I am teaching a course in multivariable calculus this semester. We are covering the basics about $\mathbb{R}^n$, including dot products and cross products, curves, and quadric surfaces. After that we learn differentiation for functions $f:\mathbb{R}\rightarrow \mathbb{R}^n$ and partial differentiation for functions $f:\mathbb{R}^n\rightarrow\mathbb{R}$. We finish off with Lagrange multipliers.
My program so far has been to lecture on a chalkboard while they take notes. I am not really keeping their attention. I was wondering if anyone had any ideas to involve them more in class. We are in a computer lab, and have access to Maple. Your answer need not be computer based, but I have computers available.
Best Answer
You could try to implement Eric Mazur's Peer Instruction. There is a great video about it here, and here are two articles discussing how it works. The latter has links to statistical evidence that students learn better with this method (for me, the jury is still out). I guess the basic idea is that classes start by asking students a multiple choice question, and they vote on it using clickers. It should be something controversial, about a conceptual point rather than a numerical computation. After the first round of voting, students talk to each other and try to convince one another of which is the correct answer. The class then votes again. The idea is to spend class time on absorbing the material rather than hearing it for the first time. It's expected that students will have done all the reading on their own before class. There are links on Mazur's website which are designed to help professors implement this. A computer lab should have everything you need.