The year is coming to a close and I’ve found something to entertain my seniors. They’re taking regular calculus. More than likely, most of them will never take a math class again. If they are going to take math in college, chances are they’re going to be taking calculus over again (I don’t teach the AP calculus classes at my school).
My school treats seniors with the deference that seniors think they deserve. They don’t have to take final exams, they don’t go to classes after May 22nd (don’t ask), and they miss a lot of May to AP exams. All in all, because of these restrictions, May is pretty hard to plan, if you teach a senior class.
I gave my last quiz recently, and I’m having students use their class time to work on a calculus project.
I only have 7 students in this class, so I decided to do something pretty radical. I pretty much gave them free reign on their project. I told them they could do anything they wanted — just as long as they’re passionate about it. They have to do something they’re going to enjoy doing. They could also choose the point value of the project (a large quiz grade or test grade).
At this point, the only way I’m going to get them to do anything is by tapping into things they like.
So I had them brainstorm, we met individually so I could guide them, and they’re off to the races, with some great projects:
- One student is doing a study of Newton’s method (we didn’t cover it in class) to find the zeros of a polynomial. She’s going to compare whether Newton’s method to finding zeros is “better” than a more simplistic method of finding zeros. That method, in case you were wondering, has you find an interval where you know there is a zero (e.g. for example, say you know there’s a zero on [-1,1] because the function is negative when x=-1 and positive when x=1). Then you divide the interval in half (into [-1,0] and [0,1]) and you find which of those two intervals has the zero. Then you divide that interval in half, and find which of those two intervals has the zero. On and on and on…
- Another student is doing a study of rainbows, which involves calculus. (Awesome resources here and here.)
- Another student really liked learning the intuitive version of the chain rule that I taught (post one and two), and wanted to make a lesson for my students next year on that! So she’s making a video tutorial and worksheet to accompany it.
- In the same spirit of teaching, one of my students wanted to do something similar by making a video tutorial on the formal definition of the derivative.
- One student is taking AP Physics B, but throughout the course, has noted connections between what he’s learned in his non-calculus-based physics class and what we’re doing in calculus class. One connection he made was between Pressure, Volume, and Work. He (rightfully) noted that . So he’s going to be making a presentation on this relationship by doing a bit of research and bringing application to the class.
- Another one wanted to learn something “new” so I suggested he do some research on a hanging string. More notably, if you hold up a string (like a necklace), it will hang down due to gravity. Surprisingly (or not?) the shape is not a parabola. It turns out that it’s this funky shape called a catenary. He’s investigating why that’s the case, and how to derive the formula.
- Last but not least, one of my students had difficulty with the sections on surface area and volume, because she couldn’t visualize the regions/spaces being formed. So she’s making two mechanical thingamajiggers out of wire. You bend the wire to be whatever function you’re going to be rotating, and then there’s a handle that rotates the wire. I am so excited about this one — I hope it works out so I can use the model next year in class!