I’m currently teaching the second semester of BC Calculus (which is new for me this spring). It’s a pretty interesting experience picking up halfway through the semester. It’s also the first time I’ve taught a course that has a prescribed textbook. (I realize that both of those statements may sound absurd.)
I’ve decided not to give out textbooks to my students. The textbooks live in my classroom, and students are welcome to sign them out if they would like, but I find them as much of a distraction as a resource. I do use them in my planning — there’s nothing like a dense textbook to mine examples and problems from. I also use the Active Calculus textbook, which is available for free online. I use old AP tests and other AP resources. I use tidbits I find on the internet. I create reference sheets for my students — some from our text, some from other resources — that are much more efficient resources than paging through a giant textbook. I write homework in the 2-4-2 style that I was inspired to try by Steve Leinwand — 2 problems from that day’s topic, 4 problems of mixed review, and 2 problems that require extended thinking or explanation. Much of it comes from the textbook, but there are also problems I write and problems that come from other sources. Each day I type the homework up on one piece of paper to minimize confusion.
I’ve been thinking about the fact that, for an AP course, a textbook is required. I have the support of my administration, and I haven’t had pushback from students or parents, but I decided to take a few minutes to prepare a little elevator speech to defend my choice not to use a textbook, if that became necessary. It ended up a little long and unwieldy to actually say to a parent, but was useful in clarifying my own thinking. Here goes:
When people talk about “using a textbook”, they usually mean three things: teach in the order the textbook presents material; use the examples the textbook uses to introduce a topic; and assign classwork and homework from the textbook. I teach largely in the order that our text prescribes, but that order is by no means authoritative, and I choose to deviate when I feel like it best serves students. I use many of the examples from the text, but I use other resources as well — freely available calculus textbooks on the internet, a range of AP preparation materials, and my own experiences with this mathematics. Finally, students do a great deal of math in my class, and some of it comes from the textbook. They always have access to a textbook if they would like it as a reference. But one of the things I like best about the AP Calculus test is that the questions ask students to make connections between different ideas in calculus, synthesize complex topics, and combine tools in new ways. Our textbook treats many topics in calculus as silos, and misses opportunities to look at the larger themes that make up the substance of calculus. By bringing in broader resources and breaking down the silos of the textbook, I hope to help students learn in a way that they will retain what they know — not just for the AP test, but in a way that allows them to apply these habits of mind more broadly outside of calculus class.