Super brief post here – class starts in 15 minutes. One of my Geometry colleagues asked me about a HW question I had written. I asked the students to find two cylinders that were not congruent but that had the same surface area AND the same volume. I thought it was a pretty interesting question, but I realized I did not have a coherent strategy for discussing it other than playing with numbers. I threw the question out to Twitter and engaged in a terrific conversation with Matt Enslow (@CmonMattTHINK), John Stevens (@Jstevens009), Dave Radcliffe (@daveinstpaul), and David Wees (@davidwees) Some good math was tossed around, but what really has my brain bubbling is an exchange with David Wees. He said he thought it was a great question but he would not have used it as a homework question. When I asked him why he said something that reminded me of a conversation with a former colleague. My former colleague once said that he sees a difference between exercises and problems and that he liked to keep problems for times together with the students where they could work together. I find that I feel (hope) that meaningful conversations can happen in class more readily about a problem like this one if the students have had time to think about it first. However, his words carry some weight with me as do David’s. I feel as if there is some conclusion I want to reach, but I also suspect that there is no right answer to this. I would love to hear some opinions about this in the comments or through Twitter where you find me at @mrdardy
Can only add good food for thought. It is good for students to do some wrestling on their own, engage siblings, mom, dad, neighbor, grandpa, or in my case with my nephew, Auntie. Let them find someone OUTSIDE of school to wrestle math with. Sounds good to me.
I mean your post was good food for thought!!! (not my comment!)