A teacher shows a graph with seven dots climbing slowly. A parent asks, "Is that good?" Without a line to compare to, nobody can answer. The dots are data, but they are not yet a decision.
An aimline and a trendline give those dots meaning. This guide explains both and how to compare them.
Why the graph needs a goal line
NCII's goal-setting guide says some teachers make graphs with scores but no goal or goal line. That is a problem, it says, because without one you cannot assess whether the student's rate of improvement is adequate. The goal line shows the rate of progress needed to reach the chosen goal. A graph with only scores shows a pattern, but does not help parents or staff interpret progress toward the goal.
The parts of a progress graph
Understood's explainer describes the usual layout. The vertical axis (y) shows the skill being measured, such as words per minute. The horizontal axis (x) shows weeks of instruction. The baseline is the first point. The goal line shows the average weekly progress needed. The trend line shows actual performance over time.
| Part | Where it comes from | What it tells you |
|---|---|---|
| Baseline point | Baseline score and start date | Where measurement began |
| Goal point | Goal in the IEP and end date | Where the team wants to be |
| Aimline | Straight line from baseline to goal | Growth needed per week |
| Data points | Each score, plotted by date | What actually happened |
| Trendline | Line fitted through the data points | The direction and speed of actual growth |
Drawing the aimline
- Mark the baseline at the start date.
- Mark the goal at the end date, such as the end of the IEP year.
- Connect the two with a straight line.
The slope of that line is the growth required each week: (goal minus baseline) divided by the weeks between them. With a baseline of 42, a goal of 70, and 12 weeks, the aimline climbs 28 over 12 weeks, or about 2.33 per week.
Drawing the trendline
The trendline summarizes scores, not individual days. There are two ways to get one.
By software. A spreadsheet fits a straight line through the points, usually by least squares. NCII's handout recommends the trend line method if you have a system that calculates it.
By hand. NCII's guide shows an estimate: split the data into three roughly equal groups, find the median of the first and last groups, then compute slope as the third median minus the first median, divided by the number of data points minus one. Its example uses scores of 2, 3, 5, 5, 5, 6, 7, 4: the medians are 3 and 6, so the slope is 3 divided by 7, or 0.43.
Try both with the calculator
Seven weekly scores, a baseline of 42, a goal of 70, and 12 weeks are loaded. Change them to your own numbers.
Runs in your browser. Nothing is sent or saved. Enter three or more scores in time order, evenly spaced. The trendline is an ordinary least squares line through the points. Compare it with the aimline, the straight line from baseline to goal. A slope is a summary of the points, not a decision.
With the starting numbers, the trend is about 2.11 per data point, and the aimline is about 2.33 per week. The trend is a little flatter than the aimline. By week 7 the aimline would be near 58, and the last score is 55. The tool assumes one point per week, so treat it as a rough check.
How NCII compares them
NCII's decision rules handout describes the trend line analysis. Once at least four weeks of instruction have passed and eight data points have been collected, determine the trend and compare it with the goal line.
| If the student's trend line is | NCII says |
|---|---|
| Steeper than the goal line | Increase the goal |
| Flatter than the goal line | Consider adapting the intervention and assess fidelity |
| The same as the goal line | Keep collecting data and continue to monitor |
The handout lists its advantages: it is highly accurate and easy to use if you collect enough data, especially with a system that calculates the line. It also lists cautions: you need enough points for a reliable trend, outliers can affect the slope, and data collection must be systematic and frequent enough to detect meaningful trends. The full set of rules is in decision rules: when to change an intervention.
When one point looks wrong
NCII's handout warns that the slope of a trend line can be affected by outliers. Suppose a student scores 47, 49, 51, 22, 53. The 22 pulls the line down, but the cause may be a fire drill, a substitute, or a sick day.
A reasonable practice, not a rule from the sources: keep the point on the graph, mark it, and write the reason beside it on the data sheet. Do not erase it. Then look at the next two or three points. If they return to the earlier range, the dip was probably the day. If they stay low, the dip was probably the student. Either way the graph tells the truth, and the team can see how you reasoned.
Reading the lines for a family
Understood tells parents what to look for. A trend line not moving toward the goal line means not enough progress is being made. A trend line moving toward it means the intervention is working. Meeting it means the intervention succeeded, though monitoring should continue. If a parent asks for the graph after each assessment, give it. A short sentence with it helps: "The dotted line is where we need to be. The solid line is where Jordan is."
Common graph slips
- No aimline. Dots alone cannot be judged.
- A stretched scale. A vertical axis that runs only from 40 to 60 makes small changes look large. Start the scale where the data make sense and keep it the same across graphs.
- Mixed measures on one line. If the tool changes, start a new section and label it.
- Missing dates. Plot by date, so gaps for breaks show as gaps.
- Redrawing the line to fit. Change the aimline only when the team changes the goal.
A graph built in a spreadsheet follows the same logic. See graphing IEP data in a spreadsheet. Terms are in the glossary.
Thresholds are options, not laws
NCII's handout gives minimum data (four weeks and eight points) but says these are common options, not the only methods. Your district or tool may set different thresholds. Follow local procedures, and note the rule you used on the graph. If your tool draws the lines for you, check once by hand that the baseline and goal points it uses are the ones written in the IEP.