Yesterday my calculetes took their first assessment — a algebra boot camp to help us prepare for limits. We focused on rational functions, piecewise functions, and basic function transformations (focusing on exponential and logarithmic functions). I haven’t graded their assessments. You know what? I don’t know why I’m talking about that at all. This post isn’t about that. It’s about…
… what came next … today …
Each year — this is my third year doing this particular rant — I am always surprised that we can go weeks (this year, we went 2 weeks, last year it was 6 weeks) before I ask my kids:
WHAT IS CALCULUS?
We do all this algebraic review, students are settled into class and into their routines, and then POW. I hit ’em with this question.
And now I can say for three years straight, I have been met with totally silence. Followed by a student saying “the thing after pre-calculus.”
“Why are you here? What is this course you signed up to take? What’s the purpose of this course? Why have you been working your whole time in high school for this? I mean, you took a course last year called pre-calculus. And yet, here we are, already well into our year in a course called calculus, and NO ONE KNOWS WHAT THE HECK IT IS!
Well, good. Let me tell you what it is.
[Insert discussion of the “tangent problem” and the “area problem”]
It’s the study of the very small to learn about the very big — to learn about things you never knew you could know. Like the basis for much of physics. Given just a little information about something moving — a roller coaster, for example — and a knowledge of calculus, what can’t you do? And let’s talk about how little you actually know about space. What figures do you know the areas of?
[Commence students calling out things like “square” and “circle” — of course followed by figures they know the volumes of.]
How sad and pathetic is this? You can only find the areas of silly, putrid little pretty shapes. What about the real world? What about this shape [commence drawing of crazy shape on board] or the volume of this figure [commence drawing of crazy volume on board]. I mean, seriously, think about it. Look at a sphere. What’s the volume? . Fine. Great.
[slight pause, building suspence]
WHERE THE HECK DOES THAT COME FROM? I mean, really? You have no idea. It just popped out of nowhere and you never questioned it. In this course, you’ll know, not just accept, that it is true.
Your lives are about to be changed. ”
 Okay, so I didn’t say this last sentence, but dang, I wish I had. You know kids, I don’t know if it got through to them. But I love doing this each year. It never fails to shock me how it is that these kids work so hard so they can take this vague thing called “calculus” — they’ve even taken a course called “precalculus” which, if the name were accurate, was meant to prepare them for this course — and they come in not knowing anything about it. What other course could you be over 2 weeks in, and ask the students what the course is about, and they won’t be able to answer?