I just want to draw your attention to, should you happen to be teaching calculus using Calculus: Early Transcendentals (Stewart's Calculus Series), the existence of the Instructor's Guide. This text is different from the others I have used, in that the Instructor's Edition of the textbook is not that much different from the Student Edition. They are roughly the same size, and you would have to make a close comparison to find any differences. Most other textbooks I've seen, the Teacher's Edition is a crazy behemoth of a thing with marginal notes of highly variable usefulness that take up 3/4 of the page.

So ANYWAY, with the Stewart book, I got this whole other huge 3-ring binder that I barely glanced at all year until maybe four weeks ago when I started idly wondering what was in there. And holy crap, you guys, it is really full of some amazing stuff. It does have suggestions for how to organize and emphasize lectures, and questions to ask, which is nice. But most sections have two or three handouts called "Group Work" or "Find the Error in Reasoning" or something like it - and these are just very, very well done. They are thoughtfully-structured, with good questions and writing components. Some are simple and straightforward, but they're still nicely organized and typeset with pretty graphs and nice, realistically big spaces to write. So now when I'm tempted to sit and write an investigation or problem set or activity for Calculus, I check the binder first.

For example, today we worked through Group Work 1 for Section 5.2, "The Area Function." Students found expressions for areas under a constant function

Given f(t) = 4, find

and another linear function f(t) = 2t + 2, find , and then the same function again but starting at -1 instead of 0. They do all this just by finding areas geometrically. Then they look at the first derivatives of those, and notice hey wait a minute, the first derivative of the area function is just the original function. (Then they go, and this is a direct quote, "That's so stupid!" (The area is just the antiderivative?! Why didn't you just tell us this before instead of making us do all those limits!) and then I get sad because this is so neat and beautiful and I jump around and get very enthusiastic about how they were just a minute ago finding areas by ADDING UP TRIANGLES FOR CRYING OUT LOUD, but now they have the power to find the area under ANY CRAZY CURVY FUNCTION THEY FEEL LIKE, and sometimes it's really pretty easy, way easier than summing infinite rectangles.)

So, yeah. The binder. Check the binder.