In another post I shared what I've found to be principles of effective application problems in a calculus course. Here, I'd like to continue that discussion by sharing an additional principle: use real data.
Below is an example taken from a vector calculus book's section on level sets:
While I appreciate the simplicity of the model, I'm left unsatisfied with it merely hinting at topographical maps.
Fortunately, more than enough real data is readily available online. For instance, TopoQuest has topographical data for most of the United States. Here's a map I shared with my class of Texas' highest point, Guadalupe Peak.
But why limit ourselves to mountain climbing?
Here's a write-up on a method for combining data with Google Maps. In particular, data from the Houston Police Department was used to create a countour map of violent crime in Houston:
I've found incorporating real data into the classroom to be an effective way of engaging students in the material. Especially data that is local. Our campus is located in downtown Houston.
Thus this is more than just a contrived example. Students become invested when they see how the material they're studying will connect with the lived experiences of those in their immediate community.
Real data examples help to make this connection. Even if not fully flushed out, they indicates that the things we're learning have a purpose. They let students know that calculus can fight crime.
It's one thing to tell students that the gradient of a function lies perpendicular to its level set at a point.
It's quite another to show that a crime-fighting hero can calculate the gradient of a crime density function to find the hottest crime spots.
That's right, real heros use vector calculus.
And perhaps that's the extra motivation a student occasionally needs.