I don't like starting with all the details about limits - way too technical. (Nor do I want to start with weeks of review. Sam has some great ideas about quick reviews when needed.) I want to start with the beauty of the derivative idea. But I'll need materials to do that. (My blogging comrades will come to my aid there, all their lovely work is recorded in my google bookmarks.)
How do I approach the limits then? I've started thinking about how to bring them in at different levels, as we need them.
I'm gathering all my thoughts on a google doc. You can see my work, or you can email me (mathanthologyeditor on gmail) for edit access. I'd love to work together with others who are trying to move in the same direction.
Right now I'm working on getting all of my 50-some google bookmarks for calculus-related posts into my outline of the course. When I'm done, I'll make a version for others that focuses on the links.
My personal system is a modified SBG, I guess. I give tests on whole units, that are broken into sections for the major topics. Students can re-test on one section / topic in my office. Until now I've used percent grades, but I may put those in my gradebook and not on students' tests. Just let them know what went wrong and whether they've shown their mastery yet or not.
Right now I'm thinking 9 units. I'm not sure whether I'd test after every one. Maybe only after the 3rd, 5th, and 8th? Hmm...
Part I. Slopes and rates of change
- Exploring Slopes of curvy lines / Rate of change
- Playing with Limits (lighter treatment than most of the textbook stuff at this point)
- Exploring Derivatives (the 'rules')
- A more precise study of Limits
- Exploring Further with Derivatives (more 'rules', applications, graphing - this one's huge)
- Limits and Area
- Anti-derivatives (or "What's the big idea?")
- Exploring Integration