Alliance Marc & Eva Stern Math and Science

Each dot is one year. It shows how far the typical student's score was from the state's "meets standard" mark. Zero means right on it. Above zero is above standard; below zero is below.

Every school's results bounce around a little from year to year. A different group of students, a flu season, a new teacher: small things push the number up or down. That bounce is normal, and it doesn't mean anything has really changed.

The shaded band marks how far the bounce normally goes. We work it out from the school's own history: how much its result typically moves from one year to the next.

The small numbers under each year are how many students took the test. In a small school a few students make a big difference, so its dots bounce further and its band is wider.

• A dot inside the band is ordinary bounce. The school is doing what it has always done.
• A dot outside the band is a real signal. Something changed, for better or worse, and it's worth asking what.

A flat band with the dots inside it means the system is stable. It will keep producing about the same results year after year, however hard everyone works. Teachers aren't the reason the dots stay put. The way the school is organized is. Changing that is what moves the dots.

The little house in each year shows the share of students eligible for free or reduced-price school meals, a rough measure of family income. It sits on the same scale as the results: 0% at the top of the chart, 100% at the bottom. The fewer families with low incomes, the higher the house. Income moves results too, and it comes from outside the school.