So I did my graph translation lesson with two of my three Precalculus classes (the conversation in the third class went a different direction, and it seemed to me at the time that the students in that class were more comfortable seeing the correct direction in a horizontal translation). The lesson ended up being much smaller in scale than I initially imagined, with 5-6 students in the front of the room, each with an assigned x-value. I then gave them each a different shape to hold (I borrowed some extremely large pipe cleaner type things from a colleague). I explained carefully that the shape represented the "value" of the function. Finally, I said, "Instead of your value, please take the value from x minus 3." After some fumbling, the function moved three spaces to the right. After a few repeats, they had it cold.
So did it help them understand? They seemed to shrug it off as if I had gone to a lot of trouble to demonstrate the most obvious thing in the world. However, in the days since, I've not had a single question about why the graph moves in the "opposite" direction... except from the class that didn't do the demo. Feels like positive feedback to me!
Note: I didn't end up video taping the lesson... it felt like that would make the students think it was more of an "event" than it actually was. Plus, I started worrying about putting my students out there on the internet without notarized consent from their parents, their attorneys, and their parents' attorneys.
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