After working with volumes of revolution for 3 days in my calculus class, I asked the students to create a Flow Map for the process used for these particular kinds of problems. The students took between 5 and 10 minutes to create their Flow Map. For me, it was a good way to quickly assess their understanding without having to look at the details of the calculus and algebra of how they set up and solved the problem. In other words, I got better and quicker information about their conceptual understanding from this Flow Map assessment than I do from looking at their alebra and calculus work from a solved problem. In particular, I learned that for most students, the first decision they tried to make was whether to use a disk, washer or shell despite the fact that I had emphasized repeatedly in class that the first decision should be whether or not to use a vertical or horizontal slice. That observation of mine generated some good discussion.
It was obvious the students were using higher order thinking skills, and it obviously pushed them a bit more than the standard requirement of just solving the problem. I didn't tell them to use any specific language or to use any specific number of boxes. I did require that they follow the left to right Flow Map procedure.
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