Using open-ended situations for exam review

I'm in the process of writing 5 Steps to a 5: AP Physics 1.  The success of this book in its mission of preparing students for the new AP exam will hinge on how well I can communicate the changed expectations in the new exam:  calculation will still exist, but will take a backseat to verbal explanations, graphical analysis, semi-quantitative analysis, and other ways to describe physics that don't involve a calculator.  

My instinct is that students are willing to work through example problems in a text or prep book.  But once they start, they're extraordinarily answer-focused.  Once the answer is right, the reader moves on; the occasionally follow up questions like "what if the initial speed were increased?" remain wanting for attention, because the student got the right answer, dagburnit, and so he understands just fine and is moving on.*

*Or, the follow-up questions are ignored because the student didn't get exactly the right answer, and so it's far more urgent to him to find the math error than to keep reading.

Thing is, that's no way to learn physics.  A deep understanding of physics, like that required for the new AP exams, requires probing beyond the algorithm that obtains an answer.  And even when straight-up calculation is tested, the ability to explain the methods behind the calculation will be critical.  

In my classes, I've used class demonstrations as the starting point for teaching how to go beyond the calculation.  Sure, I focus my demonstrations on a solvable example problem, such as “predict the reading in this spring scale.”  But the actual presentation of the demonstration includes all sorts of questions and ideas beyond the final calculation.  I’m finding the correct answer, sure, but I’m also modeling the general approach to physics problem solving: determine what physics concepts are relevant and why, and then figure out how those concepts apply in this particular situation. 

An alternative approach would be to eliminate the calculational focus of a physics problem altogether.  In her blog, Kelly O’Shea describes her overarching theme of the “goal-less” physics problem: by the end of the course, she aims to present a physical situation by itself, then to make the students decide for themselves what specifics can be calculated and described.  Ability to deal with the goal-less problem is, ironically, the ultimate goal of physics teaching.  It certainly takes time and practice to bring students to the point at which they can handle a goal-less problem, as Kelly points out; but as an end result, or in a broad review of a course, the goal-less problem is where we aim.

The structure that I've adopted for my book modifies the traditional "solve a bunch of typical example problems" approach in a way that provokes the reader to consider multiple representations of a physics problem, just like my in-class demonstrations, just like Kelly’s goal-less problems.  In each chapter, I’m posing several “examples,” which include only the stem of an AP-style problem.  Then I’m citing the specific facts of physics that are relevant to each example, followed by a narrative explanation of how these facts can be used in conjunction with the example situations to make calculations, graphs, or other predictions. 

I’d encourage you to try a goal-less approach in your own class, at least in conjunction with a topic review.  After you’ve taught kinematics, offer up a situation, such as “a cannonball is shot off of a 150 m high cliff at a 30^o angle above the horizontal.”  Ask what facts of physics apply, what can be determined about the situation, what can be calculated, what could be calculated with further information, what graphs can be constructed, how all these predictions would change by changing the height or the angle, and so on.  When the class can’t contain themselves for all their ideas, that’s when you know they’re ready for AP Physics 1.