If you scour the internet for resources for AP Calculus or AP Precalculus, you'll find them. Loads of them. So how do you choose which one you will use? What things should you consider as you evaluate resources? If this process feels overwhelming, here are three tips to get you started.
1. Choose one main resource. While the idea of choosing your favorite activities from 8 different resources might sound like the best of all worlds, this strategy is time-consuming and can be stressful. Having to make a decision every. single. day. about what resource you will teach with on the following day is tough, and while it may work for the first couple of weeks, it will leave you exhausted once you hit the end of September. By choosing one main resource, you still have the freedom to supplement occasionally if you happen to find something great, but takes the pressure off because you have a default option. Default is not bad or lazy. Default is sustainable.
2. Not everything you do with students has to be "exam-prep". Certainly the content you teach throughout the year should align with the content tested on the AP Exam. However, the school year is for building deep, flexible, conceptual understanding of those topics, not just studying how this topic will appear on the exam. There will be plenty of opportunities throughout the year, and especially in the weeks leading up to the exam, to have your students practice with timed multiple choice and free-response questions, with and without a calculator. But this does not mean that every lesson and homework assignment has to be structured in this way. Focusing on true understanding of concepts, rather than question types, will equip your students to be creative and insightful problem solvers–which will certainly be to their advantage on the exam!
This also means that during the year you can put more open-ended, interesting problems in front of students that would not appear on the exam simply because they are too difficult to grade. Having students wrestle with new ideas and have discussions around these new ideas with their peers is extremely valuable for constructing understanding. In many cases, these are the types of tasks that don’t have nice answer keys! Embrace the discomfort. Our classroom norm of accepting non-closure is just as much for the teacher as it is for students! For an example of these kinds of tasks, check out “Transformation Mix-Up” in our AP Precalculus curriculum, or this Open Middle Task on derivative rules from our AP Calculus curriculum.
3. Weigh student experience more heavily than you might think. Here at Calc Medic we talk a lot about what it means to have a student-centered classroom. For me this means prioritizing students’ learning experiences above my own comfort and desire to stave off criticism from parents, students, or even other colleagues. More concretely, when I teach in a way that the research says is best for students (requiring students to collaborate, giving students time to wrestle with ideas instead of just rushing to an algorithm they will follow blindly, having students rely on each other more than me, etc.) I know I will receive push-back. Every year there’s at least one person that tells me that I’m not actually “teaching”. This is always tough to hear, but here’s what I know about teaching and learning in an inquiry-based model (like EFFL).
More students participate willingly and consistently, compared to more traditional lecture models.
Students remember concepts much longer than when I simply tell them the new information.
Students enjoy learning in my class (well, on most days, at least). Students who consider themselves “not math people” gain confidence when they realize the things they’re learning make sense and that they are the ones responsible for their new understanding.
We created the Calc Medic lessons to be a go-to resource for teaching AP Calculus and AP Precalculus. With lessons and activities for every day of the year, we hope we can eliminate some of the late night google searching for exciting new activities for your students. However, we value teacher choice and agency. YOU are the best person to decide what your students need. If you’re still debating what resource is right for your students, here’s a bit more info about the Calc Medic resources.
Teaching with Experience First, Formalize Later (EFFL) Lessons
An Experience First, Formalize Later (EFFL) lesson begins with students working in small groups on an activity that builds on students’ intuition, experiences, and prior knowledge toward the new learning of the day. This is then followed by a whole-class debrief where the teacher makes explicit the mathematical ideas embedded in the students’ solutions and attaches formal notation, vocabulary, and formulas to these ideas. This process is annotated with a different colored pen in the margins of the activity, so students have a clear record of their initial, rough-draft thinking and the "updated draft." Notably, there is no pre-teaching of concepts. Students experience the mathematical ideas first, in a way that is accessible and sensible to them, before the ideas are formalized into the versions generally accepted by the mathematical community.
I have had many conversations over the years with colleagues about the benefits and drawbacks of lecturing vs. inquiry-based learning. I remember someone sharing that a benefit of lecturing is that you can guarantee that every student got the same information and heard the same thing, and that this in and of itself made it equitable for all students. While it is true that each student would hear the same thing, it is entirely unlikely that each student would learn the same thing. Just because we said it, doesn’t mean that students learned it. While it can give us a sense of security to know that we “covered” everything, we have to prioritize actual student learning over our own comforts and preferences.
While teaching in the Experience First, Formalize Later model may seem more unpredictable or even chaotic than the classroom you’re used to, we encourage you to give it a try! You will feel more comfortable each and every day and you’ll notice the difference it makes with your students long before that!
Before we started posting our Experience First, Formalize Later (EFFL) lessons on the website, we created them for our own students at our own schools and saw that they worked. They worked at creating the classroom culture we were after, developing the conceptual understanding we knew was critical, and empowering learners to see themselves as capable doers and knowers of mathematics. Read more about why we EFFL.
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