Unlike the AP Statistics exam where students get several formula sheets, tables, and are permitted to use their calculator the entire time, on the AP Calculus exam, students do not get a formula page and they use their calculator less than 30% of the time. The way I combat the calculator issue is that I don’t teach with it nor assess with it until Unit 8 in the Course and Exam Description. This means that I am very choosy about what I ask my students to do in the first seven units whether it is problems I give in class, on an assignment, or for an assessment. It is hard to wean students off their calculators, but I find this tough-love no-access cold-turkey method works.
But what about all those formulas you have to have at your fingertips to do calculus problems… Product Rule? Chain Rule? Derivative of the tangent function? Fundamental Theorem of Calculus? The list is long and daunting. There is even stuff on the list from precalculus such as lne = 1 and cos(pi/2) = 0. Many teachers love their students so much that they make a formula page for them and even worse, allow them to use it on assessments. A better idea is to teach students how to build their own formula sheet from the beginning of the course.
Pretty early on we discover derivatives whether we are using the limit definition of the derivative to figure out y’ if y = x2, or whether we are sketching f'(x) from a graph of f(x)… hmmmm that graph of f(x) looks like the exponential function and now the derivative looks like… can it be? the exponential function?? At this time I distribute a yellow sheet of lined paper into which I have punched three holes (so it can go in their binder). I tell my students that this is their Yellow Sheet and they will be writing any important formulas on it for the remainder of the course. Sometimes I say, This should go on your Yellow Sheet but more often than not they ask Should we put this on our Yellow Sheet? I tell them that they can get another Yellow Sheet from me if theirs gets full, or if it gets messy and they want to rewrite it.
A bunch of Yellow Sheets Ready to Go!
When you build your own formula sheet it is not as daunting because it is happening over time. At first there are only 2-3 formulas on it, then 10 or so, and eventually maybe as many as 50 but you have been looking at those first 10 for months by then. In addition, you are looking at your own handwriting and hopefully this has a more approachable feel to it.
I always ask: Why is is Yellow? Unlike Algebra I students who would probably say Because yellow is your favorite color! -OR- Because that’s the kind of paper you had! My AP Calculus students always know: So it is easy to find in our binder!
Because it is calculus, what we need to know are mostly derivatives and integrals so by the time the front side is full, it’s time to write the integral formulae on the back.
The other day I ran into one of my former AP Calculus students from the class of 2022. She was able to skip Calculus I and is in Calculus II now because she scored a 5 on the AP exam last May. So, it’s been over 8 months since she did any calculus. She said that even though it’s all coming back to her fairly easily, she Facetimed her mom so she could find her Yellow Sheet. I am not sure if her mom sent the Yellow Sheet to her in the mail or took pictures and texted them to her, but either way, the Yellow Sheet remains important in my students’ lives after they leave my classroom. It’s so important that students learn more than math — they need to learn the successful systems for further academic work, and more importantly for life. Before long they’ll be crafting their own systems to ensure their future successes.