Thursday, January 31, 2013

Calculus: Finishing up Our First Unit (Meaning of Derivative)

All three of my classes seem to be going great this semester. Students seem to be working hard, and diving in enthusiastically. I'm very happy.

Last semester I figured out the order I thought made sense for Calculus, and now I get to refine it. Students seem less nervous this semester. (I asked if it made them nervous to not be working from the book, and quite a few raised their hands. I reassured them that we would use the book more when we get to the second unit. I guess they're trusting me more.) I think the students last semester eventually saw that my plan was working, and maybe they've passed the word along.

I've been feeling cranky because I haven't been able to feel caught up after my lovely little vacation this past weekend. Perhaps taking the time to write about this wonderful class will help me get over my crankiness. I've just finished making the test I'll be giving tomorrow. I feel like we've done everything we can in class to get ready. Many of them will still fail parts of it, but they'll get their second chances, and hopefully the retakes I offer are teaching them how to study. (I'm looking forward to seeing how my fall Calc I students do in Calc II, and how my fall Calc II students do in Calc III. If the ones who would have failed without retakes actually do well in the next class, I think that's evidence that they've learned how to study more effectively.)

Unit 1
This first unit was on the meaning of the derivative. Standard textbooks usually have one or two sections on this, and so it gets considered for under a week. We have spent 10 class sessions (over 12 hours) on it. Mostly, we worked from activities in Matt Boelkins' Active Calculus. (I also had them read the first 6 pages of Morris Kline's Calculus text, which gives a great start on the history of calculus.) We used all the  activities in Boelkins' section 1.1, plus activities 1.8, 1.10, preview activity 1.5, and activity 1.12. Students wanted more problems like these from activity 1.10 ...

... so one of my students pulled together graphs from other parts of the book, reversed some of the original graphs, and gave us 8 more problems, including these ...
I hope this work helps them understand the idea of the derivative better.

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