Test Prep: BC Calculus

I’m teaching AP Calculus BC for the second time this year. I have students who are motivated to do well on the AP exam and I want to support them with preparation for the test without focusing the class entirely on test prep. Here are some strategies I’ve used to try to meet those goals:

  1. Teach math well. If my students know the math they are likely to be successful on the test. This is number one, and is necessary whether or not students plan to take the AP test.
  2. Focus on the big ideas. The College Board’s framework for AB and BC Calculus names six essential mathematical practices that are useful tools for students to take away from the course, as well as the foundation of the AP exam. I try to name these big ideas whenever possible and structure my teaching around them. The mathematical practices are:
    1. Reasoning with definitions and theorems
    2. Connecting concepts
    3. Implementing algebraic/computational processes
    4. Connecting multiple representations
    5. Building notational fluency
    6. Communicating
  3. Know the test. I’ve taken several practice tests and continue working through practice tests throughout the year. I think that the AP Calculus exam is pretty high quality, in that every time I take a practice test I find questions asked in ways I would not have thought of, connections between seemingly disparate topics, and relatively few problems that can be solved by memorizing and applying a single formula or mathematical idea. The AP Course Audit site has a number of secure tests that are great for this purpose.
  4. Pull from a range of sources. If I am relying entirely on one textbook, I’m unlikely to expose students to the breadth and depth of mathematics that they need to be successful on this test. I use ideas from previous AP tests, the Exeter Math 4/5 problem sets, the Active Calculus online textbook, the MTBoS search engine, and my school’s Larson, Hostetler and Edwards Calculus textbook (eighth edition).
  5. Practice test items in small chunks. I want students to be exposed to AP-level questions on a regular basis, but I don’t want to set aside time for full practice tests early in the year. I use the secure tests to screenshot selected questions into five-question multiple choice chunks or single free-response questions that I try to give students at least weekly. Students take a few minutes to work through the questions, then we discuss ideas that come up from those problems. Secure tests are for in-classroom use only, so students shouldn’t be taking problems home but can practice their skills in small chunks, over time, and address challenges as we go.
  6. Memorization checks. There are a bunch of things that students should have memorized for the AP test — arc length formulas, Lagrange error, the Pythagorean Identities, derivatives of parametric functions, and more. I start doing regular memorization checks about two months out from the AP test. These are given like quizzes, but are not collected or graded. I don’t want dedicate too much time to, or evaluate students on, their memorization. At the same time, I want to structure practice so students have a chance to memorize what they need, and make sure students know where they stand so they can put in more work if they would like to. And doing it as a class creates a forum for students to share strategies for memorizing key information or work through common derivations so they have some tools to make connections and buttress their understanding.

This is still a work in progress, and I don’t know that I’m particularly good at prepping students for the AP test. At the same time, these tools have helped me to balance exam prep with class time focused on doing math for the sake of doing math without focusing endlessly on the test.

2 thoughts on “Test Prep: BC Calculus

  1. joeltpatterson

    Hi. I’ve been teaching BC since the 2009 school year. Consider making requirements for certain types of problems, like a limit problem needs an answer that states “indeterminate” before L’Hopital’s rule is used, and analysis problems must cite evidence, use a word like “because,” “since,” or “therefore” along with conclusions like f(3) is a maximum. Make these requirements from the get-go. Also, take a look at the Explorations by Paul Foerster and the explorations by Ruth Dover at http://staff.imsa.edu/~dover/Site/Calculus.html. Once I started using explorations, my students understanding and engagement really picked up.

    Reply
    1. dkane47 Post author

      Thanks Joel. While I appreciate the recommendations for certain requirements, I worry about the message that sends about what mathematics is. Is math about reasoning and sense-making, or about following rules handed down by the teacher? And I wonder how much those requirements benefit students on the AP exma.

      I will definitely check out those explorations. At first glance the Ruth Dover site looks really interesting.

      Reply

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