Today, I had my non AP students illustrate some related rates problems and then explain what was happening with dV/dt and dr/dt (or whatever the variables were in the situation). I blogged about this once. We had a good discussion about the drawings. Despite talking about this all week, this was the first time I felt like students were really deeply understanding everything. For example, a student would start to say dr/dt is increasing at a decreasing rate when they meant that r is increasing at a decreasing rate (so dr/dt is decreasing) and immediately correct themselves. The preciseness of the language here is huge and I made a point to let them struggle through saying something, let their classmates correct it, and then have them try again.