So, I had an idea about five minutes before I was to teach u-substitution this year. I call it the highlight-out method. I think it's easier just to show a slide with two examples rather than try to explain in words:
I had the kids "highlight out" the du portion so they could focus on what's left. Alternatively, you could have them highlight u in one color and du in another.
It may help some; it won't help others, but I think it's a step in the right direction for me.
Another thing I get asked a lot is, "What happened to the du?" This is a way I explain indefinite integrals that I've found helpful:
- The indefinite integral symbol and the differential dx (or du or d-whatever) TOGETHER are a command that mean "Find the family of antiderivatives."
- Once you have found an antiderivative, the two symbols disappear because you have completed the command.
- You cannot have an integral symbol without a differential; they're akin to a capital letter and period.
Here's a slide that seemed to clear things up a little bit more:
One kid told me the last example actually shed a lot of light. Hooray!
 Yes, I know, technically you can; I've taken Calculus on Manifolds, but these are Calc AB kids, ok?