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.
Five Twelve Thirteen 
It doesn’t say how to use the textbook!
Also, if you give an inquisitive parent the explanation as a printed sheet they will probably not get beyond the second sentence, and be satisfied.
Haha that’s true. And I think you’re probably right about the inquisitive parent…hopefully I just won’t have to deal with that.
So happy to hear you are using the 2-4-2 approach to homework. I have worried that if I use it, I may not be setting them up for success for later math classes. I teach Algebra 2. And, I agree the text is,a great problem bank. I think there are many great approaches to teaching and to assigning problems and assessment. The older I get (the bolder I get), and conclude that it’s best to mix it up. Use many techniques, capture everyone. If not with today’s question, lesson, activity, project, then maybe tomorrow’s.
I actually just began using the 2-4-2 approach in the second half of the year — I was spiraling homework before, but in a less transparent and purposeful way, and I love the new approach. I feel a similar conflict about future math classes — I feel strongly about setting students up with the content knowledge they need, but also hust heard from a former student that she is frustrated with her current math class, and I feel responsible for that.
I love your last sentence — mix it up! And figure out what works, do it again, refine, repeat!
“but also hust heard from a former student that she is frustrated with her current math class, and I feel responsible for that.”
I actually have an elevator speech for this. I see far too many teachers justify terrible pedagogy as ‘preparing kids for college’. Guess what? Just because you know the next teacher will poke them in the eye every damned day doesn’t mean that you need to start poking them in the eye once a week now. Instead, you warn them that it is coming and teach them how to protect themselves from the eye poking (maybe helping them create their own 2-4-2s from the textbook toward the end of the year or some such).
Your student has a right to be frustrated by practices that aren’t effective and it isn’t your fault for showing them a better way. It isn’t even really your fault for not giving them strategies to overcome less effective teachers in the future, even though it would be awesome if you to do so. Don’t let the solid mediocrity of others give you grief about your excellence.
I like this sentiment — I just don’t like throwing other teachers under the bus through implicit comparisons. I don’t know their experiences and feel uncomfortable judging from a distance.
Is she frustrated for good reasons – she liked your class and got a lot out of it? Or for bad – meaning she doesn’t feel prepared?
I wrote about it here: https://fivetwelvethirteen.wordpress.com/2016/02/18/affirmation/
I think for the first reason, although she has had less to say about being prepared for her current class and more about how she likes it less.
Well, I love that you have accomplished what I think is probably the most imporatant thing missing for soooo many students: enjoying math. It’s really overlooked with the traditional approach – which works for many. But, I love hearing, “I loved your class, you never made me feel stupid,” or, “It was fun!” Even better, “I learned so much.”
Your blog reinforces the need to capture them and make things reasonable and interesting.
What text, btw?
Larson, Hostetler & Edwards, 8th edition. A solid text, in my opinion, but far from perfect.
Meh. Better than his other work, but still far from solid, imo. I still find it amazing that College Board has a defined curriculum and holds regular workshops on how to teach concepts beyond the ineffective strategies in most traditional textbooks, and yet the presentation in those textbooks never gets better.
I’ve never been to one of those AP institutes, but it would be fascinating to compare them to the different available textbooks. And a good wake-up call as well.
Absolutely. There are few things that have positively affected my practice more than AP Summer Institutes, both for AP Calc and Pre-AP Math.
I completely agree with you! We have so many teachers in our district that seem to think the textbook is God and must be the best way to do everything! I’m saving your elevator speech. It’s AWESOME!
Thanks, Deb!