At this point in the school year you’re probably getting ready to give your first AP Calculus test. What should the format of the test be? Where can you find good questions? How strict should you be when you grade? Should scores be curved? These are all questions we have to consider when planning our course and writing our assessments. Here are some of our suggestions:
Include calculator and non-calculator items
Include multiple choice and free response items
Write questions that reflect learning targets and success criteria
Determine scoring rubric for FRQs before administering the assessment
On the last day of every unit in the 150 Days of AP Calculus curriculum, you’ll find a list of “Questions to Include”. These are not meant to be prescriptive or exhaustive, but to give you some ideas for problem stems you can incorporate into a particular unit.
We like to include an error analysis question on each test. This is best done by labeling each line of a sample response and asking students in which step the sample student made his first mistake. If assessing this in a multiple choice question, make sure one of the options is “there is no mistake”. For help on what common student error to highlight, check out the “Student Misconceptions” heading on the lesson posts.
The goal is to match the style of questions that students will see on the AP Calculus Exam. This includes reasoning using multiple representations, and focusing on conceptual understanding, not just procedures. One way to do this is by asking questions that address underlying structure and that can’t be solved using a known procedure--such as writing an equation for a function that has a particular discontinuity at a certain x-value. These questions tend to ask students to be generative and there are usually many right answers. To make a question like that less open-ended, you can have students solve for the value of a parameter in an equation so that a certain condition is met. (Ex: Find the value of k so that f(x) has a removable discontinuity at x=4). The best place to find questions or models for questions is AP Classroom, or other released AP Calculus exam items.
We recommend that you prepare a rubric for the free response items before you begin grading your quizzes or tests. Know what information is necessary for a complete and correct response and award points when a student presents that information. Many of the “Why did I get marked down?” questions are eliminated when you share the components that earn points.
Curving test grades in AP Calculus is common practice, and we do it on some, but not all, of our unit assessments. Generally, we don’t curve Units 1 and 2 (they’ve seen a lot of this content in Precalculus) and then start curving tests in Unit 3 if necessary. While we acknowledge students’ learning progressions throughout the year and don’t use strict AP grading on day 1, we do push students to be precise and rigorous in their communication. It takes time for students to get used to this caliber of assessment, so test scores tend to be lower than they’re used to from previous math courses. Upholding this level of accountability in our grading is our primary reason for curving test scores. While there are many methods for curving scores, we prefer the method of linearizing the data.
Going over tests
Assessments are most valuable for students when feedback is timely. For this reason, we return all quizzes and tests the day after students take them in class. Yes, that seems like a formidable night of grading, but by batch-grading, I find I can get through them much more quickly. I record only the bare minimum on their papers and exclude lengthy comments. On a free response they will see how many points they earned on each part and in class we will discuss the specifics of what was necessary for full points. We spend about 15-20 minutes going over assessments in class. First, students work in groups to make test corrections on their own and I circulate and answer group questions only. Then I usually bring the class together to talk through the rubric I used for the free response question or to highlight some frequently missed questions or common errors.