I know that most people who use these methods have more "standards" than I do. I thought about all of the content of each course, looked at what's been on my tests, and portioned it out into what I have been calling mastery tests, though I think I'll start calling them mini-tests. I came up with 15 (later 17) for calculus. (Precalc has 16.) Each time I give a test, it includes about 4 of these mini-tests. Each one gets a grade, and can be retaken. The ones I'm willing to make lots of version of, I allow students to retake in my office when they are ready to show mastery. (Below the skills list is a description of how to show they're ready to retake.) The ones I can only make a few versions of, we schedule a time for them all to do the retake together. They get at least two chances on each mini-test and the final and as many chances as they want on quizzes.
Here's what I've been handing out on day one for the past few semesters, along with the syllabus. I fine-tune it each semester:
Calculus Skills to Master
The test portion of your grade will be based on the 17 mini-tests described below. You will have more than one chance on each of them. On the mastery tests marked (RA), you may do the retake any time (in my office, after showing me your retake packet). The other retakes will be scheduled for once before class, on a day we arrange as a group. Use this sheet to record your grades.
You will have multiple chances to solve one problem that requires problem-solving skills. (Each test will have one of these, and there will be a few available during the final.)
Unit 1: Exploring the Idea of the Derivative
· Definition (RA, as oral exam)
· Tangent (RA)
· Rate of change (from a table of data)
Unit 2: Derivatives of Polynomials, Limits, Trig functions, Products & Quotients; Graphing; Optimization
· Derivatives (RA)
· Graphing Polynomials (RA)
Unit 3: Composition, Exponential Growth, Implicit Functions, Related Rates
· Basics (RA)
· Graphing with Limits (RA)
· Related rates
Unit 4: Anti-Derivatives, Area, Volume
· Anti-derivatives (RA)
· Position, Velocity & Acceleration
Unit 5: Volume
(No mastery test, but this will appear on the final exam)
Notice that graphing appears repeatedly. Graphing is a great way to visualize functions. Each graphing mini-test will cover different skills.
For the mini-test or quiz you wish to retake, you will do the following for each problem you got wrong:
1. Re-do the problem you got wrong. If you aren’t sure how to do it correctly, get help (from me, a tutor, or a friend). Once you are sure you have it right, think about what mistakes you made on the test, and explain what you did wrong.
2. Find 3 problems (in the textbook or one of our supplemental texts) like the one you got wrong, do them, and check your answers. If you needed help to get these problems right, do more. Keep working until you can get 3 right on your own.
3. Email me to request a retake appointment. When you come, be ready to show me a packet with the test on top, including your revisions and practice problems for each problem you got wrong.