My calculus class hit optimization problems this week — or it might be better to say the class got hit by optimization problems. These are tough problems because of all their many moving parts, especially the fact that one of those parts is to build the model you plan to optimize. Most of my students have had calculus in high school, but too many calculus courses in high school as well as college focus almost primarily on algorithms for computation and spend little to no time with how to create a model in the first place. Classes that are so structured are doing massive harm to students in a number of ways, but that’s for another post or two.
Careful study of worked-out examples is an essential part of understanding optimization problems (though not the only part, and this alone isn’t sufficient). The textbook has a few of these. The professor can provide more, but class time really isn’t best spent just by having the professor put examples on the board. Class time should also be spent working on optimization problems with the professor there to provide guidance. And since I can’t spend 8-10 class days both working examples and giving students time to work themselves, screencasts on optimization problems have been the obvious solution.
This week I did screencasts for four problems. Here they are (one problem needed two screencasts):
To my students’ great credit, they have embraced YouTube as a great source of help in calculus. They’ve utilized not only these screencasts but many other ones, most of them excellently produced, and now doing a search on YouTube is an essential component of studying for many of them. I think that’s a great approach, obviously.