The question that bugs me at all hours is "When is video / photo / print valuable?" This video is one minute long and gets me closer to an answer.
The intermediate value theorem says that because you picked purple when the purple slice was big and blue when the purple slice was small and because slices run continuously from small to big, there is a particular slice that makes you go, "Meh," that's exactly in between "I choose purple" and "I choose blue."
I love that students have an intuition about that slice, an informal understanding of probability that we can develop into something formal. We can access that intuition with video by showing that small slice growing continuously into the big. How do you replicate that experience in print, a medium which does a bang-up job with static quantities but has something of a panic attack when those quantities change?
Know what I’d really love. For every student to be able to click their mouse (or some equivalent) when they would make the switch and to have this data show up on my screen right after the video was done.
2011 Nov 29. Evan Weinberg hacked together something that does what Avery described. The results surprised me.