period, leaving out weeks without instruction. Add the result to the baseline.
NCII's own example is a math probe: 2 digits per week times 10 weeks, plus a baseline of 30 digits, gives a goal of 50 digits. The formula is ROI × weeks + baseline = goal.
Typical versus ambitious
NCII says typical growth is what students make with typical instruction, and ambitious growth is more than that. For students below benchmark, it says more than typical growth is often necessary to close the gap with peers. It also warns that matching the normative ROI for a student who is below grade level may keep the gap in place.
That is why a student with a very low baseline can have a goal that looks high. The team needs to see the weekly growth the goal requires, and decide whether the instruction can support it.
Three ways to set the goal, side by side
The MTSS Center's chart of progress monitoring features gives pros and cons for three goal-setting methods.
| Method | Strength | Limit |
|---|---|---|
| Benchmark | Easy to identify and tied to a proficiency criterion | May be too ambitious for students far behind |
| Average growth rates | Based on typical growth | Normative data are hard to find for some content areas |
| Intra-individual | Based on the student's prior growth | May not catch the student up in a timely manner |
These match the three options in NCII's guide, which are covered in writing measurable criteria for IEP goals.
Where two-score ROI misleads
Take the same student, but suppose the baseline of 45 came from one low day, and the typical level was 47. Now growth so far is (58 minus 47) divided by 8, or 1.38 per week. Against a needed 1.6, the student is behind, not ahead.
Nothing changed but one number. Two scores give a fragile ROI, so prefer these habits.
- Use a baseline from several probes. NCII's guide describes the median or average of three.
- Look at the trendline. NCII's decision rules compare the trend of all points with the goal line. See aimline and trendline explained.
- Report the method. Say "two-score ROI" or "slope from all points."
A hand calculation of the student's own slope
NCII's guide shows a way to estimate slope without software: divide the scores into three roughly equal groups, take the median of the first and last groups, and compute (third median minus first median) divided by the number of data points minus one.
With eight invented weekly scores of 41, 44, 43, 47, 50, 49, 52, and 55, the first three are 41, 44, 43, with a median of 43. The last three are 49, 52, 55, with a median of 52. The slope is (52 minus 43) divided by 7, or about 1.29 per week. Put the same scores into the trend calculator in the aimline guide and a fitted line gives a similar figure. The two will rarely match exactly, so note which one you used.
Saying it to a family
A rate is a bare number until it is attached to a picture. Try a sentence like this: "Jordan has been gaining about 1.6 words a week. To reach the goal by spring, Jordan needs about 1.6 a week, so we are right on pace. If the gain drops below that for a few weeks, we will meet to look at changing the plan."
Notice that the sentence gives the rate, the rate needed, and what happens next. Parents can follow it, and it ties the number to the decision rule you wrote in advance.
More cautions
- Different tools, different ROIs. A rate of 1.0 on one measure is not comparable to 1.0 on another.
- Calendar weeks versus instructional weeks. Leave out weeks with no instruction, as NCII advises.
- Local norms. NCII says local norms may be estimated when national norms are missing, but small samples and low local performance can lower expectations.
- Ceiling. Growth slows as scores near the top of a scale.
Keep a growth log
Write the growth-so-far and growth-needed figures in the margin of your graph each time you review it, with the date. Over a term, those two columns show whether the gap is closing or widening, and they give a family or a new team member the story at a glance.
Using ROI in decisions
ROI does not decide anything by itself. A growth-so-far below growth-needed is a prompt to run through the checks in decision rules: when to change an intervention, starting with fidelity. For where ROI numbers come from in reading probes, see curriculum-based measurement basics.
Norms vary by publisher
ROI norms vary by publisher and grade, and not every tool publishes them. NCII does not tell teams which ROI to pick for a given student. That is a judgment for your IEP team. Terms are in the glossary.