I recently ran into a student that I taught during my first year of teaching (ten years ago) what he remembered from my Calculus course. He remembered the word derivative and that we had to do problem sets and if he did well on those he would do well on the tests. But he didn’t really remember any “Calculus”. He works in marketing and- I assume- does not need to use any of the rules, theorems, or formulas particular to Calculus. But, I bet he has a better appreciation of the concept of change because of my course, even though he might not attribute it to my course; at least I hope he does.
So, What do I want my students to remember five or ten years after they leave my course? Really the question I am asking is “What is my main goal in my calculus course?”
For me, the answer is change. Algebra 2 and PreCalculus are about functions and points on a graph (I don’t love that description, but its serves my purpose), while Calculus is about the change at those points. Imagine Algebra 2 is about the point, and Calculus is about the slope at that point. So, as we returned from Spring Break- and were technically in the middle of our unit on the Fundamental Theorem of Calculus- I tried to gauge what my students remembered about Calculus after ten days away…
They looked in their notes and said things like chain rule, fundamental theorem of calculus, derivatives, and change. They also have every standard example in their notes (think volume of a balloon for related rates) that they can use in future Calculus courses as a resource (I have anecdotal evidence that they refer to these notes in college), but as I tried to dig deeper into what this course engrained in them, I was not sure that more than a few understood what I meant by change.
SO, I talked to a physics teacher who was excited to collaborate. I borrowed some “logger pros” and Vernier sensors to begin a two-day task/project/lab/experiment. Here it is:
The outcome of this “task” will be to:
- describe a movement in words
- By hand, graph:
- distance vs. time graph of the movement
- velocity vs. time graph of the movement
- acceleration vs. time graph of the movement
- demonstrate the movement
- use the “logger sensors” to create an actual capture of the movement, including distance, velocity, and acceleration graphs
- verify that the description, movement, and graphs all correspond
- determine a means to present this information
We are going to spend two days on this task, then return to our normal progression of finding area between two curves. But for these two days we’re going to try to see if we can reinforce what I believe to be the central theme to Calculus.
Maybe in ten years, they’ll remember this.