I handed back a graded problem set back to my multivariable calculus class last week. One student emailed me to meet to go over it with him. We did that today.
But the best part? One of my comments was that there were not enough words and motivation for each mathematical step. His response — totally unprompted by me — was something to the effect of “Now that I had to do all that writing for the Kepler paper, I now think I know what sorts of things I’m needing to explain, that I wasn’t explaining before.”
If there was any smidgen of doubt left in my mind that our Kepler “unit” wasn’t useful, it has been eradicated. The skills I wanted them to pick up? They can now apply them to the rest of the course. HUZZAH!
Now that’s education! Your student learned something that will stick with him long after he forgets how to integrate tangent etc.