So next year — as you might know from various posts this summer — I’m teaching Multivariable Calculus. I’ve spent this summer trying to refresh myself with the subject, which has remained dormant in a portion of my brain which has been unused since 1999.
The thing that has been weighing on me is how different this course is, in terms of both content and in terms of the class makeup itself. Here are the things I was grappling with when designing the course:
- The course will have only 2-4 students in it.
- The students are going to be pretty advanced who have shown they can do high school level math, and well. 
- The obvious and the most crucial: I want the students to understand the basics of MV Calculus
- I want students to acquire and master problem solving skills. By the end of the course, I want students to see that math problems can require more than 1-3 minutes each, and there are wrong directions that need to be taken.
- I want students to learn that math can be a collaborative activity. I want to foster a class atmosphere where we all are working together to conquer the material.
- I want students to learn to communicate math effectively — both in written form (in terms of writing the solutions to problems) and in verbal form (in terms of explaining concepts).
- I want students to become familiar with the use of computer software to help solve problems which don’t have algebraic solutions (or involve a lot of manipulation).