Physics is by nature a cumulative subject. Good physics problems, whether they be exam problems or active research problems, tend to combine multiple topics. For example, a problem I've seen a million times involves two blocks colliding at the edge of a cliff. To find the landing point of the blocks, it's necessary to use both momentum conservation AND projectile kinematics. The student who passed the kinematics test and then forgot all about it finds himself up a creek on such a problem.
I'm regularly asked, at least early in my course, "Will this test be cumulative?" The initial answer is usually something mildly sarcastic, like "Are you asking for my permission to forget everything we covered last month?" One time, and one time only, I explain the rationale for the cumulative test, usually with a specific example of how physics topics mesh to form interesting problems.
That said, this time of year a student is faced with an enormous amount of information to digest in preparation for a cumulative final. It's been nine months, after all. In the last marking period we've covered optics, circuits, and astronomy -- all of which have little immediate relationship to the mechanics topics from the first 2/3 of the course.
Rather than give my class the daunting and hopelessness-inspiring mandate to "just study everything," I try to focus the class's preparation. This exam is not designed as a "gotcha!" final, is not intended to show what the students don't know. No, I'm trying to set my class up for success on a serious yet managable set of problems.
How do I set them up for success? Let me start with what I will *not* do. I will never stoop to that scourge of high school teaching in which the teacher offers a "review session" at which he essentially gives out answers. Nor will I answer questions during the test such as "What are you asking on this problem?" "Success" on an exam doesn't necessarly mean a grade of 100%, it means demonstrating physics problem solving skills in an atmosphere of authentic evaluation.
I don't consider it inauthentic to state the overall topic of each problem. In fact, I do this before February's cumulative midterm as well. Students get the cover page of the exam with instructions, along with a grading sheet. The grading sheet, with the topic of each question, is the picture at the top of the post. The instructions:
Instructions:
o Part I consists of 40 multiple choice questions.
o A calculator is allowed but not necessary.
o Do not spend more than 45 minutes on these, though that is not a firm limit.
o Answer on the scantron
o Students in general physics should SKIP the questions marked “AP.” General physics will only answer 32 questions.
o Part 2 consists of four free response questions
o AP students should answer only the first three. You may look at problem 4 (about astronomy), but I will not grade your answers.
o General physics students should answer all four questions.
The list of topics doesn't truly give away anything. After all, anyone with a brain could figure out that each of the three main topics from the last marking period would be on the test; and that a cumulative exam requires at least one problem dealing with the first part of the course (mechanics). But this list does encourage the students to practice problems from each of the four topics before the exam. They come in to the exam far more confident knowing that "#2 is the optics question."
For the actual year-end FINAL exam, I go one step further, especially because I have not been able to review in class regularly (due to senior-junior issues -- see this post). I hand out part (a) of each of the four problems! Now, not only does the class know that problem 3 is about circuits, they know that part (a) is asking them to draw a circuit digram based on a sketch of four wired light bulbs. They know that the mechanics question involves a spring pushing a mass off of a table, and that they must start by figuring out the time for the mass to hit the floor.
Of course, each question on the exam will consist of parts (a) through (c) or even (f). It is the job of the student to be prepared for whatever further questions I choose to ask about the physical situation. But figuring out what kinds of questions can be asked is itself a physics skill! I am *pleased* when a group of students figures out that they'll likely be asked to calculate the current through and voltage across each light bulb. It is wonderful when the students suggest to each other than they might have to solve for the distance the spring compresses. That's how real physics works... not just solving the well-posed problem, but determining in the first place what problems are interesting and solvable.
I'd encourage folks to try this approach to exam review, and to tell me how it went. If you come to one of my summer institutes, I will be happy even to give you a copy of my handouts and my exam itself for you to use in future years.
GCJ
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