A few people suggested resources including John Golden, who introduced me to his colleague, Matt Boelkins. Matt is putting together a free calculus text currently titled Active Calculus. Chapter One is online (pdf link at bottom of page), and the rest of Calc I is available by emailing him. His text does what I want to do, weaving the limits work into the derivatives, as needed. I plan to have my students use at least some of his work. Thank you, Matt! (I've listed about 8 free or inexpensive texts in the google doc, toward the bottom.)
I went through all my calculus bookmarks and added them to the google doc. I've also included many of the links in Sam's Virtual Filing Cabinet. (What a fabulous resource! Thanks, Sam!)
My course outline was broken into 9 units at first, which seemed like too many. Active Calculus (AC) has 4 chapters, and I liked how the ideas are organized. So I streamlined my units, partly reflecting AC's organization. Now I have 5:
- Slopes, Rates of Changes, Tangents (Understanding the Derivative in AC), in which we'll consider limits in an informal way.
- Exploring the Derivative (Computing Derivatives in AC), which includes power rule, product and quotient rule, etc. I'm saving much of the limit study for the 2nd unit, so the first focuses on the more important big idea. AC has limits in chapter 1.
- Exploring the World with Derivatives (Using Derivatives in AC). I want to weave the 'derivative rules' and use of derivatives together some, so will veer from AC's cleanly defined chapters.
- Area & Anti-derivatives (The Definite Integral in AC). I don't want my language to give away the deep connection of the fundamental theorem. I want the students to uncover that as much as possible.
- Volume, which I love as a grand finale.
Students need to get stronger with their algebra skills. Sam has some great algebra bootcamp ideas. For my college students, I'll move some of it from classtime to homework, and will put much of it in 'problem sets', I think. I'm hoping that challenging problems will get them to think deeper about things they've learned superficially before.
First Unit, Approaching the Derivative
This is a rough draft, mostly listing activities. I've included a practice test below, which gives a clearer idea of the topics.
- Graphing the tangent
- Axes Exercise (math activity for group introductions)
- "What is the meaning of slope?"
- Graphing Stories (dog chasing ball video, guy on hill video, Another useful take...)
- History Webquest
- Describing graphs game (graph on board, one partner looks and describes to other partner, who draws, helps students see the need for precision in language, for limits)
- What is pi? (Circumference and area; although Fawn's students are in 6th grade and mine are college students, I think these activities will work for us)
- Limits: 60/x
- more coming...
I'm thinking the test will have 4 sections. (If students need to re-take, they can do that by section, in my office.)
I make a Unit Sheet for the students for each unit, giving a tentative schedule, homework, and practice test. Our classes begin on August 20, so my unit sheet will be complete by then. Let me know if you'd like a copy. I'm going to make a shared dropbox folder for all my course handouts. I'll post again when that's set up.
Awaiting your ideas, advice, and questions...