This is somewhat disturbing, at least for those kids that truly are above the mean...
"Students who have fall RITs below the median tend to show more
growth. Those with fall RITs above the median for that grade tend to show less growth."
That's what I cynically thought too, but of course it's a classic case of "reversion to the mean" which is not sinister but just what obviously happens with imperfect testing. If someone, by fluke, does better than they "should" do on the test, then chances are that won't happen again next time, so their next score will probably be closer to their "true" score and they will show less growth than most. Similarly, if someone does badly by "fluke", they'll probably show more growth than most. In order for that trend to show up, you don't have to posit that that's the ONLY reason for someone to test unusually high/low - just that sometimes that's the reason.
That said, it is all too plausible that there's a real effect (not just an artifact of test imperfections) there too.
The document does definitely say it's talking about SDs. The simplest interpretation would be that someone who didn't understand the document assumed other people wouldn't understand it and "helpfully" added the wrong explanation of what SD means.
