First, we’ll say that this school reports test scores instead of proficiency rates, and that the scores are comparable between grades. Second, every year, our school welcomes a new cohort of sixth graders that is the exact same size and has the exact same average score as preceding cohorts – 30 out of 100, well below the state average of 65. Third and finally, there is no mobility at this school. Every student who enters sixth grade stays there for three years, and goes to high school upon completion of eighth grade. No new students are admitted mid-year.
Okay, here’s where it gets interesting: Suppose this school is phenomenally effective in boosting its students’ scores. In fact, each year, every single student gains 20 points. It is the highest growth rate in the state. Believe it or not, using the metrics we commonly use to judge schoolwide “growth” or “gains,” this school would still look completely ineffective. Take a look at the figure below.
It is very simple, just showing the progression of scores at our hypothetical school. As we already know, every incoming cohort of sixth graders (next to the green arrows) has an average score of 30 on the test. As indicated by the yellow arrows, the next year, in seventh grade, they all pick up 20 points, for an average of 50. And, finally, they pick up another 20 points by eighth grade, and are promoted to high school (red arrows) with an average score of 70. In other words, thanks to the wonderful effectiveness of their superstar school, every cohort enters at 30, well below the state average, and leaves at 70 (slightly above the average of 65).
But here’s the big problem: The school’s average score of 50 doesn’t change. It is completely flat. Anyone looking at this school’s score each year might say it’s doing poorly. After all, the average score of 50 is below the state average, and there has been no “growth.” How can such a wonderful school not show improvement?