AP Exam Review
Week 1 - Wednesday (Day 3)
Concepts from Unit 1 and Unit 2 (limits and basic derivatives)
One helpful exercise is to have students look at their unit tests from the year. Since these are already cumulative over the whole chapter of content, students can get a good idea of the scope of the course by looking at our 8 unit tests.
A word of caution: neuroscience research tells us that “rereading notes” as a studying tool is largely ineffective. Why? There are two main reasons. First, re-reading has very few benefits to learning because the cognitive challenge of having to actively retrieve information and reason through problems is largely absent. Second, by reading through the words on the page and their own work, students gain a false sense of familiarity with the material. On later assessments (like the AP Exam!) students may be able to recognize that the question is similar to something they’ve seen before, but they still may not be able to solve it. Because students feel a sense of familiarity with the concepts, they don’t pursue other, more effective, studying strategies. For more insight on this research, we recommend reading “Make it Stick” by Mark McDaniel and Peter Brown.
Going over tests, then, must include more than just re-reading the problems and answers. Luckily, this review method can be turned from somewhat or moderately effective to very effective with a few tips and tricks.
We have students use a going-over-test protocol to guide their work (provided below). This protocol has students make a list of concepts, re-work problems, and notice patterns in the kinds of problems they missed or places where they lost points. This work allows them to reflect on their strengths and identify areas for improvement. For example, a student may realize that they can generally find antiderivatives using the basic rules or geometry, but they struggle with integrals that require u-substitution, and thus need to do more work to review that concept. Furthermore, students may recognize that though their answers to the Free Response Questions are correct, they lose points on justifications, and thus need to spend more time understanding appropriate justifications (such as through a flash-card activity).
We stress to students that they need to focus on questions they answered incorrectly AND ones they answered correctly. This is because a student may have forgotten a certain concept even though they knew how to do it on the day of the test or they happened to get the question right originally by guessing.
We go over tests in small groups so students can work collaboratively to clarify their thinking and offer support to one another. We’ve noticed students gaining deeper understanding by explaining a concept to their peers and having to really articulate the ideas behind the problem and the strategies they used to solve it.
We end the class period with one additional activity that is related to the concepts, but not the exact problems, of the test to provide students with additional opportunities to extend their learning and actively retrieve stored information. For example, we might have students make flashcards to review proper justifications or create their own test questions for their peers to solve. Socratic circles are another great way to re-articulate the major ideas and big questions of the unit.
Socratic circles are a great collaborative learning tool and especially helpful when reviewing concepts at the end of a unit or semester. In our version of the activity, we assign each student a different question or prompt related to the topic of study. Students then have 5-10 minutes to answer the prompt on a half-sheet of paper. Their work could include written descriptions, graphs, example problems, etc.
We then have students form an inner and an outer circle so that each person in the inner circle has a partner in the outer circle (see image). Students now take turns presenting the question and explanation to their partner. We usually give about 2-3 minutes per person, so about 4-6 minutes for the pair. At the end of this time frame, students switch papers and the inner circle rotates 1 position clockwise or counterclockwise. The process then repeats, except that now students aren’t presenting their own topic, but the topic that was just presented to them. You can go through as many rounds as you have time for, listening in on student conversations and encouraging students to use precise vocabulary. Students may wish to have their own paper back at the end of the activity.
You can prepare the prompts ahead of time or have students come up with them on their own, making sure that a variety of topics are covered.
The attached document gives the prompts we came up with for our Unit 1 and Unit 2 review.