I am working to write learning objectives for multivariable calculus this Fall. This article helped distinguish between overarching goals (that students are able to fit the math in the course into a greater understanding of math and of the world) and the learning objectives, of what I hope students will be able to do mathematically after taking the course.

Thinking about goals reminded me that, as in all classes, learning to learn within a disciplinary setting is a goal I think is important. In addition, specifically for multivariable, there is a real potential to start seeing the world through the lens of the course. Thinking about wind as a vector field, about falling leaves via flux, and about everyday shapes via the functions and parameterizations of the course is a possibility. The article also brought up history as a possible goal. I have not actively worked to situate the math we learn within the history of mathematical problem solving, but it is something I would like to learn more about in the longer term.