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. [1]
What I want students to get out of the course:
- 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).
With these goals in mind, I designed the course. [I think I dealt with all but #5, which is because I haven’t yet learned how to use SAGE Notebook (here). But when I do, I will incorporate questions and tutorials in the problem sets.]
But I’m nervous. It’s so different that I wanted to solicit any feedback. So if you have the time (and desire), take a peek below at the course expectations and tell me if there is anything that looks like it won’t work. (Or if there is something that looks like it will work well.)
(download pdf here or by clicking picture above)
I initially had designed this course with no tests, but I added in a few out of the fear that students — especially seniors who are going to be bombarded with work from other classes — would easily turn this course into a “back burner” course. Meaning that they would go home with a lot of homework and decide that the one course they could sacrifice (or do halfheartedly) would be math, because there was so little accountability.
And if you’re curious what the problem sets might look like, I am copying two questions (both cribbed from Anton) below.
[1] I haven’t taught any high school honors/advanced courses yet, so this is new territory for me.
Continuous Everywhere but Differentiable Nowhere 
Hi Sam,
I’m teaching on a different planet than this class, so most of my notes are just edits, not real advice. Figure they help too?
Typo: Under grading asses should be assess.
Organization: Under grading you spend a whole paragraph telling me how tests don’t matter and then the first grade you hit me with is tests. I’d recommend moving that subsection between problem sets and projects.
Revising: You still have part of a sentence from an earlier draft under the Extra Help section.
Overall: I like the flexible grading rubric. I like the approach to testing–enough to make sure students stay studying thoughout–but not just a few tests that determine your grade and terrify you. I like your goals, especially 2 through 4. Perhaps because I got less of those during high school they especially appeal to me now.
Sarah,
Haha, I’m so glad you caught the typo! That could have a hilarious disaster. And I’ll re-organize the test thing.
As for the flexible grading rubric, I talked with my department head about this, and she suggested that I leave myself more flexibility than this, even. Like, if students weren’t staying current with the material, I have to give myself the option to change things (e.g. quizzes) and if student-teaching doesn’t work out, I can nix that part. So I’m going to incorporate something akin to “but things are always up to change.”
My interest in this class, and this problem-set form, is to hopefully convince myself that I can do this with my other classes — especially Algebra II. I like traditional forms of assessment. I like them a lot, actually. But I also hope that I come away from this course saying “… but there are also other ways to assess, and other skills we can inculcate in our students.”
Thanks for taking the time!
Sam.
Sam,
Have you corrected the last paragraph yet? It looks like an edit got partially undone:
“I don’t know if you are going to finPlease definitely feel free to meet with me.”
(it could always be that my old version of Acrobat Reader is messing with the layout)