In my history of mathematics course, we are reading William Dunham's Journey through Genius, which I highly recommend for those who can admire a good proof.
The thing that has got me so excited about this class though isn't the beautiful theorems we're reading about. Far from it. It's the sense of storytelling that you can create by including some of the history of math into your teaching.
I was blown away with the historical perspective I gained in reading the following passage (p.134-135) about mathematics in the Renaissance:
"[A]cademic appointments were by no means secure. Along with patronage and political influence, continued service depended on the ability to prevail in public challenges that could be issued from any quarter at any time. Mathematicians like [Scipione] del Ferro always had to be ready to do scholarly battle with challengers, and the consequences of a public humiliation could be disastrous to one's career."Thus a major new discovery was a powerful weapon. Should an opponent appear with a list of problems to be solved, del Ferro could counter with a list of depressed cubics. Even if del Ferro were stumped by some of his challenger's problems, he could feel confident that his cubics, baffling to all but himself, would guarantee the downfall of his unfortunate adversary."Scipione apparently did a good job of keeping his solution secret throughout his life, and it was only on his deathbed that he passed it along to his student Antonio Fior."
I was so taken with this idea that I came up with some slides for a game that I'd like my students to play: Math Duel. (see slides below)
I've seen teachers have students generate their own questions for each other, but how about setting it up within the historical context of famous men and women in the course subject. I've got to give a lot of credit to Dunham for writing such a thrilling history of a subject that gets a bad reputation as too dull and black and white.
