There was clearly a disconnect between what I have been trying to get out of my History of Math class and what the instructor wants me to get out of the class.
I've never been much of a geometer. I taught it for a year, several years ago, but haven't taken a geometry class since since the spring of 1981. In other words, I was last enrolled in a geometry class when the embassy hostages were still being held in Tehran! That's my way of saying I don't know much geometry. So imagine my frustration when I'm thrust into a maelstron of Euclid, Archimedes, and Appolonius! Compound that with a horribly written textbook--the author's explanations seem to assume that you already understand the mathematics and don't need much explanation--and I've quickly gotten lost. And never having had an astronomy class I had no way of understanding so much of what was written, as much ancient mathematics was devoted to understand the movements of the heavenly bodies.
I thought I was supposed to be learning about how the ancients did math, and my inability to understand what they were doing, and why, and how, was truly frustrating. And I don't handle frustration well.
The instructor offered to have me call him, which I did the next morning--a long distance office hours! Before I knew it an hour had passed, and in that time he'd explained not only some of the "simpler" things that had been confusing me but also the expectation that the minutae in the textbook was more for background than it was a course requirement. His goal is for us to understand how this math knowledge led to that math knowledge, and how this particular lack was satisfied by that mathematician who built on the work of...you get the idea. I was lost in the weeds, he's going for the bigger picture.
We also discussed the course research project, which he said is where we get to "get into the weeds". I've long been interested in the development of logarithms so my research question will be "What types of calculations were being done that motivated John Napier to spend 20 years of his life developing logarithm tables in order to simplify them?" I already have over a half-dozen excellent sources to go through but have no idea how I'll ever find the time to read them all, especially considering that I'm the world's slowest reader. I think my first goal should be to learn what calculations Napier was trying to simplify, and then try to understand how his logarithms (which are quite different from what we use today) work--then I should be able to understand all my sources that discuss the logs.
So now, at least, I know what the instructor expects. And I know I still have a mountain of work ahead of me. And I jumped through hoops at the last minute to take this course--what was I thinking?!